Practical Statistics for Educators - User contributions [en]

Data Screening

2019-11-17T02:27:52Z

Kuslis002: /* Data Screening */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
'''Value cleaning''' is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

'''Outliers''' are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The '''Mahalanobis Distance''' statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T02:26:10Z

Kuslis002: /* Value Cleaning */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
'''Value cleaning''' is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

'''Outliers''' are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The '''Mahalanobis Distance''' statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T02:25:47Z

Kuslis002: /* Detection of Multivariate Outliers: Mahalanobis Distance */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
Value cleaning is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

'''Outliers''' are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The '''Mahalanobis Distance''' statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T02:25:27Z

Kuslis002: /* Detection of Multivariate Outliers: Mahalanobis Distance */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
Value cleaning is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

'''Outliers''' are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The '''Mahalanobis Distance''' statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T02:25:11Z

Kuslis002: /* Outliers */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
Value cleaning is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

'''Outliers''' are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The Mahalanobis Distance statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T02:24:54Z

Kuslis002: /* Outliers */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
Value cleaning is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

Outliers are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The Mahalanobis Distance statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Multiple Regression Analysis

2019-11-17T02:21:42Z

Kuslis002: /* Collinearity and Multicollinearity */

== Collinearity and Multicollinearity ==

'''Collinearity''' is "a condition that exists when two predictors correlate very strongly" (Meyers, Gamst, & Guarino, 2017, p. 189).

'''Multicollinearity''' is a condition that exists when "more than two predictors correlate very strongly" (p. 189).

Steps for How to Detect Multicollinearity in SPSS:

1. Click "Analyze"

2. Then Select "Regression"

3. Click "Linear"

4. Put all the IV's in the IV section and then move ONE IV into the DV box.

5. Uncheck all boxes in "Statistics" except for "Collinearity Diagnostics"

6. Click "Ok"

*The output should indicate if there is a VIF. If the VIF is above 3 there is likely multicollinearity issues, and if it is above 10 you are highly likely to have multicollinearity issues.

Detecting Multicollinearity in SPSS [https://www.youtube.com/watch?v=oPXjQCtyoG0]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Gaskin, James, director. ''Detecting Multicollinearity in SPSS''. YouTube, YouTube.com, 26 Mar. 2011, www.youtube.com/watch?v=oPXjQCtyoG0.

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Multiple Regression Analysis

2019-11-17T02:20:31Z

Kuslis002: /* Collinearity and Multicollinearity */

== Collinearity and Multicollinearity ==

'''Collinearity''' is "a condition that exists when two predictors correlate very strongly" (Meyers, Gamst, & Guarino, 2017, p. 189).

'''Multicollinearity''' is a condition that exists when "more than two predictors correlate very strongly" (p. 189).

Steps for How to Detect Multicollinearity in SPSS:

1. Click "Analyze"

2. Then Select "Regression"

3. Click "Linear"

4. Put all the IV's in the IV section and then move ONE IV into the DV box.

5. Uncheck all boxes in "Statistics" except for "Collinearity Diagnostics"

6. Click "Ok"

*The output should indicate if there is a VIF. If the VIF is above 3 there is likely multicollinearity issues, and if it is above 10 you are highly likely to have multicollinearity issues.

Detecting Multicollinearity in SPSS [https://www.youtube.com/watch?v=oPXjQCtyoG0]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Gaskin, James, director. Detecting Multicollinearity in SPSS. YouTube, YouTube, 26 Mar. 2011, www.youtube.com/watch?v=oPXjQCtyoG0.

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Multiple Regression Analysis

2019-11-17T02:07:09Z

Kuslis002: /* Collinearity and Multicollinearity */

== Collinearity and Multicollinearity ==

Collinearity is "a condition that exists when two predictors correlate very strongly" (Meyers, Gamst, & Guarino, 2017, p. 189).

Multicollinearity is a condition that exists when "more than two predictors correlate very strongly" (p. 189).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Multiple Regression Analysis

2019-11-17T02:04:42Z

Kuslis002: Created page with " == Collinearity and Multicollinearity == Multicollinearity is a condition that exists when "more than two predictors correlate very strongly" (Meyers, Gamst, & Guarino, 2017..."

