# Interpretation of result in reference group

If I am looking at sports data of a whole league over a year:

Dependent Variable = Goals Scored

Independent Variables:
X1 = Traditional Home Uniforms
X2 = Retro Home Uniforms
X3 = Secondary Home Uniforms

Controls:
A whole bunch


My objective is to see what the effect of different uniforms are on the number of goals scored. More specifically, the effect of Retro versus Secondary Uniforms.

When I run an OLS I get these results:

Model 1: X1 = Reference Group
X2 = -15.9 (p = 0.01)
X3 = -7.6 (p = 0.01)

Model 2: X3 = Reference Group
X1 = 7.6 (p = 0.01)
X2 = -6.2 (p = 0.34)


Is it correct to say (from Model 1) that compared to Traditional Uniforms that wearing Retro Uniforms is better for a team than Secondary Uniforms, ceteris paribus. It would be even better if it came through in Model 2 because that is a direct comparison of Retro Uniforms versus Secondary Uniforms. All models use the same controls.

My questions: 1) Is it correct to say what I am saying? 2) Why are the results 'better' for what I am saying when I use Model 1 over Model 2?

• Can you clarify -- the lines like "X2 = 3.2" are the regression coefficients? It isn't clear at the moment, and one would expect model 1's X3 coefficient to be the opposite sign, same magnitude value as the Model 2 X1 coefficient (i.e. if it is 1 for model 1, then should be -1 in model 2), ceteris paribus (thanks for the Latin tag lesson!) with respect to the choice of reference groups in your covariates... Jan 29, 2013 at 3:50
• @JamesStanley I fixed the typo. The questions still stand
– LF12
Jan 29, 2013 at 4:34
• The coefficients still don't make sense--they are inconsistent between Models 1 and 2. Are you perhaps including interactions with the $X_i$ in the models? How exactly are you encoding the groups?
– whuber
Jan 29, 2013 at 6:59
• @whuber I had to fix my example again. I misread the output twice, I am new to quantitative analysis, sorry! Does it now make more sense? The variables are coded using if statements and a mixture of various things being true. The model does not use any explicit interactions. There is no overlap between the variables: X1 + X2 + X3 = N
– LF12
Jan 29, 2013 at 7:32

## 1 Answer

You are on the right track and I congratulate you on continuing your development of skills in the area.

However, model 1 - as reported here - does not allow you to say anthing in comparing X2 to X3. Both comparisons are only to X1. If you knew the error structure of all the estimates you could convert this to an estimate of the difference between X2 and X3 but this would be a lot of bother and Model 2 does it for you.

As you intuit, Model 1 does not really address your research question, if you want to compare X2 to X3. Model 2 does a better job. It seems to suggest a lack of evidence that X2 has an effect compared to X3 (ie high p value).

My guess is that "traditional" uniforms (whatever this means) are better than either retro or secondary, but your data does not show a difference between retro and secondary.

There are doubtless ways the analysis can be improved, of course.