Extra Exercise 17
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(a) Increasing the within-group sample size makes the F-statistic larger and hence the
P-value smaller. The opposite effect is seen when decreasing the sample
size. We always see this type of impact of sample size: the larger the
sample, the more significant our (comparable) results become, because
they become less likely to have occurred by chance.

(b) A P-value of 0.0498 was obtained for F=3.81. The F-table of PSLS/IPS gives 
the 95%-percentile of F(2,12) as 3.89. Note that we have 3-1=2 DF for the
numerator and 3*(5-1)=12 DF for the denominator. It appears that the
applet actually calculates its P-value from the wrong distribution; the
values shown appear to correspond to F(2,13), which is incorrect for the
situation described.

(c) When moving one group away from the others, the between-group variation 
increases. This is because the between-group variation is computed from the 
group means as the sum of squared deviations from the overall mean. As the 
numerator of the F-statistic is a constant times this between-group variation, 
the F-statistic increases and eventually becomes significant when the groups 
get far apart. Intuitively, the larger group differences, the more indicative the
data are of group (population) means being unequal.

(d) When increasing the variation within the groups the F-statistic
decreases and the P-value increases. Mathematically, the F-statistic is
computed as a ratio with the estimated within-group variation in the 
denominator; thus it is no surprise that F decreases when the
within-group variation increases. Intuitively, the more variation in the data
(within the groups), the more difficult it should be to detect
differences between groups. Note that the between-group variation
is constant because the group means are unchanged. The F-test is one-tailed 
and the P-value includes only larger values, therefore a smaller value 
of F also implies a larger P-value.