I am testing the presence or absence of gender (Nominal -Independent Variable) differences in average anxiety scores (Ratio - Dependent Variable). My total sample size is 40 (with 20 males and 20 females).
- Does the Central Limit Theorem require each of the 2 independent groups to have at least 30 subjects (i.e., n1 ≥ 30 & n2 ≥ 30) for it to be assumed a NORMAL distribution or would a total sample size ≥ 30 (e.g., n1(20) + n2(20)=40) large enough to assume normality?
- What statistical test is appropriate if both my IV and DV is normally distributed? Is an independent t-test the correct one to use?
- What statistical test should I use if my IV is NOT normally distributed but my DV is? Do I use the Mann- Whitney U test?
IVs do not need to be normal. For the DV the only requirement on distribution is that the residuals be normal. Check that with a Shapiro-Wilk test. In order to avoid assumptions on the variances I would recommend the Welch t test. The link is:
https://www.google.com/search?client=firefox-b-1&ei=c99XW7CxPKHSjwSA44WICQ&q=welch+two+sample+t-test&oq=Welch&gs_l=psy-ab.1.0.0i67k1j0i131k1j0l5j0i131k1j0l2.8228.13004.0.18048.13.8.1.0.0.0.164.660.6j1.7.0....0...1c.1.64.psy-ab..7.6.504...0i22i10i30k1j0i22i30k1j0i131i67k1.0.1Tm-P_oZLQY
Best wishes, David Booth
Compare the anxiety scores of the two genders and see if both score of the two genders is normally distributed (Histogram is often enough to see normal/non-normal distribution), then it’s independedent t test or One-way ANOVA.
The assumptions for Independent t test include:
1) random samples,
2) independent observations,
3) in each group, n>=30 in each group or normal distribution (seen from histogram/Shapiro wilk test),
4) population variance are the same between the 2 groups (p value >= 0.05 in Levenne test).
In One-way ANOVA, the assumption 3 above is changed to “in each group, n>=30, or the combined scores is notmally distrubuted).
Dear friend. In order to use the central limit theorem, the number of data must be considered in each group of more than 30. Not total two or more groups. It does not seem that you can use parametric tests based on the normalization of data. So you should look for the correct nonparametric test. If you have two groups, use the same Mann- Whitney U test.
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