Practical Statistics for Educators - User contributions [en]

Z-scores

2022-04-22T01:04:05Z

Penas:

'''A Brief Explanation of Z-Scores:'''
A z-score is a standard score that is used by researchers to add focus and clarity to data. Z-scores indicate how many standard deviations a raw score is from the mean. The mean is fixed at zero and standard deviations are fixed at 1. For example, suppose the mean test score for a sample is 80 with a standard deviation of 12 and you scored a 98 on that test. Your z-score is +1.5, indicating that you scored 1.5 standard deviations above the mean. If a z-score is close to zero the corresponding raw score is close to the mean for the test. If a z-score is -2 the corresponding raw score is 2 standard deviations below the mean.

''contributed by Helen Knudsen''

==Impact of converting raw scores to z-scores==

When each raw score is converted to a z score:

1. The distribution of standard scores is similar in shape to the distribution of raw scores
2. The mean of the distribution of z scores will always equal 0, regardless of the value of the mean in the raw score distribution.
3. Both the variance of the distribution and the standard deviation of z scores always equals 1.

[I would like to insert an image here and am unsure how]

It is helpful to see what this looks like in a side-by-side distribution of raw and standard scores. Notice that the mean raw scores are 6.0; whereas the standard score is set at a mean of zero. And whereas the standard deviation from the raw scores was 3.18, when converted to standard scores, the standard deviation is 1.00 (Hinkle, Wiersma, & Jurs, 2003, p. 72).

In sum, calculating a z score for each raw score in a distribution will transform the original distribution of scores into one with identical shape but a mean of 0 and a standard deviation of 1 (Hinkle, Wiersma, & Jurs, 2003, p. 71).

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

''contributed by Emily Kilbourn''

== Calculating Z-scores using SPSS ==

''I, among others were having a hard time calculating Z-scores using the SPSS program. Amy, Michelle and I brainstormed last week, but had no luck. The book is vague in terms of how to approach it. Thanks for the guidance, Frank.''

'''<big>When calculating Z-scores on SPSS, follow these directions:</big>'''

1) Once you have the data entered in SPSS, click on "Analyze", "Descriptive Statistics", "Descriptives".

2) Move the variable over that you want to analyze.

3) Click on the small box that states, "Save standardized values as variables".

4) Click on "Options" if you would like to calculate mean, median, mode, etc. in addition to Z-scores.

5) Click "OK".

6) The Z-scores will appear in a separate column in the data editor.

''contributed by Chris Longo''

== Video Tutorial: How to Calculate and Interpret Z-Scores in SPSS==

https://youtu.be/Soi1iXxpGmA

''contributed by Sandra Peña''

Histograms

2022-04-22T00:43:12Z

Penas:

==Histograms==
"Histograms are used to display the distribution of a single continuous variable (e.g. age, perceived stress scores)." Examining the shape of the curve will provide information about the distribution of scores of a continuous variable. If we assume that scores of each variable measured are distributed normally, most scores will occur in the center, and taper towards the extremes. The skewness of the data is determined if the data displayed is either distributed more to right or left side of the visual.

(Pallant, 2016, pg. 68)

''contributed by Joseph W. Sullivan''

==Parts of a Histogram==
# The title: The title describes the information included in the histogram.
# x-axis: The x-axis are intervals that show the scale of values which the measurements fall under.
# y-axis: The y-axis shows the number of times that the values occurred within the intervals set by the x-axis.
# The bars: The height of the bar shows the number of times that the values occurred within the interval, while the width of the bar shows the interval that is covered. For a histogram with equal bins, the width should be the same across all bars.

''contributed by Sandra Peña''

==To create a histogram on SPSS, do the following:==

1) After entering data into SPSS, click on "Graphs", scroll down to “Legacy
Dialogs", move cursor to the right and scroll down to "Histograms".

2) Click on the variable in the left box you want entered into the right variable box

3) Click on “display normal curve” to view the bar graph data in bell curve form

4) Click "OK".

5) The histogram will appear PASW Output Statistic Viewer

''contributed by Jen Eraca''

==Video Tutorial: How to Create a Histogram on SPSS==

https://youtu.be/weonO7ZaX4Y

''contributed by Sandra Peña''

Histograms

2022-03-01T22:20:39Z

Penas:

==Histograms==
"Histograms are used to display the distribution of a single continuous variable (e.g. age, perceived stress scores)." Examining the shape of the curve will provide information about the distribution of scores of a continuous variable. If we assume that scores of each variable measured are distributed normally, most scores will occur in the center, and taper towards the extremes. The skewness of the data is determined if the data displayed is either distributed more to right or left side of the visual.

