Interpreting what this means in a paper - significantly different at the .05 level?

Question

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

Also which coefficients would you consider significant in Table 2?

Answer 1

Footnote 8 and 9 of the paper contained on page 470-471 of the paper contain information as to how the "a" is calculated.

The best way to think about it is as follows: Imagine the author has split the data 4 ways: Black Males, Black Females, White Males, White Females. The author then runs the same regression (See footnote 8 for details) on these 4 different groups and obtain 4 different estimates of the parameters on the independent variables.

Take Education in Table 3: The author runs 4 regressions and finds that a 1 additional year of schooling increases hourly wages by: 6.7% for Black Females, 7.1% for Black Males, 2.2% for White Females and 2.2% for White Males.

The author wants to test whether the parameter estimates stated above are significantly different for the 3 different groups compared to the estimates for White Males. In other words he want to test if the percentage increase in hourly wages is significantly different for the 3 groups that are not white males (the reference category).

The author uses the Kniesner, et. al (1978) test ( see footnote 9 for the test equation). In brief this tests whether the difference between 2 parameter estimates (say the impact of education on wages for black females vs white males) is different from 0. The output of the test is a t-statistic which is compared to the 95% critical value from a t-distribution. If the t-statistic exceeds the critical value, the null hypothesis that the two parameter estimates are the same is rejected.

Significance is another thing entirely and is denoted using a t-test for the single parameter estimate different from 0. These are denoted with the stars $*$. In the economics literature, a p-value $\le$ 0.05 is usually deemed as "significant".