Inference II

Hypothesis Testing Picture

Parametric vs Nonparametric Inference

Parametric inference relies on assumptions about the population distribution, and hypotheses are on the distribution parameters

• Statistically powerful

• Appropriate when data are normally distributed or the sample is large enough

Parametric vs Nonparametric Inference

Nonparametric inference does not rely on assumptions about the population distribution, and hypotheses are more general

• Less powerful, but more flexible

• Useful when the sample size is small

Comparing the methods of inference

General procedure for statistical tests

1. Decide on appropriate test based on the type of data and assumptions of the potential tests
2. Calculate the observed statistic
3. Calculate the test statistic
4. Compare the test statistic to some threshold to generate a p-value (threshold will depend on parametric vs. non-parametric)
5. Draw conclusion based on p-value