== Collinearity and Multicollinearity ==

Multicollinearity is a condition that exists when "more than two predictors correlate very strongly" (Meyers, Gamst, & Guarino, 2017, p. 189).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Main Page

2019-11-17T02:02:02Z

Kuslis002: /* Modules */

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 An introduction to probability PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.7 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

13.1 [[Multiple Regression Analysis]]

13.2 [[Multiple Linear Regression]]

14.1 Internal Consistency[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

Main Page

2019-11-17T02:01:32Z

Kuslis002: /* Modules */

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 An introduction to probability PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.7 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

13.1 [[Multiple Regression Analysis]]
13.2 [[Multiple Linear Regression]]

14.1 Internal Consistency[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

Beyond the ANOVA

2019-11-17T01:54:10Z

Kuslis002: /* ANCOVA */

The Analysis of Variance is a powerful statistical technique for analyzing data. But what happens when we have conditions that go beyond the ANOVA and we need more?

== 2-way ANOVA ==
A two-way ANOVA is used when each participant in a study has scores on three variables: two independent variables (IV) with two or more levels and a dependent variable (DV). For example, a two-way ANOVA can be used to evaluate the effects of three different methods of math instruction on math achievement scores for boys and girls. In this example the first IV is gender which has two levels: male and female; the second IV is math instruction which has three levels: Method 1, Method 2, and a Control; the third variable is the DV-math achievement scores. The two-way ANOVA starts with an omnibus test to determine if there are any significant effects on the DV based on each IV and the interaction of the IV's. If the omnibus test indicates significance, then follow-up tests are required to specifically identify where the significant differences exist. A two-way ANOVA can be used to analyze data from experimental studies, quasi-experimental studies, and field studies.

''contributed by Helen Knudsen''
== k-way ANOVA ==

== Repeated Measures ANOVA ==

Repeated measures ANOVA, as in any ANOVA, compares the means of different groups. What a repeated measures ANOVA allows the researcher to do, however, is to compare data on the same characteristic when samples are collected at different times (i.e. within a longitudinal study).

A repeated measures ANOVA can also be used when members of a random sample are matched based upon some criteria. The data collected at various points by the matched pairs in the study can then be analyzed with this method.

Submitted by Karen A. Fildes

== ANCOVA ==

ANCOVA Steps in SPSS

→ Select Analyze

→ General Linear Model

→ Univariate

→ Put the DV in the Dependent Variable box and the IV in the Fixed Factors box. Proceed to put the covariates of interest in the Covariate(s) box.

→ Click on the Options button and move the IV over to the Display Means For box.

→ Click on Compare Main Effects and select Bonferroni from the Confidence interval adjustment menu to request post hoc tests.

→ Select Descriptive Statistics, Estimate of effect size and homogeneity tests from the display options.

When writing up the results, it is common to report certain figures from the ANCOVA table.
F(df between, df within)= Test Statistic, p =

[[File:https://www.sheffield.ac.uk/polopoly_fs/1.531229!/file/MASH_ANCOVA_SPSS.pdf]]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Rothwell, Joanne. “ANCOVA in SPSS.” www.statstutor.ac.uk, University of Sheffield, www.sheffield.ac.uk/polopoly_fs/1.531229!/file/MASH_ANCOVA_SPSS.pdf.

== MANOVA ==

The Multivariate Analysis of Variance, also known as the MANOVA, is used when there are multiple dependent variables and you are looking at multiple factors. The only difference between an ANOVA and a MANOVA is that the ANOVA has the limitation of only allowing for a single dependent variable while the MANOVA allows for more. For example, using the MANOVA analysis, a researcher could examine Math Achievement and Reading Achievement scores.
 
An example research question for a MANOVA would be:
Is there a significant difference in Math Achievement (computation, problem solving and numeracy) and Math Self Efficacy for students who participate in an after school treatment program for either one day per week (Program A), three days per week (Program B), or the traditional math curriculum. 

