Dear all,
I am running a two way ANOVA with two dependent variables (domestic/cross-border (dummy variable) and industry (five categories)) on one dependent variable (performance, measured on a contiunous scale). In my test of between subjects I have found that both domestic (alpha=0.1) and industry (alpha=0.01)are signifcant and that an interaction effect between them exist. When I go to the pairwise comparison to check what the mean difference for domestic/cross-border are, they are insignificant with a p-value of 0.161. How is this possible since the there is an effect for domestic/cross-border. Can it be caused by the significance level for the between subject test for domestic/cross-border since it is only significant at an alpha of 0.1?
Thanks in advance!
Can you provide more details of what you did? Particularly
1) are domestic/cross-border and industry really between-subjects variables?
2) What software did you use to run the test?
3) What specific commands did you use (i.e., what R code, what SPSS buttons or syntax, etc.)?
As far as I know, if there was a significant F-test for a main effect of a two-level variable, then the corresponding t-test comparing the means of that level (across all levels of the other variable) should also be significant. But maybe that's not what was actually run---for example, i don't know about SPSS, but in R things are dummy-coded by default, so what looks like the "main effect" of domestic/cross-border might actually just be the simple effect of domestic/cross-border at the baseline level of industry. This situation (significant F-test with no significant pairwise comparisons) can also happen in factors with more than two levels, when the F-test is not corrected for multiple comparisons but the pairwise comparisons are (see e.g. http://stats.stackexchange.com/questions/16665/how-can-i-get-a-significant-overall-anova-but-no-significant-pairwise-difference); however, it sounds like you are having this issue in a two-level factor, so I don't think this is the issue.
Dear Stephen,
Here is additional information
1. I'm not sure if I understood this question correctly, but all observations are within the industry group and as well in the domestic/crossborder group.
2. I have used SPSS to run the test
3. I used the univariate test, where I used performance as the dependent variable and multiple independent variables, such as industry and domestic/cross-border, but also underperformance/outperformance, equal size/unequal size and those independent variables are all dummy variables except for industry. In options I wanted to display the descriptive statistics, estimates of size effect and the homogeneity tests. For all independent variables I requested the 'display means' and to compare the main effects. I did this as well for the interaction effect between industry and all other independent variables.
The ANOVA compares the variation of the system response, caused by the investigated factor with the overall variation. In case there is an additional source of variation, e.g. random scatter, the p-value of the factor will become smaller. You might want to check, how much of the total variation can be explained by the factors you deliberately changed.
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