In SPSS, the Frequencies procedure can produce summary measures for categorical variables in the form of frequency tables, bar charts, or pie charts. Show To run the Frequencies procedure, click Analyze > Descriptive Statistics > Frequencies. A Variable(s): The variables to produce Frequencies output for. To include a variable for analysis, double-click on its name to move it to the Variables box. Moving several variables to this box will create several frequency tables at once. B Statistics: Opens the Frequencies: Statistics window, which contains various descriptive statistics. The vast majority of the descriptive statistics available in the Frequencies: Statistics window are never appropriate for nominal variables, and are rarely appropriate for ordinal variables in most situations. There are two exceptions to this:
C Charts: Opens the Frequencies: Charts window, which contains various graphical options. Options include bar charts, pie charts, and histograms. For categorical variables, bar charts and pie charts are appropriate. Histograms should only be used for continuous variables; they should not be used for ordinal variables, and should never be used with nominal variables.
Note that the options in the Chart Values area apply only to bar charts and pie charts. In particular, these options affect whether the labeling for the pie slices or the y-axis of the bar chart uses counts or percentages. This setting will greyed out if Histograms is selected. D Format: Opens the Frequencies: Format window, which contains options for how to sort and organize the table output. The Order by options affect only categorical variables:
When working with two or more categorical variables, the Multiple Variables options only affects the order of the output. If Compare variables is selected, then the frequency tables for all of the variables will appear first, and all of the graphs for the variables will appear after. If Organize output by variables is selected, then the frequency table and graph for the first variable will appear together; then the frequency table and graph for the second variable will appear together; etc. E Display frequency tables: When checked, frequency tables will be printed. (This box is checked by default.) If this check box is not checked, no frequency tables will be produced, and the only output will come from supplementary options from Statistics or Charts. For categorical variables, you will usually want to leave this box checked.
By the end of this section, you will be able to...
For a quick overview of this section, watch this short video summary:
Let's suppose you give a survey concerning favorite color, and the data you collect looks something like the table below.
Clearly, we need a better way to summarize the data. The most obvious thing to do would be to make a table with the list of favorite colors and the frequency for each.
Officially, we call this a frequency distribution. A frequency distribution lists each category of data and the number of occurrences for each category. Sometimes, we really want to know the frequency of a particular category in reference to the total. We can do this just by finding the total, and dividing the frequency for each category by that total.
The relative frequency is the proportion (or percent) of observations within a category and is found using the formula
A relative frequency distribution lists each category of data together with the relative frequency of each category.
TechnologyHere's a quick overview of how to create frequency and relative frequency tables in StatCrunch.
Organizing Discrete Data into TablesIf you recall from Section 1.2, A discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of values. (Countable means that the values result from counting - 0, 1, 2, 3, ...) Since we can list all the possible values (that's essentially what countable means), one way to make a table is just to list the values along with their corresponding frequency. Example 1
Here's some data I collected from a previous students Mth120 course. It refers to the number of children in their family (including themselves).
An easy way to compile the data would then be to make a frequency or relative frequency table as we did before.
Sometimes, however, we have too many values to make a row for each one. In that case, we'll need to group several values together. Example 2
A good example might be the scores on an exam, ranging from 1-100. Here are some data from a past Mth120 class.
In this case, we'll have to set up intervals of numbers called classes. Each class has a lower class limit and an upper class limit, along with a class width. The class width is the difference between successive lower class limits. To be consistent, the class width should be same for each class. One good option might look something like this: Organizing Continuous Data into TablesOrganizing continuous data is similar to organizing multi-valued discrete data. We have to form classes which don't overlap. I usually try to design a class width that's either logical (i.e. 10 points for grades above) or so that I have 5-8 classes when complete. Example 3
For this example, let's consider the average commute for each of the 50 states. The data below show the average daily commute of a random sample of 15 states.
Do you know why this is a continuous random variable and not discrete? (Hint: It's not because of the decimal.) I think I know!
This is continuous because the variable we're measuring - time - is not finite. When, say, a marketing agent measures her commute time, she actually rounds to the nearest minute. If she reports 32 minutes, it's not exactly 32 minutes, it's 32 minute to the nearest minute. In reality, it might be 32.15323623245134... (you get the idea). To make a frequency or relative frequency for continuous data, we use the same strategy we'd use for multi-valued discrete data.
Once we have these tables, we'll need to learn how to create some charts to display the information, which is what the next few page are about. TechnologyHere's a quick overview of how to create frequency and relative frequency tables for quantitative data in StatCrunch.
Cumulative TablesCumulative tables are just what they imply - they show the sum of values up to and including that particular category. As with regular tables, we can have both cumulative frequency and relative frequency. Example 4
To illustrate the idea, let's look at the average commute data from the last section.
Technology
|