# Interaction between binary and continuous variable in OLS

#### monzur

##### New Member
I am trying to examine the association between maternal education and child school test scores using the following equation.

TestScore = β0 + β1 EduYrMom+ β2 FemaleChild+ β3 EduYrMom * FemaleChild + εij

where TestScores is the test score of the child, EduYrMom is the years of education of the child’s mother, FemaleChild is a binary value which equals 1 if the child is a girl. The following regression coefficients are obtained using Stata’s regress command.

HTML:
Model 1 Test scores of child

(1a)Years of education of mother    0.028
(1b)Years of education of motherXfemale child   0.031
Effect of mother's education on female children---- (1a+ 1b)    0.059*

Model 2

(2a)Years of education of mother    0.039**
(2b)Years of education of mother *female child  -0.005
Effect of mother's education on female children---- (2a+ 2b)    0.034

Model 3
(3a)Years of education of mother    0.303***
(3b)Years of education of mother *female child  -0.047
Effect of mother's education on female children---- (3a+ 3b)    0.256**

note:  *** p<0.01, ** p<0.05, * p<0.1
For model 1, it seems that mother’s education is positively and significantly associated with test scores of female children, but not for boys. For model 2, I find that mother’s education is significantly associated with test scores of boys only. For model 3, mother’s education is significantly and positively associated with the test scores of both boys and girls.

I was wondering whether my interpretations are correct. I am also not sure how to interpret B3, the coefficient of the interaction term, which is insignificant for all the 3 models. I look forward to your suggestions.

Monzur

#### maartenbuis

##### TS Contributor
The fact that your interaction terms are insignificant means that you cannot reject the hypothesis that effect of mother's education is the same for boys and girls. This is a common finding, girls nowadays do better at school, but the effect of social background tends to be similar for boys and girls, see e.g. M.L. Buis (2013) "The composition of family background: The influence of the economic and cultural resources of both parents on the offspring’s educational attainment in the Netherlands between 1939 and 1991", European Sociological Review, 29(3), pp. 593-602. http://maartenbuis.nl/publications/fam_backgr.html

The fact that in some models the effect of mother's background is significant for boys but not for girls does not mean that the effects of mother's education is different between boys and girls. The test whether or not the interaction effects are 0 is the test for that hypothesis. See: Andrew Gelman and Hal Stern (2006) "The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant", The American Statistician, 602(4): 328--331. http://www.stat.columbia.edu/~gelman/research/published/signif4.pdf

#### monzur

##### New Member
The fact that your interaction terms are insignificant means that you cannot reject the hypothesis that effect of mother's education is the same for boys and girls. This is a common finding, girls nowadays do better at school, but the effect of social background tends to be similar for boys and girls, see e.g. M.L. Buis (2013) "The composition of family background: The influence of the economic and cultural resources of both parents on the offspring’s educational attainment in the Netherlands between 1939 and 1991", European Sociological Review, 29(3), pp. 593-602. http://maartenbuis.nl/publications/fam_backgr.html

The fact that in some models the effect of mother's background is significant for boys but not for girls does not mean that the effects of mother's education is different between boys and girls. The test whether or not the interaction effects are 0 is the test for that hypothesis. See: Andrew Gelman and Hal Stern (2006) "The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant", The American Statistician, 602(4): 328--331. http://www.stat.columbia.edu/~gelman/research/published/signif4.pdf
Thank you very much. I am still a little confused though. If the insignificance of the interaction term means that we cannot reject the null hypothesis that the effect of maternal education is the same for both boys and girls, what would be a good way to interpret the results of model 1, for example? Do we say that although mother’s education is positively and significantly associated with test scores of female children we cannot reject the null that maternal education affects boys and girls in the same way? Or for model 3, would we say that maternal education is positively and significantly associated with both male and female tests scores, but we cannot reject the null (as mentioned before)?

#### maartenbuis

##### TS Contributor
That is correct. Though I typically just interpret the model without interaction effects when the interaction effects are not significant.