The One-Way ANOVA applet lets you see how the F statistic and the P -value depend on the variability of the data within groups, the sample size, and...

One-Way ANOVAapplet FP

http://digitalfirst.bfwpub.com/stats_applet/stats_applet_1_anova.html

The black dots are at the means of the three groups. Move these up and down until you get a configuration that gives a P-value of about 0.01. What is the value of the F statistic?

Now increase the variation within the groups by sliding the standard deviation bar to the right. Describe what happens to the F statistic and the P-value.

Using between- and within-group variation, explain why the F statistic and P-value change in this way.