2.18 Tests for normality + the central limit theorem

Although a significant result was obtained for the Shapiro-Wilk test, we choose to perform a parametric t-test to compare the BMI between the groups of Walkability (see slides session 3 part III “Central limit theorem”).

t.test( BMI ~ Walkability, data=BEPAS)

Central limit theorem

• If sample sizes per subgroup are large, the central limit theorem can be applied:
  • The underlying distribution of a sample mean of an outcome variable, based on a sufficiently large sample, approximates a normal distribution, regardless of the underlying distribution of the outcome variable.
• “Large” sample sizes:
  • 30 or 40 per group when data are approximately normally distributed
  • Hundreds-> ignore the distribution
• Based on simulation studies: apply tests assuming normality (=parametric tests) only when the data are approximately normally distributed.
• Reference: “Normality Tests for Statistical Analysis: A Guide for Non-Statisticians” Asghar Ghasemi and Saleh Zahediasl, 2012 Reference¹.