# High t-val for one explanatory variable, while the other has a significant coefficient. How to interpret???

I have question with some results I'm working with.

Model: avg_score = β0 + β1(nonwhite) + β2(hhold_avginc) + u

For some background, I'm seeing if average income and race influence state standardized test scores. And I got the results displayed in the attached tables. There are two different tables for each test type (math and language arts). Also should point out that in the tables, subgroupid stands for the explanatory variable 'nonwhite'.

So, my understanding is that in both cases, hold_avginc shows insignificant coefficients, but has high t-values. So it shows that the error terms are correlated with the independent variables. Right? So should I go ahead a do a two-stage least squares regression analysis? But I guess since the nonwhite variable is significant, I'm not completely sure if that's what I should do.

Initially I was going to just point out the significance I found in the nonwhite variable, but that was before I noticed the high t-values.

Thank you in advance. I really just need guidance in what comes next...and how.

• You got the interpretation of the p-value mixed up: a small p-value corresponds to significant, while a large p-value to nonsignificant. So income has a significant effect, while white is not significant. It is also impossible to reach different conclusions when looking at the t-value and the p-value; one is fully determined by the other. So when you draw different conclusions, you know you have made a mistake. Commented May 1, 2018 at 6:16
• thank you for responding. So my understanding is that the opposite is true from what i initially said: hold_avginc is significant while subgroupid is not, correct? I think I might be a little confused by your last statement of drawing different conclusions. Could you elaborate? Commented May 1, 2018 at 6:23
• Yes, you had things backwards. Commented May 1, 2018 at 10:47
• If you know the t-valu and the degrees of freedom, than you can look the p-value up in a table (typically there is one at the end of any introductory statistics book). So there is a one to one relationship between the t-value and the p-value. So any conclusion based on the t-value must be the same as the conclusion based on the corresponding p-value. They contain the exact same information. Commented May 1, 2018 at 10:55
• I am unable to understand your subgroupid . How do you code - non whites and whites ? Are you working on categorical variable + a continuos multicategory variable(household income). which regression model did you implement for the results. Moreover, please state your specific hypotheses - 1, 2, 3 etc. Regression analysis does not always and in all situations give you valid results.
– user10619
Commented May 1, 2018 at 12:31

• The p-value for subgroupid is high because it's confidence interval covers zero. Please note your individual t statistic measures if each coefficient against zero.
• hold_avginc is significant because it's standard error is much lower than the other predictor. Thus, there's sufficient evidence that the true coefficient is not zero.

I suspect your variables might not be on the similar scale. You have a variable that is over 2000 in coefficient.

• Oh alright that makes sense. Thank you. Not too sure what you mean when you say that the variables are not on a similar scale. If by that you mean that they are completely different measures then, yes. Subgroupid is meant to represent non-white ethnicities, while hold_avginc is average household income levels. Commented May 1, 2018 at 6:07
• Also, sorry to add on to this...but if you were trying to present this data, do you think further analysis needs to be made? For example, 2SLS or something like that? Sorry my questions are basic. I'm relatively new to stats. Commented May 1, 2018 at 6:09
• @sandral What analysis do you want to present? Commented May 1, 2018 at 6:13
• So my research paper is trying to examine if the causal variables of non-white ethnicity and household income impact average test scores. I am using data from a county, and looking at the average test scores in each district, and also using average income levels for each district. Ultimately, to see if there is evidence of inequality in education bc these variables influence the test scores they get. If that makes sense. I am just not too sure if the results I got from this regression will be enough evidence to support it . Commented May 1, 2018 at 6:18