(Pallant, 2016, pg. 68)

''contributed by Joseph W. Sullivan
==Parts of a Histogram==
# The title: The title describes the information included in the histogram.
# X-axis: The X-axis are intervals that show the scale of values which the measurements fall under.
# Y-axis: The Y-axis shows the number of times that the values occurred within the intervals set by the X-axis.
# The bars: The height of the bar shows the number of times that the values occurred within the interval, while the width of the bar shows the interval that is covered. For a histogram with equal bins, the width should be the same across all bars.
''Contributed by Sandra Peña''

==To create a histogram on SPSS, do the following:==

1) After entering data into SPSS, click on "Graphs", scroll down to “Legacy
Dialogs", move cursor to the right and scroll down to "Histograms".

2) Click on the variable in the left box you want entered into the right variable box

3) Click on “display normal curve” to view the bar graph data in bell curve form

4) Click "OK".

5) The histogram will appear PASW Output Statistic Viewer

''contributed by Jen Eraca''

The Greek Alphabet

2022-03-01T16:30:58Z

Penas:

[[Image:greek.jpg]]

alpha: significance level

eta: effect size for analysis of variance

mu: mean

rho: (Spearman rho) rank correlation

SIGMA: sum

sigma: standard deviation

chi: (chi square) non-parametric inferential analysis for categorical data

''contributed by Frank LaBanca, EdD''

Directions on how to inserting Greek letters into your statistical analysis paper using Google Docs.

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1:
| Click on Insert
|-
| Step 2
| Scroll down and highlight to Special Characters
|-
| Step 3
| A window appears that reads insert special characters
|-
| Step 4
| The default window will read for Symbols and Arrow selection
|-
| Step 5
| Click on Symbols and scroll down to Other European Scripts
|-
| Step 6
| Click on Arrows and scroll down to Historic-Greek
|-
| Step 7
| Select the appropriate character
|}

''contributed by Héctor Huertas''

=Note=
Pronunciation: In the US, Greek letters which names end in i may be pronounced either with a long-i sound, or (except for pi and chi) with a long-e sound. Thus, phi (f) can sound like the beginning of "final" or like "fee"; but pi (p) sounds like "pie" and never like "pea." The ch in chi sounds like the ch in "chemistry," and, among knowledgeable statisticians, are almost never pronounce like ch in "church." These conventions of pronunciation among US statisticians have little to do with authentic Greek pronunciation, either ancient or modern.

''Contributed by Sandra Peña''

Internal Consistency Reliability

2022-01-31T23:37:46Z

Penas: /* Example: */

"Internal consistency reliability relates to the extent to which all the variables that make up the scale are measuring the same thing" (Muijs, 2011, pg. 217).
''contributed by Joseph W. Sullivan''

==Example:==
You have just opened a restaurant and would like to find out how satisfied your costumers are with the level of customer service from your staff. You send out a survey to your costumers asking them to answer 3 specific questions to measure their overall satisfaction:
# Satisfied with the staff service
# Most likely to recommend your restaurant
# My tip will reflect my satisfactory experience
When you provide a survey that has good internal consistency, their answers should also show consistency. This could translate to:
# Agree
# Somewhat agree
# Strongly agree
Most researchers choose to provide at least two questions that measure the same thing. ''Contributed by Sandra Peña''

Internal Consistency Reliability

2022-01-31T23:29:50Z

Penas:

"Internal consistency reliability relates to the extent to which all the variables that make up the scale are measuring the same thing" (Muijs, 2011, pg. 217).
''contributed by Joseph W. Sullivan''

==Example:==
You have just opened a restaurant and would like to find out how satisfied your costumers are with the level of customer service from your staff. You send out a survey to your costumers asking them to answer 3 specific questions to measure their overall satisfaction:
#1. Satisfied with the staff service
#2. Most likely to recommend your restaurant
#3. My tip will reflect my satisfactory experience
When you provide a survey that has good internal consistency, their answers should also show consistency. This could translate to:
#1. Agree
#2. Somewhat agree
#3. Strongly agree
Most researchers choose to provide at least two questions that measure the same thing. ''Contributed by Sandra Peña''