STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

EXERCISE: In a Canadian experiment to examine the claim that
the use of vitamin C helps to prevent the common cold, 818
volunteers were randomly divided into 2 groups (one of 411 and
the other of 407), and received a supply of either vitamin C
or placebo. The results are shown below:
TREATMENT
OUTCOME
placebo Vitamin C TOTALS
Has Colds 335 302 637
No Colds 76 105 181
TOTALS 411 407 818
Do these data suggest that getting a cold is independent of
whether or not the subjects received vitamin C?
Can the risk of a cold be reduced by using vitamin C?
vitamin C
Observed counts
response
determinant yes no total
placebo 335 76 411
vitamin C 302 105 407
total 637 181 818
Expected counts
response
determinant yes no total
placebo 320.1 90.9 411.0
vitamin C 316.9 90.1 407.0
total 637.0 181.0 818.0
Chi-squared decomposition
response
determinant yes no total
placebo 0.698 2.455 3.153
vitamin C 0.704 2.479 3.184
total 1.402 4.934 6.337
Test:
df
chisq
p-val
Indep 1 6.34 0.012
determinant response OR 95% CI
placebo /
vitamin C yes / no 1.53 1.10 2.14
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Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.