DV 1: Math Achievement 
Level 1: Computation 
Level 2: Problem Solving 
Level 3: Numeracy 

DV 2: Self Efficacy 
1V 1: Math Program 
Level 1: Program A 
Level 2: Program B 
Level 3: Comparison/Control 

''contributed by Karen Fildes''

== MANCOVA ==

Beyond the ANOVA

2019-11-17T01:53:35Z

Kuslis002: /* ANCOVA */

The Analysis of Variance is a powerful statistical technique for analyzing data. But what happens when we have conditions that go beyond the ANOVA and we need more?

== 2-way ANOVA ==
A two-way ANOVA is used when each participant in a study has scores on three variables: two independent variables (IV) with two or more levels and a dependent variable (DV). For example, a two-way ANOVA can be used to evaluate the effects of three different methods of math instruction on math achievement scores for boys and girls. In this example the first IV is gender which has two levels: male and female; the second IV is math instruction which has three levels: Method 1, Method 2, and a Control; the third variable is the DV-math achievement scores. The two-way ANOVA starts with an omnibus test to determine if there are any significant effects on the DV based on each IV and the interaction of the IV's. If the omnibus test indicates significance, then follow-up tests are required to specifically identify where the significant differences exist. A two-way ANOVA can be used to analyze data from experimental studies, quasi-experimental studies, and field studies.

''contributed by Helen Knudsen''
== k-way ANOVA ==

== Repeated Measures ANOVA ==

Repeated measures ANOVA, as in any ANOVA, compares the means of different groups. What a repeated measures ANOVA allows the researcher to do, however, is to compare data on the same characteristic when samples are collected at different times (i.e. within a longitudinal study).

A repeated measures ANOVA can also be used when members of a random sample are matched based upon some criteria. The data collected at various points by the matched pairs in the study can then be analyzed with this method.

Submitted by Karen A. Fildes

== ANCOVA ==

ANCOVA Steps in SPSS

→Select Analyze
→ General Linear Model
→ Univariate
→ Put the DV in the Dependent Variable box and the IV in the Fixed Factors box. Proceed to put the covariates of interest in the Covariate(s) box.
→ Click on the Options button and move the IV over to the Display Means For box
→ Click on Compare Main Effects and select Bonferroni from the Confidence interval adjustment menu to request post hoc tests.
→ Select Descriptive Statistics, Estimate of effect size and homogeneity tests from the display options.

When writing up the results, it is common to report certain figures from the ANCOVA table.
F(df between, df within)= Test Statistic, p =

[[File:https://www.sheffield.ac.uk/polopoly_fs/1.531229!/file/MASH_ANCOVA_SPSS.pdf]]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Rothwell, Joanne. “ANCOVA in SPSS.” www.statstutor.ac.uk, University of Sheffield, www.sheffield.ac.uk/polopoly_fs/1.531229!/file/MASH_ANCOVA_SPSS.pdf.

== MANOVA ==

The Multivariate Analysis of Variance, also known as the MANOVA, is used when there are multiple dependent variables and you are looking at multiple factors. The only difference between an ANOVA and a MANOVA is that the ANOVA has the limitation of only allowing for a single dependent variable while the MANOVA allows for more. For example, using the MANOVA analysis, a researcher could examine Math Achievement and Reading Achievement scores.
 
An example research question for a MANOVA would be:
Is there a significant difference in Math Achievement (computation, problem solving and numeracy) and Math Self Efficacy for students who participate in an after school treatment program for either one day per week (Program A), three days per week (Program B), or the traditional math curriculum. 

DV 1: Math Achievement 
Level 1: Computation 
Level 2: Problem Solving 
Level 3: Numeracy 

DV 2: Self Efficacy 
1V 1: Math Program 
Level 1: Program A 
Level 2: Program B 
Level 3: Comparison/Control 

''contributed by Karen Fildes''

== MANCOVA ==

Data Screening

2019-11-17T01:39:46Z

Kuslis002: /* Outliers */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
Value cleaning is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

Outliers are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The Mahalanobis Distance statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T01:39:23Z

Kuslis002: /* Outliers */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
Value cleaning is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

Outliers are values that are "extreme or unusual values on a single variable (univariate) or on a combination of variables (multivariate)" (Meyers, Gamst, & Guarino, 2017, p. 48).

