# Joint Significance of Interaction Term in LPM / OLS

In an OLS model with binary dependent variable (linear probability model) I have (among others) two independent binary variables (ß1 and b2) which interact with each other (ß1 * ß2).

y = ß0 + ß1x1 + ß2x2 + ß3(x1*x2) + e


As results results I get:

ß1 = 0.06 *** (St.Dev.: 0.007)
ß3 = -0.04 *** (St.Dev: 0.008)


If both x1 and x2 become TRUE, then I'd calculate ß1+ß3. In this case this would mean: 0,06 - 0,04 = 0,02.

How can I know, that 0,02 is significantly different to 0?

• This is a linear hypothesis and can be tested by standard methods, see for example here: sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/… - however the test is not valid (actually no test is) if you only decide after seeing results that you'd like to test this. Dec 3, 2020 at 17:21
• Thanks, that helps! However, could you please explain the second part of your answer on validity and decisions?
– pzfn
Dec 3, 2020 at 17:29
• The theory behind tests assumes that the data are generated from the null hypothesis, and under this assumption can guarantee that you only reject it falsely in 5% of cases (or whatever the test level is) in which the test is run with the null hypothesis true. This however does no longer hold if you decide whether to run a test based on already seeing in the data something that suggests that the H0 looks good or bad; in the former case you will hardly ever reject, in the latter almost always, and the theory behind the 5% is violated. Dec 3, 2020 at 20:54
• You may find this interesting: stat.columbia.edu/~gelman/research/published/ForkingPaths.pdf Dec 3, 2020 at 20:54
• Coincidentally somebody else asked this more or less directly, and I responded in more detail: stats.stackexchange.com/questions/499226/… Dec 3, 2020 at 21:24