At this point you might be wondering what to do if you want to run a
goodness-of-fit test but your null hypothesis is not that all categories are
equally likely. For instance, let's suppose that someone had made the
theoretical prediction that people should choose red cards $60\%$ of the time,
and black cards $40\%$ of the time (I've no idea why you'd predict that), but
had no other preferences. If that were the case, the null hypothesis would be to
expect $30\%$ of the choices to be hearts, $30\%$ to be diamonds, $20\%$ to be
spades and $20\%$ to be clubs. In other words we would expect hearts and
diamonds to appear 1.5 times more often than spades and clubs (the ratio $30\%$ :
$20\%$ is the same as 1.5 : 1). The expected counts are now shown in
@tbl-tab10-7.
