The picture is a table comes from a research paper and you don't need to know the Chinese words. Researcher runs linear regression of every Chinese stock's return with 5 factors (market, size, value, profitability, investment)(Over 4000 regressions) . Then he took the mean of each estimated coefficient which is in ROW Mean (e.g. the mean of thousands of estimated market factor coefficient is 1.38). Also, he got the t statistic of the hypothesis that the real coefficient equals the estimated coefficient( e.g. the real average market factor coefficient =1.38 and t statistic for testing is 1.92). Panel B is just same but changes the sample from chinese stock to us stock.

My question is : why you can use a t statistic to check the accuracy of the average estimated Beta(coefficient)(cause each stock has a different sample size when running regression, some have 1 year's data some get 2) ?

(1) Please give me the formula of the t statistic (2) and show why it follows a t distribution.

Thank you very much.

Panel A : A KiBUTIKa KAJiBHBit(2x3) 199407 - 201508 Ry - RF SMB HML RMW CMA Mean 1. 38* 0. 86* * * 0. 23 -0. 07 - 0. 02 t - Statistic 1. 92 2. 70 1. 16 - 0. 21 - 0. 09 Panel B: XinKOJIMAHiBMSi(2x3) 199407 -201508 Ry - RF SMB HML RMW CMA Mean 0. 65* * 0. 20 0. 18 0. 34* 0. 26* t - Statistic 2. 31 0. 99 0. 90 1. 81 1.91Panel A : A KiBUTIKa KAJiBHBit(2x3) 199407 - 201508 Ry - RF SMB HML RMW CMA Mean 1. 38* 0. 86* * * 0. 23 -0. 07 - 0. 02 t - Statistic 1. 92 2. 70 1. 16 - 0. 21 - 0. 09 Panel B: XinKOJIMAHiBMSi(2x3) 199407 -201508 Ry - RF SMB HML RMW CMA Mean 0. 65* * 0. 20 0. 18 0. 34* 0. 26* t - Statistic 2. 31 0. 99 0. 90 1. 81 1.91