Martin your query is a common one. Analysing percentages in a 2x2
contingency table is used in initial exploratory work. The %
difference across rows is used to gain insight into a possible
relationship between variables. The use of percentages helps clarify
the figures.
In confirmatory analysis the chi-squared test is used to determine
formally if any relationship is due to chance or not i.e.
statistically significant. The test uses actual counts. Using
percentages or any other method of transformation is incorrect.
Look what happens to the figures when they are percentaged across
rows.
Original figures (% scores)
total
19 (50%) 19 (50%) 38 (100%)
22 (58%) 16 (42%) 38 (100%)
total 41 35
The relationship between the figures within each row is maintained.
19 is 50% of 38.
22 is 58% of 38
16 is 42% of 38
However, the relationship between the figures in each column has been
lost.
19 is not 50% of 41
22 is not 58% of 41
19 is not 50% of 35
16 is not 42% of 35.
The chi-square is computed using row totals and column totals and if
these are not derived from the original data then the test will give
a misleading result.
Hope this helps
Denis Martin
Dept Physiotherapy
Queen Margaret College
Edinburgh
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