The presence of outliers can greatly impact the results of an analysis for two major reasons:

(1) The mean of the variable might no longer be a good variable and

(2) Outliers will yield a difference that when squared will produce a value too large that will skew the computation.

Outliers may signal "anomalies within the data" that will likely need to be addressed prior to moving forward with the statistical analysis (Meyers, Gamst, & Guarino, 2017, p. 48).

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The Mahalanobis Distance statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T01:33:55Z

Kuslis002: /* Value Cleaning */

== Data Screening ==

Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret their results. Valid interpretation of data is reliant on two data features:

1. The data must meet the assumptions of the analysis procedure.

2. The data in the data file are "an accurate representation or transcription of what was provided by research participants as their original responses or what was provided by archival sources as original data" (Meyers, Gamst, & Guarino, 2017, p. 31).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:

Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

----

== Data Cleaning ==

== Value Cleaning ==
Value cleaning is ensuring the values are "within the limits of reasonable expectation" within the "to the extent that it is possible...within the bounds of feasibility"(Meyers, Gamst, & Guarino, 2017, p. 32). For example, you want to ensure the age of a presumed adult is not 9 years old or that a response to an item rated on a likert scale of 1-5 is not a 6 or an otherwise value that is not within the bounds of the study.

''Contribution by: Britany Kuslis, WCSU Cohort 8''

Reference:
Meyers, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

== Outliers ==

== Causes of Outliers ==

== Detection of Multivariate Outliers ==

== Detection of Multivariate Outliers: Scatterplot Matrices ==

== Detection of Multivariate Outliers: Mahalanobis Distance ==

The Mahalanobis Distance statistic measures "the multivariate 'distance' between each case and the group multivariate mean (known as centroid) taking into account the correlations between the variables" (Meyers, Gamst, & Guarino, 2017, p. 52). This method is used to determine if there are scores that vary from the mean of a set of DV's. The Mahalanobis distances details how far a case is from the group center mass of the predictor or IV's. The greater the distance the higher the possibility of a multivariate outlier. According to Lawrence S. Meyers, Glenn Gamst and A.J. Guarino, "Each case is evaluated using the chi square distribution with a stringent alpha level of .001. Cases that reach this significance threshold can be considered multivariate outliers and possible candidates for elimination. This approach is also not without its critics (e.g., Wilcox, 2012) for alternative approaches to multivariate outlier detection" (Meyers, Gamst, & Guarino, 2017, p.53).

Identifying Multivariate Outliers with Mahalanobis Distance-->[https://www.youtube.com/watch?v=AXLAX6r5JgE]

Mahalanobis Distance -->[https://www.youtube.com/watch?v=spNpfmWZBmg]

''Contribution by: Britany Kuslis, WCSU Cohort 8''

References:

Clapham, Matthew E. “Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=spNpfmWZBmg.

Grande, Dr. Todd. “Identifying Multivariate Outliers with Mahalanobis Distance.” YouTube, YouTube.com, 2016, www.youtube.com/watch?v=AXLAX6r5JgE.

Meyers, L., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation.'' Thousand Oaks, CA: Sage Publications.

Data Screening

2019-11-17T01:29:02Z

Kuslis002: /* Detection of Multivariate Outliers: Mahalanobis Distance */

Data Screening

2019-11-17T01:27:04Z

Kuslis002: /* Detection of Multivariate Outliers: Mahalanobis Distance */

Data Screening

2019-11-17T01:07:39Z

Kuslis002: /* Causes of Outliers */

Data Screening

2019-11-17T01:03:20Z

Kuslis002: /* Data Screening */

Shapes of distribution

2019-11-17T01:02:40Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Meyers, Gamst, & Guarino, 2017, p. 53).

There are three types of kurtosis:

1. Mesokurtic: A normal distribution; has a kurtosis value of 0.

2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).

3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Meyers, Gamst, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Meyers, L., Gamst, G., & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation''. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>

Data Screening

2019-11-17T01:01:21Z

Kuslis002: /* Data Screening */

Data Screening

2019-11-17T00:58:31Z

Kuslis002: /* Data Cleaning */

Shapes of distribution

2019-11-17T00:55:21Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Lawrence, Gamst, & Guarino, 2017, p. 53).

