Checking mean and variance differentiation in 2 data samples...

Question

I have the following 2 samples

data 1 : 59.09  59.17   59.27   59.13   59.10   59.14   59.54   59.90
data 2:  59.06  59.40   59.00   59.12   59.01   59.25   59.23   59.564

And I need to check whether there is differentiation regarding the mean and the variance between the 2 data samples at significance level a=0.05

I think that the first thing I need to do is to check whether the samples come from a normal distribution in order to infer whether i should proceed using parametric or non marametric tests...

However using lillietest in matlab returned that both samples do not follow the normal distribution...

Any ideas on how should I proceed with checking the differentiation tests ? Should I perform ttest ? Or should I proceed by using something like Wilcoxon ? (p.s please confirm that that both data samples do not follow normal distribution...)

Answer 1

For a t-test, you need the samples to follow a normal distribution, so you're right to check this assumption first. I did a Shapiro-Wilk to test the normality, and it is rejected for the first sample, but it is not for the second sample. Thus you can't use a t-test.

The alternative is to use the Wilcoxon test, which is non-parametric.

Here is the code I have used with R :

data1 <- c(59.09, 59.17, 59.27, 59.13, 59.1, 59.14, 59.54, 59.9)
data2 <- c(59.06, 59.4, 59, 59.12, 59.01, 59.25, 59.23, 59.564)
shapiro.test(data1)
# P-value = 0.007987. Normality is rejected.
shapiro.test(data2)
# P-value = 0.3873. Normality is not rejected.
wilcox.test(data1, data2)
# P-value = 0.5054. No significative difference.