Hi there.
I have a problem with my research.
I conducted a two-way ANOVA analysis (2x2).
There is no interaction effect of the two independent variables on the dependent one (p=0.062), but the pairwise comparisons return a statistically significant difference.
So the question is the following:
How could I interpret this result?
- The main effect of 1st independent variable is significant
- The main effect of 2nd independent variable is significant
- Interaction effect of 1st and 2dr independent variables is NOT significant
-pairwise comparisons show statistically significant differences in at least one of the two independent variables.
Your results show that:
- The Industrial - Academic difference (133.375) is statistically significantly different from 0 for 2D instructions (p = .003)
- The Industrial - Academic difference (19.562) is not statistically significantly different from 0 for AR instructions (p = .643)
- The difference in those differences (133.375 - 19.562) is not statistically significantly different from 0 (p = .062)
You appear to expect that because the first simple effect is statistically significant and the second simple effect is not statistically significant, then the difference between the two simple effects must be statistically significant. But there is no such requirement, as your output shows. Whether the difference in differences is significant is a completely different question, and it is addressed by the interaction term.
HTH.
Thanks you Bruce for your answer, but I dont understand something yet.
From the first table, it Is possible to confirm that both skill levels of users and instruction approaches significantly impact on the completion time. These are the main effects. Then, we can see at the interaction effect that doesn't reveal any statistically significant difference (p = 0.062).
As a consequence, I expect that there are no significant differences in pairwise comparisons section. This because there Is no interaction effect.
The question is:
When there is no significant interaction effect but there are differences in pairwise section, how can I interpret this result? There Is a relationship between interaction effect and pairwise comparisons values?
As Bruce Weaver pointed out, these are different questions. Your results show, that a) there is a significant difference between academic and industrial within 2D instructions and b) no significant difference between academic and industrial within AR instructions and c) that these differences do not differ from each other (i.e. the interaction)
Although this might seem paradoxical, you have no evidence that these two comparisons differ from each other. But it is not, since they measure different things. The simple effect tests, if every comparison is different from zero. But the interaction tests, if the difference between these comparisons is different from zero (i.e. the difference of differences), which is something else. To get a grasp, look at the confidence intervals. For the first comparison it is [-217; -48], which is clearly below zero, therefore significant. The second one ist [-104, 65], which clearly includes zero, hence non significant. The interaction now tests, if these two differences are different from each other, but you can see a larger overlab of the two confidence intervals, i.e. a large overlap of compatible values from each comparison. The second CI's lower bound is -104, whereas the first one's upper bound is -48. So, all values from -104 till -48 are compatible with both CI's, although one overlaps zero, where the other one does not. Therefore, both plausible values of each difference are quite compatible with each other, although one is not compatible with zero itself, whereas the other is.
Sounds paradoxical, but it isnt!!!
E. Marino, the attached syntax file shows that the tests for the main effects of A and B and the test for the AxB interaction from a 2x2 ANOVA can also be obtained via one-way ANOVA with appropriate contrasts. You might find it instructive. The web page it refers to is no longer active, so I have attached the data file too. HTH.
PS- You'll have to modify the FILE HANDLE command on line 14 to indicate where you stored the data file on your computer.
Dear Marino
I hope the following link will be useful for your question.
https://www.researchgate.net/publication/377387674_Procedure_for_Analysis_of_Variance_and_Multiple_Comparisons_for_Full_Factorial_Experiment_Using_SPSS_Software
Good Luck
- Badges
- Science topic
- Similar topics
- Philosophy
- Esthetics
- Interpretation