I want to compare 3 groups of samples. Each sample contains 5 measurements. I want to know if the samples differ significantly. First I wanted to do a ANOVA, but my samples are not normal distributed. I tested this with a Shapiro-Wilks Test. For statisitical analyses I use the python library scipy.stats.
import numpy as np import scipy.stats as stats sample1 = np.array([0.0016, 0.0012, 0.0009, 0.0011, 0.0016]) sample2 = np.array([0.0018, 0.0016, 0.0015, 0.0015, 0.0015]) sample3 = np.array([0.0007, 0.0005, 0.0013, 0.001 , 0.0015]) stats.shapiro(sample1) #returns p-Val >0.33173635601997375 stats.shapiro(sample2) >0.021380668506026268 stats.shapiro(sample3) >0.8324998021125793
For sample2 we can not assume a normal distribution because the p-Value is smaller 0.05, thats why I decided to test for differences with the Kolmogorov-Smirnov Test where $H_0$ is that 2 independent samples are drawn from the same continuous distribution.
stats.ks_2samp(sample1, sample2) #returns p-Val >0.20898483057516717 stats.ks_2samp(sample1, sample3) >0.69740487802059081 stats.ks_2samp(sample2, sample3) >0.03614619076928504
My conclusion is that there is only a significant difference between sample2 and sample3.
- Is this statistically correct or are there any assumptions I missed?
- Is there maybe a better way to compare this data?
- Is there a statistical test for more than 2 groups where $H_0$ says that all groups are different?