Chapter 10 - Inferences Concerning Two Population Means

What do we use the t-distribution to test?

Whether two population means differ from each other.

How does the degrees of freedom vary for t-statistic?

Depends on sample sizes and our assumption about the population variances.

High statistical power refers to the probability of…

a type II error.

What’s a robust t-test?

When a t-test’s characteristics of data depart from assumptions. Generally valid when sample sizes are large.

What do you use the Mann-Whitney U test for?

The nonparametric equivalent of the t-test for two independent samples.
Generally better when the assumptions of the t-test aren’t met.

What does the Mann-Whitney U test do?

Examines whether two samples could have been drawn from identical populations. Specifically, it tests whether two populations differ with respect to their medians.

What are the assumptions of the Mann Whitney U Test?

1. Random and independent samples are collected from each of the two populations.

2. The variable is either ordinal or measurement.

3. The two population distributions have the same shape and dispersion (spread).

The null hypothesis is rejected if the U-statistic is ______________________ the critical value.

greater than or equal to

What is the Wilcoxon rank sum test?

Calculates for “W” and reports an exact p-value. Uses ranks and should generate a similar p-value as the Mann-Whitney U test.

What is the power of the test?

The chance of rejecting the null hypothesis when it is indeed false and is equivcalent to 1 - B (one minus the type II error rate).

What is Power influenced by?

1. Choice of statistical test

2. Choice of alpha

3. The minimum detectable difference we wish to discriminate

4. Sample Size

5. Variance