Which stasticial test is best to use in my case?

Hello

I've conducted an experiment with around 100 people. I have 48 male and 52 female. Now I would like to accept or reject the following three hypothesis (i.e. to determine the p-value):

1. There is a difference in performance between male and female (The people had to perform some tasks which gives me a continuous performance value for every person, i.e. I have a value per person).
2. There is a difference in performance between groups of people (independent of the gender). The performance metric is the same as under 1. but now I have divided the people in four different groups. The groups have unequal sizes.
3. There is a difference in performance depending on the age of people (I have also recorded the age of the people). I have ages from 18 to 30. For example, for age 18 I only have one person, for other ages there are multiple persons.

What statistical test (like t-test, ANOVA, chi-squared, Friedmann, Kruskal-Wallis, Mann-Whitney) would be appropriate for the three cases described above?

Second, does it matter if I choose There is a difference in performance between male and female or the negation There is no difference in performance between male and female as the null hypothesis?

Answer 1

[TED MOSBY]

Hi,

I found some matlab functions for all the 3 cases, have a look at these below:

1. Difference in Performance Between Male and Female

Test: Use the "ttest2" function for an independent samples t-test if the data is normally distributed. If not, use "ranksum" for the Mann-Whitney U test.

MATLAB Function:

h = ttest2(malePerformance, femalePerformance)

for t-test.

p = ranksum(malePerformance, femalePerformance)

for Mann-Whitney U test.

2. Difference in Performance Between Groups

Test: Use "anova1" for one-way ANOVA if the data is normally distributed and variances are equal. If not, use "kruskalwallis" for a non-parametric test.

MATLAB Function:

p = anova1(performanceGroups, groups) 

for ANOVA.

p = kruskalwallis(performanceGroups, groups)

 for Kruskal-Wallis test.

3. Difference in Performance Depending on Age

Test: Use "fitlm" for linear regression if age is treated as a continuous variable. If age is treated as categorical, use "anova1" or "kruskalwallis".

MATLAB Function:

mdl = fitlm(ages, performance)

•  for linear regression.

p = anova1(performance, ageGroups) 
% or 
p = kruskalwallis(performance, ageGroups)

•  if age is categorical.

Null Hypothesis Consideration

• Null Hypothesis: In MATLAB, the null hypothesis is generally the default assumption of no effect or no difference. For example, "ttest2" assumes no difference in means between two groups as the null hypothesis.

www.mathworks.com/help/stats/ttest2.html?searchHighlight=ttest2&s_tid=srchtitle_support_results_1_ttest2

www.mathworks.com/help/stats/anova1.html?searchHighlight=anova1&s_tid=srchtitle_support_results_1_anova1

www.mathworks.com/help/stats/kruskalwallis.html?s_tid=doc_ta

Refer these links for the above MATLAB functions used.

Hope this helps!