There are three types of kurtosis:

1. Mesokurtic: A normal distribution; has a kurtosis value of 0.

2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).

3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Lawrence, Gamst, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Lawrence, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation''. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>

Shapes of distribution

2019-11-17T00:55:04Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Lawrence, Gamst, & Guarino, 2017, p. 53).

There are three types of kurtosis:

1. Mesokurtic: A normal distribution; has a kurtosis value of 0.

2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).

3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Lawrence, Gamst, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Lawrence, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation''. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>

Data Screening

2019-11-17T00:54:27Z

Kuslis002: /* Data Screening */

Data Screening

2019-11-17T00:54:03Z

Kuslis002: Created page with "== Data Screening == Once data from a research study is gathered and has been entered into SPSS, researchers must examine their data to be sure they can validly interpret the..."

Main Page

2019-11-17T00:47:58Z

Kuslis002: /* Modules */

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 An introduction to probability PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.7 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

13.1 [[Multiple Linear Regression]]

14.1 Internal Consistency[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

Contributions here

2019-11-17T00:40:23Z

Kuslis002: /* Student Contributors */

== Editor ==
Frank LaBanca, EdD

== Faculty Contributors ==
Karen Burke, EdD

Patricia Cosentino, EdD

Deborah Hardy, EdD

Jennifer Mitchell, EdD

== Student Contributors ==
David Bozzuto

Karen Fildes

Michael Minzloff

Damien Holst

Jennifer Eraca

John Ryan

Kara Kunst

Emily Rhew

Cassandra Cosentino

Kristina Hislop

Mary Fernand

Thomas Fox

Helen Knudsen

Ashley Brooksbank

Scott Trungadi

Sheri Prendergast

Britany Kuslis

Shapes of distribution

2019-11-17T00:37:32Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Lawrence, Meyer, & Guarino, 2017, p. 53).

There are three types of kurtosis:

1. Mesokurtic: A normal distribution; has a kurtosis value of 0.

2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).

3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Lawrence, Meyer, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Lawrence, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation''. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>

Shapes of distribution

2019-11-17T00:37:09Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Lawrence, Meyer, & Guarino, 2017, p. 53).

There are three types of kurtosis:

1. Mesokurtic: A normal distribution; has a kurtosis value of 0.
2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).
3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Lawrence, Meyer, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Lawrence, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation''. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>

Shapes of distribution

2019-11-17T00:32:37Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Lawrence, Meyer, & Guarino, 2017, p. 53).

There are three types of kurtosis:

1. Mesokurtic: A normal distribution; has a kurtosis value of 0.

2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).

3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Lawrence, Meyer, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Lawrence, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation''. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>

Shapes of distribution

2019-11-17T00:32:11Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Lawrence, Meyer, & Guarino, 2017, p. 53).

There are three types of kurtosis:
1. Mesokurtic: A normal distribution; has a kurtosis value of 0.

2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).

3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Lawrence, Meyer, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Lawrence, S., Gamst, G, & Guarino, A.J. (2017). ''Applied multivariate research: Design and interpretation''. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>

Shapes of distribution

2019-11-17T00:23:43Z

Kuslis002: /* Kurtosis */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

''contributed by Cassandra Cosentino''

[[File:skewness.png]]

== Kurtosis ==

Kurtosis describes “the clustering of scores toward the center of the distribution” (Lawrence, Meyer, & Guarino, 2017, p. 53).

There are three types of kurtosis:
1. Mesokurtic: A normal distribution; has a kurtosis value of 0.
2. Leptokurtic: Positive values of kurtosis; indicate that the bulk of scores are drawn in toward the middle (sharply peaked with heavy tails, for instance).
3. Platykurtic: Negative values of kurtosis; scores are more equally distributed across the entire continuum (a more rectangular distribution). (Lawrence, Meyer, & Guarino, 2017, p. 53).

Contribution by: Britany Kuslis, WCSU Cohort 8

Reference:
Lawrence, S., Gamst, G, & Guarino, A.J. (2017). Applied multivariate research: Design and interpretation. Thousand Oaks, CA: Sage Publications

-----------------------------
Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>