T-tests for a matrix

[Juan Gonzalex]

Hi,

This is a sample of my data:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(time change5 interest3 excess_ri_port)
578 1 3  -.6925126
579 1 3   3.500199
580 1 3   2.992766
581 1 3  -7.831552
582 1 3  -5.636639
583 1 3   1.427559
584 1 3 -14.535248
585 1 3  -26.12037
586 1 3  -6.152879
587 1 3   7.726166
657 2 1  -.8846533
658 2 1    3.60806
660 2 1   1.938433
661 2 1    6.38167
662 2 1  -2.021422
663 2 1   5.012726
664 2 1   .4726349
665 2 1  -1.480696
666 2 1   3.192597
667 2 1  -5.435805
668 2 1 -2.5471926
669 2 1   7.368956
670 2 1   .8326083
671 2 1 -1.6570904
672 2 1  -5.966536
673 2 1   .4660656
674 2 1   8.600153
675 2 1  1.5384797
676 2 1   .4725932
677 2 1  -6.599574
678 2 1   6.505339
679 2 1   .5697324
680 2 1  2.1315773
681 2 1  -4.011961
682 2 1  -1.068154
683 2 1   4.434777
684 2 1  4.2806845
685 2 1  2.0386615
686 2 1  4.1449623
687 2 1   6.499111
688 2 1   5.262307
689 2 1 -1.0671136
690 2 1   4.645394
691 2 1  1.3541282
692 2 1  4.2406955
693 2 1  1.0949044
694 2 1  .43575725
695 2 1  1.9311043
696 2 1   7.963739
697 2 1  -4.701449
698 2 1 -1.0655196
end
format %tm time

My data is divided into 5 portfolios depending on the leverage change (change5) and into terciles depending on the interest rate (interest3). I have computed the average excess return for each change5 for each interest3 as following:

bysort change5 interest3 (time): tabstat excess_ri_port, stats(count mean p50 sd min max)

What I want is to perform a t-test between the lowest and highest group. Because I get a matrix, there are 8 t-tests (see picture). For example, for interest3 == 1, calculate the t-test between change5 == 1 and change5 == 5. Or for change5 == 1, calculate the t-test between interest3 == 1 and interest3 == 3.

Here is the matrix to make it a little bit more clear:

Thanks

[Fei Wang]

Juan, you may generate all group means and conduct all t tests from a single regression.

regress excess_ri_post bn.change5#bn.interest3, noc

* Ttest 1
lincom 1.change5#1.interest3 - 5.change5#1.interest3

* Ttest 2
lincom 1.change5#2.interest3 - 5.change5#2.interest3

* Ttest 3
lincom 1.change5#3.interest3 - 5.change5#3.interest3

* Ttest 4
lincom 1.change5#1.interest3 - 1.change5#3.interest3

* Ttest 5
lincom 2.change5#1.interest3 - 2.change5#3.interest3

* Ttest 6
lincom 3.change5#1.interest3 - 3.change5#3.interest3

* Ttest 7
lincom 4.change5#1.interest3 - 4.change5#3.interest3

* Ttest 8
lincom 5.change5#1.interest3 - 5.change5#3.interest3

[Juan Gonzalex]

Thank you very much!

[Carlo Lazzaro]

Juan:
as an aside to Fei's helpful code, as you seemingly have multiple comparisons, you may want to consider something like Bonferroni's correction (which is not directly available from -lincom-, but can be easily calculated by hand; see -contrast- entry, Stata .pdf manual).