# Insignificant interaction term - but only for low values of main effect - decline hypothesis?

I run a regression with multiple predictors. I am interested in relationship satisfaction (fictional example). I use gender and hours of time spent together (continuous) as predictors. In my hypothesis I assume that time spent together will have a positive effect on relationship satisfaction, but I assume that this effect differs by gender. So I add an interaction effect. Both main effects are significant and the interaction effect is not. I'm fine with that and normally I would decline my hypothesis. But through margins plots I saw that the insignificance only refers to a few lower values of my continuous variable. Higher values show significant differences by gender. What does that mean for my hypothesis testing? Is it just partially confirmed/declined?

Results are:

           Hazard Ratio   rob.SD   z-Score       p
gender          0.85       0.06     -2.36      0.018
time            1.19       0.02      9.08      0.000
gender*time     0.92       0.05     -1.45      0.147

• It mght be a case of lack of power. What are your results exactly?
– POC
Commented Apr 17, 2021 at 16:30
• @POC what results exactly do you wish to see? Commented Apr 17, 2021 at 17:12
• Regression estimates, standard errors, t-values and p-values, at the very least. It would help to help you.
– POC
Commented Apr 17, 2021 at 17:22
• @POC of course, i edited my question Commented Apr 17, 2021 at 17:24
• I should have asked for you $n$ also.
– POC
Commented Apr 17, 2021 at 17:32

## 2 Answers

This is not so surprising. Because you specify different slopes per gender, you will find big differences when you extrapolate. Here is an example

library(tidyverse)

set.seed(0)
d = tibble(
t = rnorm(25, 0, 1),
g = rbinom(25, 1, 0.5)
)

d$$y = 2*d$$t + d\$g + rnorm(25, 0, 2)

model = lm(y ~ t*g, data = d)

modelr::data_grid(d, t, g) %>%
modelr::add_predictions(model) %>%
ggplot(aes(t, pred, color = factor(g)))+
geom_line()



The true process has no interaction, but allowing the model to have an interaction results in large differences when extrapolating despite the failure to reject the null. Small differences taken in big quantities lead to big changes.

This is not to say an interaction does not exist. It may, and as POC has noted you may be under powered to detect it. However, large differences in predictions are completely consistent with the null being true.

• So saying that there is a significant difference by gender but only for higher values of time still won't allow me to reject the null hypothesis? If i mean center time, then I do get a significant interaction term and wouldn't have questioned that lower values might not be significant. Commented Apr 17, 2021 at 20:19

It is probably a lack of statistical power. A clue is the $$p=.147$$ not so far from the significance threshold.

You have to reject the hypothesis of an interaction. Your results suggest that there may be an interaction, but the effect size was smaller than expected and needed more power.