Chapter 6 – FrequenciesTHIS CHAPTER deals with frequencies, graphical representation of frequencies (bar charts and pie charts), histograms, and percentiles. Each of these procedures is described below. Frequencies is one of the SPSS commands in which it is possible to access certain graphs directly (specifically, bar charts, pie charts, and histograms) rather than accessing them through the Graphs command. More information about editing these graphs is treated in some detail in Chapter 5. Bar charts or pie charts are typically used to show the number of cases (“frequencies”) in different categories. As such they clearly belong in a chapter on frequencies. Inclusion of histograms and percentiles seems a bit odd because they are most often used with a continuous distribution of values and are rarely used with categorical data. They are included here because the Frequencies command in SPSS is configured in such a way that, in addition to frequency information, you can also access histograms for continuous variables, certain descriptive information, and percentiles. The Descriptives command and descriptive statistics are described in Chapter 7; however, that procedure does not allow access to histograms or percentiles.6.1 FrequenciesFrequencies is one of the simplest yet one of the most useful of all SPSS procedures. The Frequencies command simply sums the number of instances within a particular category: There were 56 males and 37 females. There were 16 Whites, 7 Blacks, 14 Hispanics, 19 Asians, and 5 others. There were 13 A’s, 29 B’s, 37 C’s, 7 D’s, and 3 F’s. Using the Frequencies command, SPSS will list the following information: value labels, the value code (the number associated with each level of a variable, e.g., female = 1, male = 2), the frequency, the percent of total for each value, the valid percent (percent after missing values are excluded), and the cumulative percent. These are each illustrated and described in the Output section.6.2 Bar ChartsThe Bar chart(s) option is used to create a visual display of frequency information. A bar chart should be used only for categorical (not continuous) data. The gender, ethnicity, and grade variables listed in the previous paragraph represent categorical data. Each of these variables divides the data set into distinct categories such as male, female; A, B, C, D, F; and others. These variables can be appropriately displayed in a bar chart. Continuous data contain a series of numbers or values such as scores on the final exam, total points, finishing times in a road race, weight in pounds of individuals in your class, and so forth. Continuous variables are typically represented graphically with histograms, our next topic.6.3 HistogramsFor continuous data, the Histograms option will create the appropriate visual display. A histogram is used to indicate frequencies of a range of values. A histogram is used when the number of instances of a variable is too large to want to list all of them. A good example is the breakdown of the final point totals in a class of students. Since it would be too cumbersome to list all scores on a graph, it is more practical to list the number of subjects within a range of values, such as how many students scored between 60 and 69 points, between 70 and 79 points, and so forth.6.4 PercentilesThe Percentile Values option will compute any desired percentiles for continuous data. Percentiles are used to indicate what percent of a distribution lies below (and above) a particular value. For instance if a score of 111 was at the 75th percentile, this would mean that 75% of values are lower than 111 and 25% of values are higher than 111. Percentiles are used extensively in educational and psychological measurement.The file we use to illustrate frequencies, bar charts, histograms, and percentiles (pie charts are so intuitive we do not present them here) is the example described in the first chapter. The file is called grades.sav and has an N = 105. This analysis computes frequencies, bar charts, histograms, and percentiles utilizing the gender, ethnic, grade, and total variables.6.5 Step by StepTo access the initial SPSS screen from the Windows display, perform the following sequence of steps:Mac users: To access the initial SPSS screen, successively click the following icons:After clicking the SPSS program icon, Screen 1 appears on the monitor. Step 2 Create and name a data file or edit (if necessary) an already existing file (see Chapter 3) Screens 1 and 2 (displayed on the inside front cover) allow you to access the data file used in conducting the analysis of interest. The following sequence accesses the grades.sav file for further analyses:Whether first entering SPSS or returning from earlier operations the standard menu of commands across the top is required. As long as it is visible you may perform any analyses. It is not necessary for the data window to be visible.After completion of Step 3 a screen with the desired menu bar appears. When you click a command (from the menu bar), a series of options will appear (usually) below the selected command. With each new set of options, click the desired item. The sequence to access frequencies begins at any screen with the menu of commands visible:6.5.1 FrequenciesA screen now appears (below) that allows you to select variables for which you wish to compute frequencies. The procedure involves clicking the desired variable name in the box to the left and then pasting it into the Variables(s) (or “active”) box to the right by clicking the right arrow () in the middle of the screen. If the desired variable is not visible, use the scroll bar arrows ( ) to bring it to view. To deselect a variable (to move it from