Chapter 1. One-way ANOVA
Introduction
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.
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.
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 and the value of p .
2.
If sample size and sample means are held constant and the standard deviation of the samples is raised, the value of f and the value of p .
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 and the value of p .
4.
Suppose you are planning an experiment involving three conditions. Which of the three parameters illustrated in this applet—sample means, sample standard deviation, and sample size—do you think you would have the most control over as an experimenter? What should you do, if possible, to give yourself the best chance of demonstrating a statistically significant result?