ayahhanda

Lesson 4:

Analysis of Variance for One-Independent Variable Designs

Purpose

This lesson describes how to compute the analysis of variance for between-subjects designs that contain only one independent variable. This analysis is used to determine if two or more group means differ significantly. In the case of two-group designs, it yields the same probability level as the T-Test procedure. An F ratio is the statistic that is calculated and a significant F indicates that at least two-group means differ.

An Example: Preparation Courses and Scholastic Aptitude Test (SAT) Performance

As an educational researcher, assume that you conducted an experiment to test whether preparation courses (independent variable) affect Scholastic Aptitude Test (SAT) performance (dependent variable). Specifically, 5 high school juniors (normally, you would use many more students but we are using only 5 for purposes of demonstration) were randomly assigned to each of three study conditions:

1. 0 hours of coursework preparation.
2. 20 hours of coursework preparation
3. 40 hours of coursework preparation

After all the coursework was completed, all 15 students were given the SAT and their scores on the verbal and math sections are listed below.

Student	Study Group (hours)	Verbal SAT Score	Math SAT Score
1	0	350	500
2	0	480	520
3	0	395	450
4	0	440	510
5	0	385	470
6	20	500	560
7	20	490	540
8	20	560	580
9	20	495	590
10	20	495	550
11	40	550	610
12	40	590	630
13	40	580	620
14	40	550	590
15	40	620	580

You should now create a data file that represents these data. Remember that you need to put each participant's data on one line and that you need to create a variable for the study group. You might create a data file that looks like the one below. You will also need to create a numeric code for your independent variable. In this case, we can assign 1 to 0 hours of coursework, 2 to 20 hours of coursework, and 3 to 40 hours of coursework.

Variable View File for the SAT Experiment

Data File for the SAT Experiment

Performing the Analysis

There are several ways to compute the analysis of variance with SPSS. We will use a procedure called One-Way ANOVA.

Step 1. Click on Analyze, then Compare Means, then One-Way ANOVA.

Step 2. Move the dependent measure that you wish to analyze into the Dependent List field. Let's analyze the data for the verbal SAT and math SAT, so move both "verbsat" and "mathsat" into the field. Next, you should move the independent variable into the Factor field. In our case, this is the "studygrp" variable. Now click on Options and select Descriptive statistics. When you have done this, click Continue and then on OK.

Step 3. You may also want to compute a total SAT score (using the Transform and Compute menu) and then perform an analysis of variance on this total score.

Examining the Output

You will notice that SPSS provides you with several types of information in the output for the analysis of variance.

ANOVA Output

1. First, you are presented with the F statistic for each analysis that you requested. In this case, you requested one analysis of variance for the verbal SAT measure and one for the math SAT measure. If your F is large and your significance level is low (usually less than .05 or .01), then you can conclude that your results were not due to chance. In this case, course preparation had a significant influence on verbal SAT scores, F (2, 12) = 24.90, p < .05. Note that another name for the Mean Square Within Groups is the mean square of the Error Term.
2. Because we asked for descriptive statisics, the mean and number of valid participants in each condition is presented.

Creating Tables for Your Data

If you want SPSS to list descriptive information about your groups in tabular form, you can do this through the Tables command. Assume that we would like to have the mean, standard deviation, and standard error of the mean for verbal scores for each of our three groups.

Step 1. Click on Analyze, then Custom Tables, then Basic Tables.

Step 2. Move the dependent variable measure ("verbsat") into the Summaries field.

Step 3. Move the independent variable ("studygrp") into the Subgroups Down field.

Step 4. Click on Statistics and Add the statistics that you would like to see. For this example, calculate the mean, standard deviation, and standard error of the mean (S. E. Mean), and any other statistics that you would like to see.

Step 5. Click on Continue and then OK. The statistics should then appear in a table like the one shown below. Note that the value labels appear in your output (that is, if you specify the value label when entering the variables of data).

Showing a Table

Creating a Simple Bar Graph

Data are often best communicated in a visual form. SPSS has a variety of graphs that you can use to display your data. You can make a simple bar graph of your data from this experiment by following the steps listed below.

Step 1. Click on Graphs, then Bar.

Step 2. In the Bar Charts menu, click on Simple and then Define.

Step 3. In the Define Simple Bar menu, first select Other summary function (this enables you to plot the means of your groups) and then select your dependent variable measure ("verbsat") and move it into the Variable field. The default will be to compute the mean for that variable, but you can modify this (to select the median, mode, or other summary statistics) by clicking Change Summary. Given that we wish to calculate the mean, we will leave it as is.

Step 4. Now move the independent variable ("studygrp") into the Category Axis field.

Step 5. If you wish to create a title for your figure, click on Titles, and type a title.

Step 6. When you are ready, click on OK, and compare your figure with the one below.

Initial Figure

Step 7. SPSS uses default options in creating your graph and you can modify it by double clicking on your graph. This will access the SPSS Chart Editor. In the graph below, you can see that the title does not fit with the default font size. Also, you may want to change the font, size, and location of the X- and Y-axis labels. With a bit of editing, you can get it to look like the one below.

Modified Figure

Step 8. You should note that when you are in the SPSS Chart Editor, you can save the settings that you created in your graph by clicking on File and then Save Chart Template. Doing this will save your preferences for the various graph options (e.g., font size, centering vs. left or right justification of labels) and will enable you to apply these to future graphs.