Why do assumptions matter in regard to inferential stats with non-normal distributions?

We assume there is a normal distribution, so any estimate of the p value is wrong.

What is skewness a measure of?

The symmetry of a distribution.

What is Kurtosis a measure of?

The “peakedness.”

What is the third moment about the mean?

Skewness.

What is the fourth moment about the mean?

Kurtosis.

What inferential test of normality is appropriate for large sample sizes (2000+)?

Jarque-Bera test.

What inferential test of normality is appropriate for small sample sizes?

Kolmorogov-Smirnoff test.

What does the one sample case of Kolmorogov-Smirnov compare?

The sample distribution against H0/the normal distribution.

What does the two sample case of Kolmorogov-Smirnov compare?

Two distributions and whether they come from the same population.

Give one strength of the one sample case of Kolmogorov-Smirnov.

It is good for checking normality: calculate sample mean and SD and compare to normal distribution.

What does Shapiro-Wilk examine?

The ratio of two estimates of variance: usually best estimator and corrected SS.

What is a quantile?

A regular interval of a distribution.

Describe a Q-Q plot for 2 data sets with equal n.

Use n quantiles, order values, and plot like a scatter plot.

Describe a Q-Q plot for comparing with a normal distribution.

Use n quantiles, estimate sample mean and variance and plot days against the inverse of the cumulative for each quantile.

What does Levene’s test examine?

Absolute differences from the mean.

What characterises the SQRT(X) transform?

Removes linear mean-variance and skew-positive nature.

What characterises the In(X) transform?

Removes mean-SD relationship and strongly reduced skew-positive nature.

What characterises the 1/X transform?

It it the most extreme and causes the strongest reduction in skew-positive nature.