00:01
Okay, so we want to test at a 5 % significance level if the mean commuting times of working -class people is the same as middle -class people is the same as higher -income people.
00:17
Against the alternative hypothesis that at least one of the means differs.
00:27
And we do this by doing an anova test.
00:29
So we're going to construct our anova table which is going to have the mean, the statistics between groups and the statistics within groups.
00:44
Now we need our degrees of freedom, we need our sum of squares for these guys, we need our mean square and then we can compute our s -statistic and our p -value.
01:02
Now remember that the sum of squares for between groups is given by adding up the size of each group times the mean of each group minus the overall mean squared.
01:23
And here we've got three groups, we'll call group 1 working -class, group 2 the middle -class and group 3 the upper -class.
01:38
And so you compute the means for each group, you compute the overall mean and you sum this up.
01:45
Similarly for the within group sum of squares, this time we're just doing for a particular group, we're doing each value in that group minus that group's mean.
01:58
So here in each group there are eight values, so j is running from 1 to 8.
02:07
And the mean square is given by the sum of squares for that group divided by degrees of freedom.
02:15
And the f -statistic is given by the mean square for between groups divided by the mean square for within groups.
02:24
If we compute all of that we find that between groups we have, the degrees of freedom is just one less than the number of groups...