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Activity 9.3
The goodness-of-fit test is also known as the:
(a) r ¥ c g 2
(b) One-variable g 2
(c) 2 ¥ 2 g 2
(d) None of the above
CHAPTER 9 Measures of association 271
9.2.3 Comparing observed frequencies with any set of expected
frequencies
Sometimes we want to compare our observed frequencies with a particular set of expected
frequencies. For instance, researchers have found that left-handed people are overrepresented
in people with Infl ammatory Bowel Disease (IBD). That is, the prevalence of left-handers is
higher than would be expected in that sample of people. Let’s assume that we tested 150
people with IBD and found the following:
Right-handed Left-handed
Observed 120 30
Expected under the null hypothesis 75 75
If you simply divided 150 by 2 in order to fi nd the expected frequencies under the null
hypothesis, you would end up with 75. It should be immediately apparent that we do not
expect there to be equal numbers of people who are right- and left-handed in the population,
because we know that there are far fewer left-handed people in the population than righthanders.
The real expected frequencies are the ones that we know from previous research
that exist in the population. There is also a sex difference in handedness – the prevalence of
left-handedness is greater in men than women. This means that men and women cannot be
included together in one group. Approximately 10% of women are left-handed.
We decided to see whether there was a greater prevalence of left-handedness in women
with Irritable Bowel Syndrome (IBS) rather than IBD. Three hunded and seventeen women
were given a questionnaire that included questions on handedness; 268 of them were righthanded,
and 49 were left-handed. As we expect 90% of women to be right-handed, then we
would expect 285.3 of our sample to be right-handed (90% of 317 = 285.3). This means that
we would expect 31.7 of them to be left-handed (317 - 285.3 = 31.7).
Right Left
n n
Observed 268 49
Expected 285.3 31.7
We actually found that only 268 were right-handed, representing 84.5% of the total of 317,
and 49 were left-handed, representing 15.5% of the total, rather than the 10% that we would
expect to fi nd.