I am doing statistics to get normative data.
The distribution is non normal.
N = 192
Mdn = 61, M = 60,29
Range 49-62
1. Outlier : At first, I used -2.5 SD to identify outliers. But Reviewer asked for a reference, because it could have been 3 SD. Then, with the boxplot in SPSS, I noticed that only one participant was obviously different from others. He is also the only one to be at more than 3 IQR from the 25th percentile.
I think that IQR is more appropriate for the detection of outliers in this distribution (skewness -1.905, kurtosis 5.809) than SD.
What do you think ? Do you have references to recommend ?
2. Mean comparaison: I compared groups with t-tests for independant samples (n1 = 66, n2 = 125) and Welch's t-Test for scores with unequal variances across groups. My distributions are not normal. I assumed the robustness of T tests in this case because of the large sample. However, Reviewer would like some precisions. Would it be better to use nonparametic or to justify the t-test with the large sample ? Do you have references to recommend ?
Thank you !!
Valérie
Inspect the histogram of the distribution. Does the histogram really look heavily skewed? The Shapiro test is known to be biased by size. A Q–Q plot is required for verification in addition to the test.
https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test
Indeed, the t-test is known to be robust. You could try the Yuen robust version of the t-test, described by Patrick Mair & Rand Wilcox. See:
https://pdfs.semanticscholar.org/5f5c/186fceb1598528fbd2f798878055549f792b.pdf
If the Reviewer still is not convinced, rely on the Mann-Whitney U test. This test should yield the same results.
Thank you for your answer. When I look at the histogram, the distributions of scores to at least 4 tasks are really skewed (I attached the file showing the results for one of the two groups).
The Yuen version of the t-test seems very interesting. I am not familiar with R so I'll try it later, but not for this paper.
Because I want to show that there is no significant difference between group and the t-tests and Mann-Whitney U tests both show this point, I will used the Mann-Whitney U test.
Thanks again !
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