Title: Row percentages
Course: UGQuants (SSPS) > Section: Associations Between 2 Variables

Row percentages

Table 3 represents the same data shown in tables 1 and 2, but here the data are shown as row percentages. This is indicated by the % sign at the beginning of the rows of data.

Table 3: Cigarette smoking in England by whether has university degree

(row percentage to the nearest 1%)

Currently smokes cigarettes? | Has a university degree? | All
Degree | No Degree
Smoker (%) | 15 | 85 | 1181
Non-Smoker (%) | 27 | 73 | 2350
Total | 23 | 77 | 3531

 Source: Health Survey for England, 2010

Row percentages show, for each value of the variable shown in the rows, the % of cases that fall into each category of the variable shown in the columns. So e.g. in table 3, the figure 86 indicates the percentage of smokers who do not have a degree. Notice how different this is from the figure of 37 in table 2, which was the percentage of people who do not have a degree who are smokers. These two phrases sound very similar and are easily confused, but their meanings are very different and so, therefore, are the figures that result. This is why it is so important that you do not confuse row and column percentages.

As with column percentages, we can think of row percentages as showing a separate frequency table of the independent variable for each value of the dependent variable. So we could understand table 3 as showing two frequency tables for whether someone has a degree: one for people who smoke and one for people who don’t. And, just as column percentages should always sum to 100% (or near 100%) when we add them up reading down the column, row percentages should sum to 100% (or near 100%) when reading across the row: e.g. in the row of table 3 showing the degree qualifications of non-smokers, 27+73=100

Presenting row rather than column percentages is not ‘wrong’ (provided the data are presented and interpreted correctly) and may be useful in certain circumstances, but there are key reasons why row percentages are often less informative than column percentages. These can be illustrated by looking at table 3 again:

86%

Of smokers don’t have a degree
73%

Of non-smokers don't have a degree
This is largely because a clear majority of all people in the table don't smoke This might give the

rather misleading impression that smoking behaviour does not differ all that much depending on whether or not

individuals have university degrees. In terms of the relative proportions they represent, the difference between

21% and 37% (the column percentages for smokers shown in table 2) is more marked than the difference between

73% and 86% and thus gives a better reflection of the association between two variables.

- This points us to the key reason why column percentages are usually better, at least where the likely independent variable is reasonably clear and, following convention, is presented in the columns. The reason is that our primary interest is always with the dependent variable and how its distribution varies depending on the values of other variables: in this example we are interested in how smoking varies according to level of education, which is what table 2 (using column percentages) shows us. Table 3 (using row percentages) largely turns this on its head and shows us how level of education varies according to smoking behaviour.