Question

The One-Way ANOVA applet displays the observations in three groups, with the group means highlighted by black dots. When you open or reset the applet, the scale at the bottom of the display shows the ANOVA F statistic and P-value for these groups. (The P-value is marked by a red dot that moves along the scale.)

Use the mouse to slide the Standard Deviation at the top of the display to the right (to increase it). You see that the group means do not change, but the spread of the observations in each group increases.
What happens to F and P as the spread among the observations in each group increases?
O The value of F decreases while the p-value decreases.
O The value of F increases while the P-value increases.
O The value of F decreases while the P-value increases.
O The value of F increases while the P-value decreases

Answer 1

As the spread among the observations in each group increases, the value of F increases while the P-value decreases. The correct answer is C.

Step-by-step explanation:

When the spread among the observations in each group increases, the value of F increases while the P-value decreases. The F statistic measures the ratio of the variation in the group means to the variation within the groups. As the spread increases, the numerator of the F statistic becomes larger and the denominator remains the same, resulting in a larger F value and a smaller p-value.

Increasing the spread among observations in each group in a One-Way ANOVA applet leads to a decrease in the F statistic and an increase in the p-value.

When using the One-Way ANOVA applet and increasing the standard deviation, which indicates an increase in the spread among the observations within each group, we expect certain changes to the F and P values. The F statistic is the ratio of the variation between group means to the variation within the groups. If the spread within groups increases without changing the group means, the denominator of the F ratio increases, which should, in turn, decrease the F statistic.

Because the F distribution is always right-skewed and a high F corresponds to a low p-value (inverse relationship), an increase in within-group variation leading to a decrease in the F statistic should result in an increase in the p-value. Therefore, as the spread among observations in each group increases, the correct conclusion is that the value of F decreases while the p-value increases.