Practical Statistics for Educators - User contributions [en]

Effect size

2022-04-28T20:29:37Z

Ldaigle:

Effect size for ANOVA

Partial Eta Squared

Trivial: <0.2
Small: 0.2-0.49
Moderate: 0.5-0.79
Large: >0.8

______________________________________________________________________________________________________________________________________________________________________________________

Knowing that the relationship is significant does not tell us whether this effect is strong or weak. So we need to calculate an effect size as well as the t-test.

Muijs, D. (2016).''Doing Quantitative Research in Education With SPSS'' (2nd ed.). Sage Publications.

An effect size is a way to quantify the difference between two groups.

While a p-value can tell us whether or not there is a statistically significant difference between two groups, an effect size can tell us how large this difference actually is. In practice, effect sizes are much more interesting and useful to know than p-values.

Bobbit, Z. (2020, January 1). Effect Size: What It Is and Why It Matters. ''Statistics. Simplified. Statology''.
https://www.statology.org/effect-size/

contributed by ''Tania Nicole Sutherland''

When the p-value is less than or equal to .05, this means there is a statistical significance. This is when we need to take effect size value into account. If the p-value is greater than .05, then there is no statistical difference so there would not be an effect size.

''contributed by Lisa Daigle''

Selecting a Post Hoc test

2022-04-21T20:52:11Z

Ldaigle:

''Note: The editor is unsure of the source of this material. A citation would be greatly appreciated!''

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“Once you have determined that differences exist among the means, post hoc range tests and pairwise multiple comparisons can determine which means differ. Range tests identify homogeneous subsets of means that are not different from each other. Pairwise multiple comparisons test the difference between each pair of means, and yield a matrix where asterisks indicate significantly different group means at an alpha level of 0.05” (SPSS, Inc.).

== Post Hoc tests that assume equal variance ==

{| class="wikitable"
|-
! Multiple Comparison Tests AND Range Tests
! Range Tests Only
! Multiple Comparison Tests Only
|-
| Tukey’s HSD (honestly significant difference) test
| Tukey’s b (AKA, Tukey’s WSD (Wholly Significant Difference))
| Bonferroni (don't use with 5 groups or greater)
|-
| Hochberg’s GT2
| S-N-K (Student-Newman-Keuls)
| Sidak
|-
| Gabriel
| Duncan
| Dunnett (compares a control group to the other groups without comparing the other groups to each other)
|-
| Scheffe (confidence intervals that are fairly wide)
| R-E-G-W F (Ryan-Einot-Gabriel-Welsch F test)
| LSD (least significant difference)
|-
|
| R-E-G-W Q (Ryan-Einot-Gabriel-Welsch range test)
|
|-
|
| Waller-Duncan
|
|}

== Post Hoc tests that do not assume equal variances ==

Tamhane’s T2

Dunnett’s T3

Games-Howell

Dunnett’s C

== About the more popular Post Hoc tests ==

''Fisher's LSD (Least Significant Different)''

This test is the most liberal of all Post Hoc tests and its critical t for significance is not affected by the number of groups. This test is appropriate when you have 3 means to compare. It is not appropriate for additional means.

''Bonferroni (AKA, Dunn’s Bonferroni)''

This test does not require the overall ANOVA to be significant. It is appropriate when the number of comparisons (c = number of comparisons = k(k-1))/2) exceeds the number of degrees of freedom (df) between groups (df = k-1). This test is very conservative and its power quickly declines as the c increases. A good rule of thumb is that the number of comparisons (c) be no larger than the degrees of freedom (df).

''Newman-Keuls''

If there is more than one true null hypothesis in a set of means, this test will overestimate they familywise error rate. It is appropriate to use this test when the number of comparisons exceeds the number of degrees of freedom (df) between groups (df = k-1) and one does not wish to be as conservative as the Bonferroni.

''Tukey's HSD (Honestly Significant Difference)''

This test is perhaps the most popular post hoc. It reduces Type I error at the expense of Power. It is appropriate to use this test when one desires all the possible comparisons between a large set of means (6 or more means).

''Tukey's b (AKA, Tukey’s WSD (Wholly Significant Difference))''

This test strikes a balance between the Newman-Keuls and Tukey's more conservative HSD regarding Type I error and Power. Tukey's b is appropriate to use when one is making more than k-1 comparisons, yet fewer than (k(k-1))/2 comparisons, and needs more control of Type I error than Newman-Kuels.

''Scheffe''

This test is the most conservative of all post hoc tests. Compared to Tukey's HSD, Scheffe has less Power when making pairwise (simple) comparisons, but more Power when making complex comparisons. It is appropriate to use Scheffe test only when making many post hoc complex comparisons (e.g. more than k-1).

== Post Hoc Tests SPSS Directions ==

On SPSS, find analyze and select univariant. Then, choose post hoc and move over your independent variable into the box. Finally, select the post hoc test that you want to run.