the Variable(s) box back to the original list), click on the variable in the active box and the in the center will become a . Click on the left arrow to move the variable back. To clear all variables from the Variable(s) box, click the Reset button.Screen 6.1 The Frequencies windowThe following sequence of steps will allow you to compute frequencies for the variables ethnic, gender, and grade.You have now selected the three variables associated with gender, ethnicity, and grades. By clicking the OK button, SPSS proceeds to compute frequencies. After a few moments the output will be displayed on the screen. The Output screen will appear every time an analysis is conducted (labeled Screen 6.2), and appears on the following page.The results are now located in a window with the title Output# [Document#] – IBM SPSS Statistics Viewer at the top. To view the results, make use of the up and down arrows on the scroll bar ( ). Partial results from the procedure described above are found in the Output section. More complete information about output screens, editing output, and pivot charts are included in Chapter 2 (pages 17–22, 34–39 for Mac users). If you wish to conduct further analyses with the same data set, the starting point is again Screen 6.1. Perform whichever of Steps 1–4 (usually Step 4 is all that is necessary) are needed to arrive at this screen.Screen 6.2 SPSS Output Viewer6.5.2 Bar ChartsTo create bar charts of categorical data, the process is identical to sequence Step 5 (in previous page), except that instead of clicking the final OK, you will click the Charts option (see Screen 6.1). At this point a new screen (Screen 6.3, below) appears: Bar charts, Pie charts, and Histograms are the types of charts offered. For categorical data you will usually choose Bar charts. You may choose Frequencies (the number of instances within each category) or Percentages (the percent of total for each category). After you click Continue, the Charts box disappears leaving Screen 6.1. A click on OK completes the procedure.Screen 6.3 The Frequencies: Charts windowScreen 6.1 is the starting point for this procedure. Notice that we demonstrated a double click of the variable name to paste it into the active box (rather than a click on the button).After a few moments of processing time (several hours if you are working on a typical university network) the output screen will emerge. A total of three bar charts have been created, one describing the ethnic breakdown, another describing the gender breakdown, and a third dealing with grades. To see these three graphs simply requires scrolling down the output page until you arrive at the desired graph. If you wish to edit the graphs for enhanced clarity, double click on the graph and then turn to Chapter 5 to assist you with a number of editing options. The chart that follows (Screen 6.4) shows the bar chart for ethnicity.Screen 6.4 A Sample Bar Chart6.5.3 HistogramsHistograms may be accessed in the same way as bar charts. The distinction between bar charts and histograms is that histograms are typically used for display of continuous (not categorical) data. For the variables used above (gender, ethnicity, and grades), histograms would not be appropriate. We will here make use of a histogram to display the distribution for the total points earned by students in the class. Perform the following sequence of steps to create a histogram for total. Refer, if necessary, to Screens 6.1, 6.2, and 6.3 on previous pages for visual reference. The histogram for this procedure is displayed in the Output section.This procedure begins at Screen 6.1. Perform whichever of Steps 1–4 (pages 102–103) are necessary to arrive at this screen. You may also need to click the Reset button before beginning.Note the step where you click Display frequency tables to deselect that option. For categorical data, you will always keep this option since it constitutes the entire non-graphical output. For continuous data (the total variable in this case), a display of frequencies would be a list about 70 items, indicating that 1 subject scored 45, 2 subjects scored 47, and so on up to the number of subjects who scored 125. This is rarely desired. If you click this option prior to requesting a histogram, a warning will flash indicating that there will be no output. The Show normal curve on histogram allows a normal curve to be superimposed over the histogram.6.5.4 Percentiles and DescriptivesDescriptive statistics are explained in detail in Chapter 7. Using the Frequencies command, under the Statistics option (see Screen 6.1), descriptive statistics and percentile values are available. When you click on the Statistics option, a new screen appears (Screen 6.5, below) that allows access to this additional information. Three different step sequences (on the following page) will explain (a) how to create a histogram and access descriptive data, (b) how to calculate a series of percentiles with equal spacing between each value, and (c) how to access specific numeric percentiles. All three sequences will utilize the total points variable.Screen 6.5 The Frequencies: Statistics WindowFor any of the three procedures below, the starting point is Screen 6.1. Perform whichever of Steps 1–4 (pages 102–103) are necessary to arrive at this screen. Step 5c gives steps to create a histogram for total points and also requests the mean of the distribution, the standard deviation, the skewness, and the kurtosis. Click the Reset button before beginning if necessary.To calculate percentiles of the total variable for every 5th percentile value (e.g., 5th, 10th, 15th, etc.) it’s necessary to divide the percentile scale into 20 equal parts. Click Reset if