I have data where I estimate regression coefficients/slopes for two groups (e.g. sex-specific regression coefficients) for a number of single effect regression models. I have used Bayesian methods which allow me to test, individually for each model, whether the regression coefficients of each group are significantly different (and they are generally not significant).
However, there seems to be a trend, that one group has consistently lower coefficients (nearer to zero) than the other.
Could I then use (/would it be appropriate to use) a paired t-test to see if the (absolute) value of the regression coefficients for one group is consistently lower than the other to test whether one group is more sensitive to explanatory variables?
E.g. (in R)
> a = data.frame("Coefficient" = c(1:10), "GroupA" = abs(rnorm(10,1,1)), "GroupB" = abs(rnorm(10,4,1)))
> a
Coefficient GroupA GroupB
1 1 1.2359143 4.528682
2 2 0.1260180 5.703323
3 3 1.1529601 5.998172
4 4 2.3689296 4.343029
5 5 1.8734228 4.245404
6 6 1.1287780 4.699337
7 7 1.8684325 3.829195
8 8 0.2723389 4.646488
9 9 3.1309934 4.158523
10 10 3.3550409 5.042786
> t.test(a[,2],a[,3],paired=TRUE)
Paired t-test
data: a[, 2] and a[, 3]
t = -6.4382, df = 9, p-value = 0.0001198
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.146265 -1.990157
sample estimates:
mean of the differences
-3.068211