Gender and Daytime Sleepiness
IV = Gender (male or female)
DV= Daytime sleepiness (Total score on Epworth Sleepiness Scale)
Sample size: 20 males and 20 females = total (n=40)
H0 = There is no difference in daytime sleepiness between men and women.
Ha = There is a difference in daytime sleepiness between men and women.
Assumptions of Normality Test showed:
IV = 5/7 results "REJECT NORMALITY" (NON NORMAL distribution) and 2/7 results "CAN'T REJECT NORMALITY" (NORMAL distribution)
DV = 7/7 results 'CAN'T REJECT NORMALITY" (NORMAL distribution)
What is an appropriate statistical test to use?
I ran an independent t-test and got a NO statistically significant difference among men and women in daytime sleepiness even if my IV showed more of a NON NORMAL distribution but I applied the Central Limit Theorem and assumed normality for sample size ≥ 30 and used the parametric t-test. Am I correct?
Please see attached data output.
It appears that you are correct but I would have used a Welch test which doesn't assume equal variances for men and women. Your results will probably be the same if you do that. IVs don't have to be normal. You don't specify what your variables are in the context of the t-test but that is obvious. I would test the normality assumption with a Shapiro-Wilk test. Best wishes, David Booth
I think the t - test is okay. However, depending on the nature of your data, if you are concerned about normality, you can use the Kruskal-Wallis test. The statistic is a non-parametric equivalent of the one-way analysis of variance, ANOVA. Unlike the ANOVA however, it is not bound by normality assumptions. It is suitable for testing categorical data. It is used to test the null hypothesis that two or more independent samples come from identical populations. The test will tell you if there is a significant difference between groups - in your case, the male and female samples
Thank you for your reply.
David, I actually have the Shapiro-Wilk test result in the attached "descriptive stats gender pdf" file and the result showed "REJECT normality". I also ran tests of equal variance assumption and got a p=0.84740 for Variance -Ratio (1.0936) and p=0.68087 for the Modified-Levene (0.1718). Both seem to indicate that group variances are equal.
Chukwuma, I only have 2 categorical variables for my IV (male and female) and a continuous variable for my DV (Total ESS Score). My research question is: Is there a difference in men compared to women in their average total ESS score? Hence, I decided to assume normality based on CLT and used an independent t-test. I am not sure though if the CLT meant that each gender group should have ≥ 30, which will make my total sample size n = 60 (30 males + 30 females) or if it is referring to the combined total of both groups, which in my case is n=40 (20 males + 20 females).
Thus, if CLT needs each independent group to have ≥ 30, then I guess I cannot assume normality for my test and would need to use a nonparametric test. I was debating whether to use the Mann Whitney U test if I cannot assume normality for my IV. The Kruskal-Wallis test I believe is for testing differences in ranks of scores of 3 or more independent groups, so I think this won't be the test I should use because I only have 2 groups (Male/Female).
So here are my questions:
1) Does the Central Limit Theorem require each independent group to have at least 30 participants (n1 ≥ 30 and n2 ≥30) to allow it to be considered NORMAL or is it referring to the total sample size is at least 30 (n1 + n2 ≥ 30)?
2) Based on assumption of normality tests, my IV could either be NOT NORMAL according to 5 tests - Shapiro-Wilk W, Anderson-Darling, Kolmogorov-Smirnov, D'Agostino Kurtosis, and D'Agostino Omnibus) OR it could also be NORMAL according to 2 tests - Martinez-Iglewicz and D'Agostino Skewness). Which assumption should I follow?
3) If I assume all my data to be normal (IV and DV) then I should use the independent t-test. But if I assume that my IV is NOT NORMAL but my DV is NORMAL, then I must use Mann-Whitney U test. Am I correct? Which test do you think is more appropriate for my data?
I greatly appreciate any feedback.
Warm Regards.
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