''Contributed by Lisa Daigle''

Rules of thumb for interpreting the size of a correlation coefficient

2022-04-03T21:20:02Z

Ldaigle:

{| class="wikitable"
|-
! Size of positive correlation
! Size of negative correlation
! Interpretation
|-
| .90 to 1.00
| -.90 to -1.00
| Very high positive (negative) correlation
|-
| .70 to .90
| -.70 to -.90
| High positive (negative) correlation
|-
| .50 to .70
| -.50 to -.70
| Moderate positive (negative) correlation
|-
| .30 to .50
| -.30 to -.50
| Low positive (negative) correlation
|-
| .00 to .30
| .00 to -.30
| Little, if any, correlation
|}

''contributed by Frank LaBanca EdD''

Interpreting the line of best fit can show outliers. Outliers can lead to different interpretations of data, and an easy method for spotting outliers is through a scatterplot.

''contributed by Lauren Moyer''

Recall that this is the r value, not the p value, when interpreting the r value. The Pearson correlation does not show causation. For example, if the r value has a high positive correlation between a teacher shortage and the deterioration of the ozone layer, it does not necessarily mean that the teacher shortage caused the deterioration of the ozone layer.

''Contributed by Lisa Daigle''

Levene's p versus the test statistic p

2022-03-05T22:21:47Z

Ldaigle:

Levene's p versus the test statistic p
When an  value is set at .05, any p that is smaller than .05 is producing a statistically significant different result, while any value greater than .05 is producing a statistically similar result.

p≤.05  statistical difference

p>.05  statistical similarity

When do we want one or the other? It depends on the question asked.

For example, when we are looking at two sets of data to see if they are homogenous to one another for the purpose of equal variances, we want p>.05 so there IS statistical similarity. Therefore the Levene’s test demonstrates homogeneity (equal variance) when p>.05. (This generally results in an F≈1.) When Levene’s is statistically similar this is a GOOD thing, because it gives us confidence that data sets have similar distributions (even though their means might be different). In other words, the curves look similar, even though their centers might be at different points on the number line.

On a t test, you are generally trying to show a difference (although not always the case). Therefore the p≤.05. If p≤.05 then we know that tcrit<tstat. If p>.05, then tcrit>tstat.

''contributed by Frank LaBanca, EdD''

This is a great visual for 'significantly different and similar'.

[[File:Statistics.JPG|200px|thumb|left|alt text]]

''contributed by John Ryan''
''drawing by Frank LaBanca, EdD''

This is an informative video I found that explains Levene's Test for Equality of Variances (also known as Levene's Test for Homogeneity of Variance).
[https://youtu.be/4mkEZxgxMRA Levene’s Test of Homogeneity of Variance in SPSS]

''contributed by Scott Trungadi''

== Levene's in SPSS ==

On SPSS, go to Analyze then Compare Means. Click on Independent Samples T test. Then, choose the variable you are testing and choose the group variable. Click on definite groups and use the numbers that correlates with the two groups you are comparing. Then, you will have your Levene's p value. If the Levene's test is greater than .05, use the top row of statistics. If it is less than .05, use the bottom row of statistics.

''Contributed by Lisa Daigle''

Pearson r

2022-02-19T20:26:31Z

Ldaigle:

Also known as Pearson's product-moment correlation. This technique is used to correlate the raw scores of two variables.

Also visit http://psych.csufresno.edu/psy144/Content/Statistics/relationship_strength.html for more information on Pearson r.

''contributed by Kara Kunst''

Also referred to as the Pearson Correlation Coefficient Squared, it is the proportion of variance in the criterion variable that can be accounted for by the predictor variable. (from Dr. Nancy Heilbronner)

''contributed by Mary Fernand''

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Note: Pearson r scores cannot exceed 1.00 or -1.00 (range is between -1.00 and 1.00).

The Pearson r score (say for example .80) is the number where the distribution will peak, and the remaining distribution will spread out around the number.

''contributed by Mykal Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). Applied multivariate research: Design and interpretation. Thousand Oaks, CA: Sage Publications. (P. 21)

==A "real life example" of using correlations to gauge winter weather==

Every teacher in New England has a vested interest in understanding how winter weather may impact the school calendar. I recently heard an interview with Judah Cohen on NPR, and sourced an older article from the Washington Post which includes a graph, which illuminates how this meteorologist who works for the firm, Atmospheric and Environmental Research, uses correlations to forecast East Coast weather. Specifically, Cohen evaluates the Siberian snow cover in October to predict winter weather in New England (Samenow, 2013).

