# Does a huge difference in the number of observations in a dummy variable influence its regression result?

I'm currently working on my thesis where I performed a multiple linear regression. The analysis is basically about the impact of projects. Among other independent variables I have the dummy variable team composition which is divided into functional(0) and cross-functional(1).

Independent Variable                       N
---------------------------------------------
....
Team composition                          77
Functional teams (0)                 70
Cross-Functional teams (1)            7


As can be seen the number of observations (N) is quite different between those two. From the regression analysis it turned out that the team composition is not statistically significant which was contrary to what I actually expected.

Now I'm trying to figure out what could be the reasoning behind such a result. My question is on whether the huge difference in the number of observations between functional and cross-functional could be one of the influencing factors for the missing statistical significance in the regression analysis??

thx

It's not the difference that's the problem, it's the small number in the smaller group. If you had 700 and 70, then much smaller effect sizes would be significant. If you had 38 and 38, smaller effect sizes. I tried this

set.seed(38483810)
IV1 <- c(rep('A', 7), rep('B', 70))
IV2 <- c(rep('A', 38), rep('B', 38))
IV3 <- c(rep('A', 70), rep('B', 700))

DV1 <- c(rnorm(7, 0, 2), rnorm(70, 1, 2))
DV2 <- c(rnorm(38, 0, 2), rnorm(38, 1, 2))
DV3 <- c(rnorm(70, 0, 2), rnorm(700, 1, 2))

lm1 <- lm(DV1~IV1)
lm2 <- lm(DV2~IV2)
lm3 <- lm(DV3~IV3)


lm1 shows p = .47, lm2 p = .04, lm3 p = .001