Performing A Comparison of Means with SPSS

SPSS calculates an F-statistic (ANOVA) or an H-statistic (Kruskal-Wallis) with exact probability. In other words, you do not need to check a table to determine if a finding is significant.

Determine whether the data in the exercises meet the stringent assumptions of the comparison of means. For ANOVA, determine that the dependent variable has interval data and that the independent variable is nominal. Also, determine whether the data meet the assumption of homogeneity of variance. Check Brown's discussion carefully. Finally, you will need to determine whether the dependent data for each group are normally distributed.

Because the dependent data in the data files are not listed by groups, learn the following procedures to calculate descriptive statistics for each group.

Performing ANOVA
First create or open a data file in SPSS. Do the necessary descriptive statistics. To access individual groups in the dependent data, select that group of data using the independent variable. The following procedure selects the part of the dependent data that matches the equation. Verify this selection by moving through the data file itself.

  1. Click "Select Cases" in the "Data" menu to open the window
  2. Click "If condition is satisfied"
  3. Click on "Independent Variable"
  4. Select the relevant equation (e.g., "=0")
  5. Click "Ok"
  6. Click "Ok" (again)

Next, perform descriptive statistics on the selected data from the dependent variable. Repeat the procedure above to select other data on the dependent variable. Repeat descriptive statistics on this data. Repeat these steps for all of the individual groups defined by the independent variable. 

When you finish, click "Select Cases" and click "All Data."

One-way ANOVA
To perform one-way ANOVA 

  1. Select "Analyze" then "Compare Means"  then "One-Way ANOVA"
  2. Click on "Dependent Variable"
  3. Click on "Independent Variable"
  4. Click on "Post-Hoc" then "Scheffe" for more than two levels on the independent variable
  5. Click "Ok"
Two-way ANOVA
Note that no Scheffe can be performed on a two+-way ANOVA. To
perform two+-way ANOVA
  1. Select "Statistics" then "Analyze" then "General Linear Model" then "Univariate"
  2. Click on "Dependent Variable"
  3. Select each independent variable
  4. Click "Ok"
The result of calculating a one-way ANOVA (three levels) and a Scheffe test is shown below: 

                       - - - - -  O N E W A Y  - - - - - 

      Variable  TWO
   By Variable  ONE

                                  Analysis of Variance 

                               Sum of         Mean          F      F
        Source        D.F.    Squares       Squares       Ratio  Prob.

Between Groups          2   686960.1067   343480.0533    4.7115  .0119
Within Groups          72   5249007.280    72902.8789
Total                  74   5935967.387

This is the ANOVA table; F-ratio and P are on the right.

                                     Standard  Standard
Group  Count   Mean    Deviation     Error     95 Pct Conf   Int for Mean

Grp 0    25   1447.4800  264.2297    52.8459   1338.4113  TO  1556.5487
Grp 1    25   1273.8000  262.6573    52.5315   1165.3804  TO  1382.2196
Grp 2    25   1224.2800  282.6702    56.5340   1107.5995  TO  1340.9605

Total    75   1315.1867  283.2239    32.7039   1250.0228  TO  1380.3506
 

GROUP        MINIMUM     MAXIMUM

Grp 0       986.0000   2071.0000
Grp 1       885.0000   1906.0000
Grp 2       715.0000   1926.0000

TOTAL       715.0000   2071.0000
  

                       - - - - -  O N E W A Y  - - - - -
 

      Variable  TWO
   By Variable  ONE

Multiple Range Tests:  Scheffe test with significance level .05

The difference between two means is significant if
  MEAN(J)-MEAN(I)  >= 190.9226 * RANGE * SQRT(1/N(I) + 1/N(J))
  with the following value(s) for RANGE: 3.53

   (*) Indicates significant differences which are shown in the lower triangle

                          G G G
                          r r r
                          p p p

                          2 1 0
     Mean      ONE

  1224.2800    Grp 2
  1273.8000    Grp 1
  1447.4800    Grp 0      * 

The information above is from Scheffe. This one shows a significant difference only between groups "0" and "2".

Homogeneous Subsets (highest and lowest means are not significantly different)

Subset 1

Group       Grp 2         Grp 1

Mean     1224.2800     1273.8000
- - - - - - - - - - - - - - - - -

Subset 2

Group       Grp 1         Grp 0

Mean     1273.8000     1447.4800
- - - - - - - - - - - - - - - - -