Tests:

Shapiro-Wilk test

• $H_0$: the population is normally distributed
  • p >= 0.05, accept,
    • The Shapiro-Wilk test showed no significant departure from normality, W(df) = stat = sig.
  • p < 0.05, reject
    • A Shapiro-Wilk test showed significant departure from normality, W(df) = stat = sig.

Skewness

Stats:

• p-value is evidence against the null hypot.
• A small p-value = data unlikely under null hypothesis.
• Reject the null hypothesis if p < 0.10.
• CI of 90% is used
  • The population is small and the sample does not include the entire population as participation was voluntary.

Normal distribution:

• http://www.maths-statistics-tutor.com/normality_test_pasw_spss.php
• Shapiro-Wilk test
  • The null-hypothesis of this test is that the population is normally distributed.

Skewness:

• https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3591587/
• Divide Skewness by Std. Error of Skewness
  • The null-hypothesis of this test is that there is no skew
  • If < 1.96, accept, otherwise reject
  • If < 1.645

Comparing Groups

Ordinal or Continuous

• Mann-Whitney U Test
  • Can be used if not normally distributed
  • different shape → you can only use the Mann-Whitney U test to compare mean ranks
  • same shape → you can use the Mann-Whitney U test to compare the medians