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Paired proportions have traditionally been compared using McNemar's test but an exact alternative due to Liddell (1983) is preferable. Two proportions are paired (as opposed to independent) if they share a common feature that affects the outcome. For example, when comparing two laboratory methods to detect bacteria in samples of blood, if blood from the same sample is put into both methods, this is the "pairing". Matched samples can also occur when individuals are given two different treatments, asked two different questions, or measured in the same way at two different points in time. Liddel exact test is a special case of the sign test. The b count in the table below is treated as a binomial variable from the sample b+c. Using the ratio R' (R' = b/c) as a point estimate of relative risk, a two sided probability is calculated that R' = 1 (the null hypothesis). Confidence limits for R' are also calculated.
| + | - | |
| + | a | b |
| - | c | d |
Examples:
Two alternative commercials have been shown to sample of consumers, so that each participant has seen both. Test compares number of cases in which consumer liked one commercial and disliked the other one. Test decides whether one commercial is more appealing than the other.
An experiment was conducted to study the effect of a risk factor on 73 individuals with a certain disease. Of the 73 individuals, 37 were exposed to the risk factor. For each of the 73 individuals, a control individual was found that matched the diseased individual according to several demographic variables such as sex, age, etc. The question being asked is whether the incidence of the disease changes with exposure to the risk factor.