# INTERPRETING A FREQUENCY TABLE

## INTERPRETING A FREQUENCY TABLE

When you run a job with the FREQUENCIES command, you get back something called a frequency table . This is simply a table that tells you how frequently each of the responses occurs. Generally, the table will provide you with the file name , the variable, and the details of the frequency command, which include: value, actual frequency, percent, valid percent, cumulative percent, missing, and totals.

If you find codes in the frequency table that are not supposed to occur in the data, you need to go back and correct or at least check them.

## VALID PERCENTAGES

Sometimes you want to compute percentages using only cases with real responses. For example, suppose you have asked 100 people whether life is exciting or routine, and 25 said that it is exciting, 25 said that it is routine, and 50 told you to bug off. It would be a bit misleading, though it is correct, to state that 25% of those people think that life is exciting. A naive reader or listener would probably assume that the other 75% of the people find life unexciting. That is not really true, since the remaining 75% include people who declined to answer as well as those who find life routine. You can describe the results better by saying that half of the people who answered the question find life exciting, and half find life routine. You should also mention that half of the people in your sample refused to answer the question. You can find the percentages based only on cases with real answers (so-called valid cases ) in the column labeled VALID PERCENT in the frequency table.

## BAR CHARTS

Usually the frequency command has a column, labeled CUM PERCENT, which is also valuable . To transform your frequency table into a picture, you merely add a slash and the word BARCHART to your FREQUENCIES command.

When you execute this command, the computer produces a type of display that is called a bar chart because each line in the frequency table is turned into a bar. The length of the bar depends on the number of cases. (The actual frequency is given beside the bar.) At a glance, you can tell how often each of the responses was selected. You can also see whether one of the responses was an overwhelming favorite, and which responses are about equally likely.

Since computer screens and printers have a limited ability to show detail, responses that have similar frequencies may end up with bars of equal length even though the actual frequency counts are slightly different. This does not really matter. The point of a bar chart is to provide a visual summary of the data, and such minor distortions do not change the overall impression . If you want precision, look at the numbers , not the chart.

## CUMULATIVE PERCENTAGES

Yet another statistic presented as an output of the frequency command is the CUM PERCENT. The cumulative percentage for a response is the sum of the valid percentages for that response plus all responses that precede it in a frequency table.

## LEVELS OF MEASUREMENT

Depending upon the type of variable that you have used, the numbers in your data table may have different meanings.

### CATEGORIES

If you think about the numbers used to code some of variables in many experiments and surveys, you will realize that the particular number assigned to a category conveys no numerical information. The codes just represent the categories.

### ORDERED CATEGORIES

Sometimes the order of categories is significant. Think about the exciting-routine-dull variable. The responses to the question can be arranged in a meaningful order. If we arrange them in terms of decreasing excitement, then the response "Exciting" comes first, followed by the response "Routine," and finally the response "Dull." Of course, we could have arranged the responses in the other order as well (from low excitement to high excitement). In both instances, the response "Routine" falls between the other two. There is no order to those categories, but it does mean something that Routine is between Exciting and Dull.

### NUMBERS

Although the codes assigned to the exciting-routine-dull variable are ordered from high to low, they convey only order; they have no other numerical meaning. Someone who was bored with life (code 3) did not differ by two "excitement units" from someone who found life exciting (code 1). Subtracting or dividing the codes makes no sense.

On the other hand, let us say that "education" is one of the variables under study. This variable is different. The numerical code assigned to each category is not merely a code. It is the highest grade completed. It is an actual number, and we can treat it as such. For example, someone with 8 years of education has twice the number of years of education as someone with 4 years. Someone with 16 years of education has 4 more years than someone with 12 years . We can add, subtract, and divide the codes and understand the results.