I've spent hours trying to interpret my data but I can't figure out how to explain the results when both the main effect and the interaction are not significant.

I'm suppose to discuss my results, but I'm not sure how.

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    $\begingroup$ Is it ANOVA, regression, GLM..? What is your data? $\endgroup$ – Tim Dec 4 '14 at 9:28

It would help to know what kind of analysis you ran. How many explanatory variables do you have? Are they continuous, ordinal, or categorical? How about your response variable?

To answer your question in general:

No significant interaction generally that means you can correctly interpret the main effects (if there are any) in a consistent manner. We usually test for an interaction before paying attention to main effects because when explanatory variables interact, the coefficients of their main effects don't have a simple interpretation.

Lack of statistically significant main effects doesn't mean that your response variable is pure noise, it just means that you don't have evidence that your explanatory variables affected your response variable. The response variable could be noise, or it could depend on a variable you didn't measure, or it could depend on some/all of your explanatory variables - you just don't have evidence to prove it because your sample is too small or you are testing the wrong thing (e.g. simple linear regression doesn't model nonlinear relationships).

Judging by the fact that you spent hours trying to interpret a lack of significance, I'll bet there's more to the story. Did you fit a linear regression model with multiple predictors and get a significant F-statistic suggesting good model fit? If that's the case, your lack of significance for each individual explanatory variable is likely due to correlation between explanatory variables (multicollinearity). You can test for this by calculating the variance inflation factor.


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