# Chapter 1. One-way ANOVA

## Introduction

Statistical Applets

Move the group means by dragging the black dots with the mouse. Increase or decrease the spread within the groups by dragging the slider at the top. Change the sample size n with the slider on the left. Watch the P-value change on the scale at the bottom as you perform all these manipulations. The value of the F statistic appears in red under the P-value scale. Click NEW SAMPLES to generate a new set of sample data.

Click the "Quiz Me" button to complete the activity.

The F statistic for one-way ANOVA—and its P-value—depend both on the group means (black dots in this applet) and the spread (standard deviation) and number (n) of observations within each group (colored dots). This applet allows you to see how varying the means, standard deviation, and sample size affects the F statistic and resulting P-value for an ANOVA.

### Question 1.1

If the sample size is increased while the standard deviation and means of the samples are held relatively constant, the value of f generally 2+YpLAlBfLjjeAM+EdW71RKJy3IMk7CF and the value of p Z1sFeNjn21dFR6hgV/I0OLPyd1RYjxmk.

2
Try again.
Incorrect. See above for the correct answers.
Great job.

### Question 1.2

If sample size and sample means are held constant and the standard deviation of the samples is raised, the value of fZ1sFeNjn21dFR6hgV/I0OLPyd1RYjxmk and the value of p 2+YpLAlBfLjjeAM+EdW71RKJy3IMk7CF.

2
Try again.
Incorrect. See above for the correct answers.
Great job.

### Question 1.3

Click and drag the sample means so that the means of all three samples are approximately 5.0. Now, keeping sample size and standard deviation constant, drag the center up to 10.0. As this sample mean increases, the value of f generally 2+YpLAlBfLjjeAM+EdW71RKJy3IMk7CF and the value of p Z1sFeNjn21dFR6hgV/I0OLPyd1RYjxmk.

2
Try again.
Incorrect. See above for the correct answers.
Great job.

### Question 1.4

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
Generally speaking, the means and standard deviations for the samples in an experiment are determined by the nature of the conditions involved, but the experimenter often has some level of control over the size of the samples. The larger the sample size, the greater the chances of demonstrating a statistically significant result.