necessary.Note that when you type the 20 (or any number) it automatically writes over the default value of 10, already showing.Finally, to designate particular percentile values (in this case, 2, 16, 50, 84, 98) perform the following sequence of steps. Click Reset if necessary.Note: Quartile values (the 25th, 50th, and 75th percentiles) may be obtained quickly by clicking the Quartiles box (see Screen 6.5), clicking Continue, and then clicking OK (see Screen 6.1).6.6 Printing ResultsResults of the analysis (or analyses) that have just been conducted require a window that displays the standard commands (File Edit Data Transform Analyze …) across the top. A typical print procedure is shown below beginning with the standard output screen (Screen 1, inside back cover).To print results, from the Output screen perform the following sequence of steps:To exit you may begin from any screen that shows the File command at the top.Note: After clicking Exit, there will frequently be small windows that appear asking if you wish to save or change anything. Simply click each appropriate response.6.7 OutputFrequencies, Histograms, Descriptives, and PercentilesIn the output, due to space constraints, we often present results of analyses in a more space-conserving format than is typically done by SPSS. We use identical terminology as that used in the SPSS output and hope that minor formatting differences do not detract from understanding.6.7.1 FrequenciesWhat follows is partial results (and a slightly different format) from sequence Step 5, page 103.The number of subjects in each category is self-explanatory. Definitions of other terms follow: Term Definition/Description Value label Names for levels of a variable. Value The number associated with each level of the variable (just in front of each label). Frequency Number of data points for a variable or level. Percent The percent for each component part, including missing values. If there were missing values, they would be listed in the last row as missing along with the frequency and percent of missing values. The total would still sum to 100.0%. Valid percent Percent of each value excluding missing values. Cum percent Cumulative percentage of the Valid percent. 6.7.2 HistogramsWhat follows is output from sequence Step 5b on page 106. To produce an identical graph you will need to perform the edits described on pages 96–97.Note that on the horizontal axis (graph below) the border values of each of the bars are indicated. This makes for clear interpretation since it is easy to identify that, for instance, 11 students scored between 90 and 95 points, 20 students scored between 95 and 100 points, and 8 students scored between 100 and 105 points. The graph has been edited to create the 5-point increments for bars. For creation of an identical graph several of the editing options would need to be applied. Please see Chapter 5 to assist you with this. A normal curve is superimposed on the graph due to selecting the Show normal curve on histogram option.6.7.3 Descriptives and PercentilesWhat follows is complete output (slightly different format) from sequence Step 5d on page 107.DescriptivesPercentilesFor Percentiles: For the total points variable, 5% of values fall below 70 points and 95% of values are higher than 70 points; 10% of values fall below 79.6 points and 90% are higher, and so forth.Descriptive information is covered in Chapter 7 so we will not discuss those terms here. Note that when the skewness and kurtosis are requested, the standard errors of those two measures are also included.ExercisesAnswers to selected exercises can be downloaded at www.spss-step-by-step.net.Notice that data files other than the grades.sav file are being used here. Please refer to the Data Files section starting on page 364 to acquire all necessary information about these files and the meaning of the variables. As a reminder, all data files are downloadable from the web address shown above. Using the divorce.sav file display frequencies for sex, ethnic, and status. Print output to show frequencies for all three; edit output so it fits on one page. On a second page, include three bar graphs of these data and provide labels to clarify what each one means. Using the graduate.sav file display frequencies for motive, stable, and hostile. Print output to show frequencies for all three; edit output so it fits on one page. Note: This type of procedure is typically done to check for accuracy of data. Motivation (motive), emotional stability (stable), and hostility (hostile) are scored on 1- to 9-point scales. You are checking to see if you have, by mistake, entered any 0s or 99s. Using the helping3.sav file compute percentiles for thelplnz (time helping, measured in z scores) and tqualitz (quality of help measured in z scores). Use percentile values 2, 16, 50, 84, 98. Print output and circle values associated with percentiles for thelplnz; box percentile values for tqualitz. Edit output so it fits on one page. Using the helping3.sav file compute percentiles for age. Compute every 10th percentile (10, 20, 30, etc.). Edit (if necessary) to fit on one page. Using the graduate.sav file display frequencies for gpa, areagpa, and grequant. Compute quartiles for these three variables. Edit (if necessary) to fit on one page. Using the grades.sav file create a histogram for final. Include the normal curve option. Create a title for the graph that makes clear what is being measured. Perform the edits on pages 96–97 so the borders for each bar are clear.George, Darren. IBM SPSS Statistics 23 Step by Step, 14th Edition. Routledge, 20160322. VitalBook file.The citation provided is a guideline. Please check each citation for accuracy before use.