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

Some of the advanced effect size information came from:

Mangiafico, S.S. 2016. Summary and Analysis of Extension Program Evaluation in R, version 1.18.8. rcompanion.org/handbook/.

Tomczak, M. & Tomczak, E. (2014). The need to report effect size estimates revisited. An overview of some recommended measures of effect size. Trends in Sport Sciences. 19-25. PDF Available from Research Gate: https://www.researchgate.net/publication/303919832_The_need_to_report_effect_size_estimates_revisi ted_An_overview_of_some_recommended_measures_of_effect_size

Once you decide on the effect size test, you need to be able to interpret it. There are dozens of articles of interpreting effec t size and I’ve tried to bring the most relevant information here.

Effect size – What does it mean?

Effect size threshold

Type of test

Title

Small Medium Large Very large

“mean” difference

Cohen’s d, Glass Delta, Hedges’s correction

.20

.50

.80

Over 1

η 2

Sum of squares effect/sum of squares total

.010

.060

.140

Over .200

(or Eta Squared)

Correlation

r

.10 .10

.30 .30

.50 .50

.70 .70

Uses mean ranks

Glass rank biserial correlation

Table 123: Ellis, P. (2009). Thresholds for interpreting effect sizes & Lenhard, W. & Lenhard, A. (2016). Calculation of Effect Size.

Communicating Results – using APA 7 th edition

Review the output illustration of MannWhitney U test. Be consistent throughout. A caution: always review the latest APA updates. Requirements and suggestions change!

#1 – Include the median of both groups #2 – Include the U test results #3 - Include the sample size of each group #4 – Include the z score

#5 – Include the significance (report p significance from Exact) #6 – Include the effect size (and in narrative indicate which one used) #7 – Include the confidence interval

Please note that the APA manual section 6.36 suggests that standard deviations should be one decimal, but the APA Sample Tables show several sample tables with three decimal places! So please be consistent as well as discuss this with your dissertation committee.

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