Because we’ve learned about correlational statistics, specifically what’s implied by the correlation coefficient or r-value, we can look beyond the narrative offered in the Washington Post article, which describes the statistical correlation as “striking.” In fact, we can look at the r =.810 in the graph below, and determine that because this number is close to 1, the Snow Advance Index (which relates to the Siberian snow cover) and the Arctic Oscillation (which produces the winter weather patterns in the Northeast) are strongly positively correlated (Hinkle, Wiersma, & Jurs, 2003, pp.98-99).

[[File:winter.jpg]]

Given the strong positive correlation, teachers in New England might pay a little more attention to what’s happening in Siberia in October to determine how much hot chocolate to buy in advance of snow days and how far those snow days will cause us to overshoot our districts’ June calendars.

References:
Hinkle, D.E., Wiersma, W., & Jurs, S.G. (2003). Applied statistics for the behavioral sciences (5th edition). Boston, M.A.: Houghton Mifflin Company.

Samenow, J. (2013). Judah Cohen’s winter outlook: A downer for East Coast winter weather lovers. The Washington Post.

''contributed by Emily Kilbourn''

It is important to keep in mind that Pearson r is not reporting a cause and effect relationship, since consideration for classification of independent and dependent variables is not taken into account. However, it is a good measure for seeing the strength of relationship between two variables.

''contributed by Lauren Moyer''

==How to Find the Pearson Correlation (r) in SPSS==

In SPSS, follow these steps to find the r value:

1. Once you have the two variables you want to compare, click correlate.
2. Choose bivariate
3. Move the variables you want to compare over to the right box using the arrow.
4. Make sure Pearson is checked off in the window
5. Select two-tailed
6. Click flag significant correlations- asterisks will flag a significant correlation.
7. Click ok and a table will be generated with the Pearson correlation

''Contributed by Lisa Daigle''

Pearson r

2022-02-19T20:25:05Z

Ldaigle:

Also known as Pearson's product-moment correlation. This technique is used to correlate the raw scores of two variables.

Also visit http://psych.csufresno.edu/psy144/Content/Statistics/relationship_strength.html for more information on Pearson r.

''contributed by Kara Kunst''

Also referred to as the Pearson Correlation Coefficient Squared, it is the proportion of variance in the criterion variable that can be accounted for by the predictor variable. (from Dr. Nancy Heilbronner)

''contributed by Mary Fernand''

----
Note: Pearson r scores cannot exceed 1.00 or -1.00 (range is between -1.00 and 1.00).

The Pearson r score (say for example .80) is the number where the distribution will peak, and the remaining distribution will spread out around the number.

''contributed by Mykal Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). Applied multivariate research: Design and interpretation. Thousand Oaks, CA: Sage Publications. (P. 21)

==A "real life example" of using correlations to gauge winter weather==

Every teacher in New England has a vested interest in understanding how winter weather may impact the school calendar. I recently heard an interview with Judah Cohen on NPR, and sourced an older article from the Washington Post which includes a graph, which illuminates how this meteorologist who works for the firm, Atmospheric and Environmental Research, uses correlations to forecast East Coast weather. Specifically, Cohen evaluates the Siberian snow cover in October to predict winter weather in New England (Samenow, 2013).

Because we’ve learned about correlational statistics, specifically what’s implied by the correlation coefficient or r-value, we can look beyond the narrative offered in the Washington Post article, which describes the statistical correlation as “striking.” In fact, we can look at the r =.810 in the graph below, and determine that because this number is close to 1, the Snow Advance Index (which relates to the Siberian snow cover) and the Arctic Oscillation (which produces the winter weather patterns in the Northeast) are strongly positively correlated (Hinkle, Wiersma, & Jurs, 2003, pp.98-99).

[[File:winter.jpg]]

Given the strong positive correlation, teachers in New England might pay a little more attention to what’s happening in Siberia in October to determine how much hot chocolate to buy in advance of snow days and how far those snow days will cause us to overshoot our districts’ June calendars.

References:
Hinkle, D.E., Wiersma, W., & Jurs, S.G. (2003). Applied statistics for the behavioral sciences (5th edition). Boston, M.A.: Houghton Mifflin Company.

Samenow, J. (2013). Judah Cohen’s winter outlook: A downer for East Coast winter weather lovers. The Washington Post.

''contributed by Emily Kilbourn''

It is important to keep in mind that Pearson r is not reporting a cause and effect relationship, since consideration for classification of independent and dependent variables is not taken into account. However, it is a good measure for seeing the strength of relationship between two variables.

''contributed by Lauren Moyer''

'''How to Find the Pearson Correlation (r) in SPSS'''

In SPSS, follow these steps to find the r value:

1. Once you have the two variables you want to compare, click correlate.
2. Choose bivariate
3. Move the variables you want to compare over to the right box using the arrow.
4. Make sure Pearson is checked off in the window
5. Select two-tailed
6. Click flag significant correlations- asterisks will flag a significant correlation.
7. Click ok and a table will be generated with the Pearson correlation

''Contributed by Lisa Daigle''