I am having a hard time interpreting what something means in a paper I'm trying to get through. If you care, this is the paper: Gender Differences in the Effect of Education on the Slope of Experience-EarningsProfiles: National Longitudinal Surveyof Youth,1979-1988. By KEVINC. DUNCAN*
In one of the tables of the regressions, it explains that a little "a" (next to the coefficient) means the coefficient is significantly different at the .05 level from the comparable coefficient for white males.
What exactly does this mean?
Here is my understanding: If there are 2 correlations with sample sizes n’s, they are each changed into z values. Under the null hypothesis that the population correlations are equal, the following has a standard normal distribution (one equation using both z’s). If the z is great than or equal to 1.96 or less than or equal to -1.96, the two correlations are significantly different at the .05 level of significance. If the z is not significant at the .05 level, sampling error is a possible explanation for the difference. If the two are significantly different, the null hypothesis is rejected! There must be fairy large sample sizes used. Coefficients with p value of .05 or less would be judged to be statistically different.
Is this correct? Can you explain it a little more if I'm wrong.
Here is a link to the paper? http://www.jstor.org/stable/3487620?seq=3#page_thumbnails_tab_contents