## 6.11 Calculating Power and the Probability of a Type II Error (A One-Tailed Example)

An example of calculating power and the probability of a Type II error (beta), in the context of a one-tailed Z test for one mean. Much of the underlying logic holds for other types of tests as well.

## 6.12 Calculating Power and the Probability of a Type II Error (A Two-Tailed Example)

An example of calculating power and the probability of a Type II error (beta), in the context of a two-tailed Z test for one mean. Much of the underlying logic holds for other types of tests as well.

## 6.13 What Factors Affect the Power of a Z Test?

A look at what factors influence the power of a test. This discussion is in the setting of a one-sample Z test on the population mean, but the concepts hold for many other types of test as well. I discuss what factors affect power, and illustrate the concepts visually using various plots. There are no … Read more

## 6.14 Hypothesis Testing in 17 Seconds

An ultra-brief summary of hypothesis testing.

## 6.15 t Tests for One Mean: Introduction

An introduction to t tests for one population mean. I briefly discuss when we use the test, and when we would use a z test instead. I also briefly discuss the hypotheses of the test, and the p-value for different alternatives. I then work through an example. (If you are comfortable with the basics of … Read more

## 6.16 t Tests for One Mean: An Example

of a t test, then briefly investigate the influence of 3 outliers on the conclusions. The sleep misperception index data is simulated data with the same summary statistics as found in: Manconi et al. (2010). Measuring the error in sleep estimation in normal subjects and in patients with insomnia. Journal of Sleep Research, 19:478–486.

## 6.17 t Tests for One Mean: Investigating the Normality Assumption

A discussion of the assumptions of the t test on one mean. (The assumptions are the same as those of the t confidence intervals for one mean.) The assumptions are discussed, and the effect of different violations of the normality assumption is investigated through simulation.

## 6.18 Hypothesis tests on one mean: t or z?

I look at at what influences the choice of the t statistic or z statistic in one-sample hypothesis tests on the population mean mu, then work through an example of a t test. I compare the p-value of the t test to what we would have found had we (incorrectly) used a z test.

## 6.19 Using the t Table to Find the P-value in One-Sample t Tests

I work through examples of finding the p-value for a one-sample t test using the t table. (It’s impossible to find the exact p-value using the t table. Here I illustrate how to find the appropriate interval of values in which the p-value must lie.)

## 6.20 Finding Areas Under the t Distribution

Here I work through two examples of finding areas under the t distribution, using both R and the t table.