Introduction to Summary Statistics

A summary statistic refers to a formula used to summarize data. For example, the mean, standard deviation, and variance are all summary statistics.

Counts

The table below shows counts. It tells us that, for example:

• 134 males and 166 females are in the data, of a total sample size of 300.
• 20 males said I would definitely buy it.

Column percentages

Counts are the simplest summary statistic shown on tables. Although they contain a lot of information, they are often not a good way of presenting data.

In survey research, as an example, a much better presentation of the table above is to instead show column percentages, as shown below.

For example, look at the middle row of counts, which shows I am not sure whether I would buy it or not. This number is higher for females than for males (47 versus 40). But, there are more females in the study, making such a direct comparison meaningless. By contrast, when we look at the column percentages (shown in the table above), we can more meaningfully perform the comparison.

Column percentages mean that the sub-groups we wish to compare are in the columns. There are a number of ways that we can deduce that the table above is showing the column percentage statistic:

• Most tables created by professions will show column percentages. Outside of Japan, this is a pretty good rule to rely on. Yes, some other statistics are used, but column percentages are most common.
• The table explicitly labels the percentages as column %, in the top-left corner.
• The percentages in each column add up to 100%. We can deduce this by adding them up, or, by looking at the NET.

While column percentages are the most common percentages used in crosstabs, with the table above we could also calculate:

• Row percentages. In the I would definitely not buy it row, we have 38 for Male and 33 for Female. So, the row percentages for this row of the table are 38/71 = 54%, 48%, and 100%.
• Total percentages. For example, 38 people in the study are Male and said they would definitely buy, and this equates to 38 / 300 = 13%.

Tables with multiple statistics

Although survey researchers typically focus on column percentages, there are situations where other statistics can be useful For this reason, some researchers use tables with multiple statistics shown in each cell of the table, as is shown below.