采用SPSS进行Two-way ANOVA统计分析

Published with written permission from SPSS Inc, an IBM Company.

1. 

   Published with written permission from SPSS Inc, an IBM Company.

   You will see that "Edu_Level*Gender" has been added to the "Plots:" box.

2. Click the button. This will return you to the "Univariate" dialogue box.
3. Click the button. You will be presented with the "Univariate: Post Hoc Multiple Comparisons for Observed..." dialogue box as shown below:
   

   Published with written permission from SPSS Inc, an IBM Company.

   Transfer "Edu_Level" from the "Factor(s):" box to the "Post Hoc Tests for:" box. This will make the "Equal Variances Assumed" section become active (loose the "grey sheen") and present you with some choices for which post-hoc test to use. For this example, we are going to select "Tukey", which is a good, all-round post-hoc test.

   [You only need to transfer independent variables that have more than two levels into the "Post Hoc Tests for:" box. This is why we do not transfer "Gender".]

   You will finish up with the following screen:

   

   Published with written permission from SPSS Inc, an IBM Company.

   Click the button to return to the "Univariate" dialogue box.

1. Click the button. This will present you with the "Univariate: Options" dialogue box as shown below:
   

   Published with written permission from SPSS Inc, an IBM Company.

2. Transfer "Gender", "Edu_Level" and "Gender*Edu_Level" from the "Factor(s) and "Factor Interactions:" box into the "Display Means for:" box. In the "Display" section, tick the "Descriptive Statistics" and "Homogeneity tests" options. You will presented with the following screen:
   

   Published with written permission from SPSS Inc, an IBM Company.

   Click the button to return to the "Univariate" dialogue box.

3. Click the button to generate the output.

SPSS Output of Two-way ANOVA

SPSS produces many tables in its output from a two-way ANOVA and we are going to start with the "Descriptives" table as shown below:

Published with written permission from SPSS Inc, an IBM Company.

This table is very useful as it provides the mean and standard deviation for the groups that have been split by both independent variables. In addition, the table also provides "Total" rows, which allows means and standard deviations for groups only split by one independent variable or none at all to be known.

Levene's Test of Equality of Error Variances

The next table to look at is Levene's Test of Equality of Error Variances as shown below:

Published with written permission from SPSS Inc, an IBM Company.

From this table we can see that we have homogeneity of variances of the dependent variable across groups. We know this as the Sig. value is greater than 0.05, which is the level we set for alpha. If the Sig. value had been less than 0.05 then we would have concluded that the variance across groups was significantly different (unequal).

Tests of Between-Subjects Effects Table

This table shows the actual results of the two-way ANOVA as shown below:

Published with written permission from SPSS Inc, an IBM Company.

We are interested in the Gender, Edu_Level and Gender*Edu_Level rows of the table as highlighted above. These rows inform us of whether we have significant mean differences between our groups for our two independent variables, Gender and Edu_Level, and for their interaction, Gender*Edu_Level. We must first look at the Gender*Edu_Level interaction as this is the most important result we are after. We can see from the Sig. column that we have a statistically significant interaction at the P = .014 level. You may wish to report the results of Gender and Edu_Level as well. We can see from the above table that there was no significant difference in interest in politics between Gender (P = .207) but there were significant differences between educational levels (P < .0005).

Multiple Comparisons Table

This table shows the Tukey post-hoc test results for the different levels of education as shown below:

Published with written permission from SPSS Inc, an IBM Company.

We can see form the above table that there is some repetition of the results but, regardless of which row we choose to read from, we are interested in the differences between (1) School and College, (2) School and University, and (3) College and University. From the results we can see that there is a significant difference between all three different combinations of educational level (P < .0005).

Plot of the Results

The following plot is not of sufficient quality to present in your reports but provides a good graphical illustration of your results. In addition, we can get an idea of whether there is an interaction effect by inspecting whether the lines are parallel or not.

Published with written permission from SPSS Inc, an IBM Company.

From this plot we can see how our results from the previous table might make sense. Remember that if the lines are not parallel then there is the possibility of an interaction taking place.

Procedure for Simple Main Effects in SPSS

You can follow up the results of a significant interaction effect by running tests for simple main effects - that is, the mean difference in interest in politics between genders at each education level. SPSS does not allow you to do this using the graphical interface you will be familiar with, but requires you to use syntax. We explain how to do this below:

1. Click File > New > Syntax from the main menu as shown below:
   

   Published with written permission from SPSS Inc, an IBM Company.

2. You will be presented with the Syntax Editor as shown below: （在SPSS 16中界面不是这样的）
   

   Published with written permission from SPSS Inc, an IBM Company.

3. Type text into the syntax editor so that you end up with the following (the colours are automatically added):

   [Depending on the version of SPSS you are using you might have suggestion boxes appear when you type in SPSS-recognised commands, such as, UNIANOVA. If you are familiar with using this type of auto-prediction then please feel free to do so, but otherwise simply ignore the pop-up suggestions and keep typing normally.]（在SPSS 16中，你只管如下图右框显示输入命令，然后点击上面菜单中的Run－all，结果就输出了）

   

   Published with written permission from SPSS Inc, an IBM Company.

   Basically, all text you see above that is in CAPITALS, is required by SPSS and does not change when you enter your own data. Non-capitalised text represents your variables and will change when you use your own data. Breaking it all down, we have:

   UNIANOVA	Tells SPSS to use the Univariate Anova command
   Int_Politics BY Gender Edu_Level	Your dependent variable BY your two independent variables (with a space between them)
   /EMMEANS	Tells SPSS to calculate estimated marginal means
   TABLES(Gender*Edu_Level)	Generate statistics for the interaction term. Put your two independent variables here, separated by a * to denote an interaction
   COMPARE(Gender)	Tells SPSS to compare the interaction term between genders

4. Making sure that the cursor is at the end of row 2 in the syntax editor click the button, which will run the syntax you have typed. Your results should appear in the Output Viewer below the results you have already generated.

SPSS Output of Simple Main Effects

The table you are interested in is the Univariate Tests table:

Published with written permission from SPSS Inc, an IBM Company.

This table shows us whether there are statistical differences in mean political interest between gender for each educational level. We can see that there are no statistically significant mean differences between male and females' interest in politics when individuals are educated to school (P = .465) or college level (P = .793). However, when individuals are educated to University level, there are significant differences between males and females' interest in politics (P = .002).