Statistical analysis

Numbers resulting from a piece of research seldom provide much meaning by themselves. Using percentages can facilitate our understanding. A figure of 300 pairs of shoes means little, if anything, completely on its own. However, if we ask 'What is the 300 pairs of shoes a part of?', it begins to assume some meaning if we are told that out of 1000 sales of shoes over the past month, 30% have been bought within the last three days. It means even more if we know that this 30% is responding to a special promotional offer that was introduced three days ago.

There are pitfalls in the use of percentages, however. Just because they are an easy-to-understand form of quantifying data does not make them the universal solution to all problems. Percentages from different groups of people should not be averaged unless they are weighted.

AVERAGING PERCENTAGES SHOULD ALWAYS INVOLVE WEIGHTING

The percentage of car owners for three age groups is shown below. We want to determine the percentage of car owners in the first two groups to arrive at a figure showing usage among those aged 18 to 49. Averaging the two percentages gives a figure of 28.4%.

Percentage of car owners among three age groups

18-29 30-49 50 and over

Total interviews Car owners

100.0% 100.0% 100.0% 22.0% 34.8% 65.4%

Average of 18-49

28.4%

However, if a third column is added to show the total for the combined 18-49 group, as shown below, when the two age groups are combined in terms of their real weights in the study, the resultant correct car-ownership figure for the 18-49 group turns out to be 29.1%. While the difference from the average percentage may not appear all that great, the two figures might be of rather different marketing significance in terms of the particular problem. And the difference between an averaged percentage and a weighted one might be far greater.

Number and percentage of car owners among two age groups

18-29

30-49

18-49

No.

%

No.

%

No.

%

Total interviews

200

100.0

250

100.0

450

100.0

Car owners

44

22.0

87

34.8

131

29.1

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