Assumptions Independent t-test - v.0.19.1 and v.0.19.3

johan_achard

Hello Team,

We have noticed a difference in the Shapiro-Wilk normality test between versions 0.19.1 and 0.19.3 of JASP when performing an independent t-test.

• In JASP 0.19.1, two Shapiro-Wilk statistics are reported (one per sample).
• In JASP 0.19.3, only one Shapiro-Wilk statistic is displayed, applied to the model residuals.

This question has already been asked on GitHub (https://github.com/jasp-stats/jasp-issues/issues/3308 ), and Thomas Langkamp explained that "version 0.19.1 was wrong. Only the residuals to be checked, this only one Test is needed." Why ?

Could you provide more theoretical details and explain how normality is tested in each of the two versions so that I can understand the theoretical foundations and the interpretation of normality tests clearly.

We get that normality assumption for independent t-tests concerns the residuals and not the samples distribution themselves. However, we have several questions about the underlying methodology and calculations made by JASP because we did not find the specific details in release nor in JASP manual :

1. How are the residuals calculated? Is it simply the difference between each observation and the average for his group?
2. Is the Shapiro-Wilk test applied to the residuals of each group separately or to all the residuals of the two groups combined? I supposed on all datasets.
3. What happens if one of the samples follows a normal distribution and the other does not? Does the test based on the residuals always allow a normality problem to be detected? Is the Shapiro-Wilk test able to detect the non-normality of the one sample? Is this about Central Limit Theorem ?
4. Is it the data or the residuals that should normally be distributed? In the manual by Navarro et al. (2019, Learning statistics with JASP v1/sqrt(2) ), section 10.8 on "checking the normality of a sample", p.241; it is mentioned that the assumptions are about the normality of the residuals for the ANOVA and of the samples.

Any thoughts?

Notes.

• We have noticed that the Shapiro-Wilk test on two independent samples can be performed outside the t-test, in descriptive statistical menu.
• The information button in independent sample t-tests (on the top right) does not match the updated Shapiro-Wilk test. It says that “The second column contains each level of the grouping variable.”, but there are none.

Thank you in advance for your clarifications, which are always interesting, and your work on JASP.

Johan