2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Effect size

When to use

Should we use for Mann Whitney U? Yes. This is calculated from the absolute value of Z divided by the total number of observations. Z is a standardized statistic.

r (sometimes called Cohen’s r)

You can use to compare the effect of any two groups to see how substantially different. The output form the Mann Whitney U contains the standardized Z-score, which can be used to calculate the correlation coefficient r (r 2 = eta squared) Use it in ANOVAs to show the total variation in Y, the proportion that can be attributed to a specific X.

Eta Squared η 2

Maybe. η 2 = SS

effect / SS total Eta squared is most often used in ANOVA models No. Cohen’s d is not appropriate. It requires a normal distribution and is based on means. However, in advanced literature, a variation of Cohen’s d. Maybe. The formula is as follows: R is the mean rank. The results will produce “r” a correlation coefficient with r ranges from -1.0 to positive 1.0. No. Hedges’ correction uses the difference in means and the pooled standard deviation.

Cohen’s d

Two groups have similar SDs and the same size sample

Glass rank biserial correlation

If the two groups are not the same shape, use the average mean ranks and sample size in each group. It also gives us “r”

Hedges’ correction

Different and/or small sample size (i.e. 20 males in group 1 and 10 females in group 2) Small sample size means less than 20. If each group has a different SD. It is also used between the experimental and control group. Reports the probability that a value from one group will be greater than a value from the other group. (A value of .50 indicates the two groups are “stochastically equal) Linearly related to Vargha. The value is from -1 to 1. A value of zero indicates stochastic equality. Use for a non-parametric test where three or more paired measurements (repeated measures)

Glass’s delta

No. Glass Delta uses mean and the standard deviation of the control group.

Advanced non-parametric effect size methods

Vargha

&

Requires an advanced understanding.

Del aney’s A

Cliff’s delta

Requires an advanced understanding.

Friedmann rank sum test

N/A to our sample data set

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