Crosstabs

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A table showing the relationship between two questions in a survey is called a crosstab.

Reading crosstabs

The following table is a crosstab of age by whether or not somebody has a listed phone number.

AgeByUnlisted.png

This table shows the number of observations with each combination of the two questions in each cell of the table. The numbers of observations are often referred to as the counts. We can see, for example, that 185 people are aged 18 to 34 and do not have an unlisted phone number.

Column percentages

Column percentages are shown on the table above. These percentages are computed by dividing the counts for an individual cell by the total number of counts for the column. A column percent shows the proportion of people in each row from among those in the column. For example, 24% of all people without an unlisted phone number are aged 18 to 34 in the sample (i.e., 185 / 779 = 24%) and thus we can say that based on this sample we estimate that 24% of people with an unlisted phone number are aged 18 to 24.

Row percentages

Row percentages are computed by dividing the count for a cell by the total sample size for that row. A row percent shows the proportion of people in a column category from among those in the row. For example, as 185 people are aged 18 to 34 in the No column and there are a total 275 people aged 18 to 34 the row percentage is 67% (i.e., 185 / 275) and thus we can say that based on this sample we estimate that 67% of people aged 18 to 34 have an unlisted phone number.

Working out whether the table shows row or column percentages

Some crosstabs do not clearly label whether percentages are row and column percentages (e.g., the example below). When reading a table, the easiest way to check if it is showing row or column percentages is to check to see which direction the numbers add up to 100%. In the table above, the percentages add up to 100% in each column and, furthermore, this is indicated on the table by the NET, and thus it shows column percentages.

Checking to see if the percentages add up to 100% only works where the categories in the rows (or columns) are mutually exclusive. Where the data is from a multiple response question it is more difficult, as the percentages will add up to more than 100% (as people can be in more than one category). An example is shown in the table below, which shows two different types of column percentages:

  • The percentage of people to have selected each option(% Valid Cases).
  • The percentage of options selected (% Total Mentions).

(See Counted Values and Missing Values in Multiple Response Questions for a more detailed discussion of how to interpret such tables).

In the crosstab below the percentages do not add up to 100% in either direction and there is nothing in the way the table is labelled to make it clear whether the table is showing row or column percentages.

MarketSightCrosstab.PNG

In most cases when a percentage is shown on a crosstab it is a column percentage. This table shows column percentages. Where the trick of adding up the percentages does not work, as in this example, there are a few ways we can deduce whether a particular set of numbers is row or column percentages.

  • The position of the sample sizes on a table. By convention, if the sample sizes appear at the top of the table then column percentages are being shown and if the sample sizes appear in a column then the row percentages are shown. In the example above the sample sizes are shown at the top, suggesting that the two percentages shown are different variants of column percentages.
  • The position of the % signs on a table. By convention, if % symbol only appears at the top of each column in a table then column percentages are being shown and if the % symbol appears at the beginning of each row then row percentages are shown.
  • The degree of variation in the totals of percentages. For example, in the table below we can see that the percentages vary quite a lot within each column, but within each row they are reasonably similar, which indicates that the table shows column percentages (similarly, if the variability was greater in the rows this would indicate that row percentages were shown).

Other statistics

Most commonly crosstabs show and percentages. However, where the variables are not categorical, then other statistics such as averages, meadians and correlations are shown in the cells of a crosstab.