Are data consistent with a normal distribution? (Shapiro-Wilkes test)

Use the simulation to demonstrate that p-values have the same distributions for other types of hypothesis test, so their interpretation (in terms of evidence against H0) is the same.

You don't need to know the details behind the test to interpret its p-value

Simulation

The page uses the Shapiro-Wilkes W test whose null hypothesis is that the data are sampled from a normal distribution. (The alternative is that the distn is non-normal.)

In the simulation, take several samples to build up the distribution of p-values when the population distribution is normal. Observe that all values between 0 and 1 are equally likely. (Click on any p-value to see the corresponding sample.)

All values between 0 and 1 are equally likely when the popn is normal.

Discuss the fact that p-values below 0.05 still occur by chance with prob 0.05, etc.

Drag the slider to make the population distn skew and repeat. Observe that the p-values are more likely to be near zero.

Data

Select PSA measurements from the pop-up menu. This applies the test to a real data set and interprets the resulting p-value.

The data are measurements of serum acid phosphatase (PSA) for 53 patients who were diagnosed as having prostate cancer.