General Advice on Running Welch t-test with Three Groups

[Farhan Hasnat]

I have three group AIC, GIC and Others and three Independent Variables AEM, REM and DA. Additionally, I have divided my sample into PRE (2003-2006), POST (2011-2014) and TRANSITION (2007-2010) PERIOD.

My ambition is to do difference in means with unequal variance/welch t-test of AEM, REM and DA for the groups AIC, GIC and Others BY YEAR BY TICKER/FIRM. For example:

- Run welch t-test on AIC, GIC and Others for PRE Period AEM, REM and DA
- Run welch t-test on AIC, GIC and Others for POST Period AEM, REM and DA
- Run welch t-test on AIC, GIC and Others for Transition Period AEM, REM and DA

Lastly for Cross Over Period:

- I will test difference in between for all the group (AIC, GIC and Other) against Pre-Period with Post period for AEM (for example - AIC of Pre-Period with AIC of Post-Period)
- I will test difference in between for all the group (AIC, GIC and Other) against Pre-Period with Post period for REM
- I will test difference in between for all the group (AIC, GIC and Other) against Pre-Period with Post period for DA

I structured my data as if variable Ticker belongs to AIC/GIC/Others then 1 otherwise missing value. Not sure, if I should have a separate indicator variable with AIC - 1, GIC -0 , Others - 3 -- but I understand that could run into a different issue.

For reference this is what I am willing achieve, instead of ROA, BEP, MB and TobinQ - my independent variables are AEM, REM and DA

* Example generated by -dataex-. For more info, type help dataex
clear
input str9 Ticker int Year byte(AIC GIC Others) float(AEM DA REM)
"TH:2S"    2003 . 1 .          .           .           .
"TH:2S"    2004 . 1 .          .           .           .
"TH:2S"    2005 . 1 .          .           .           .
"TH:2S"    2006 . 1 .          .           .           .
"TH:2S"    2007 . 1 .  .08454061  -.08454061           .
"TH:2S"    2008 . 1 .  .25864583  -.25864583   -.3590968
"TH:2S"    2009 . 1 .   .3615133    .6085715    .6866572
"TH:2S"    2010 . 1 .  .09650405   .09650405    .2233003
"TH:2S"    2011 . 1 .   .1017216   -.1017216  -.12448598
"TH:2S"    2012 . 1 .  .11378127   .11378127    .1807871
"TH:2S"    2013 . 1 .  .05965737  -.05965737    .3850421
"TH:2S"    2014 . 1 .  .04307863  -.04307863   .11161117
"TH:A"     2003 1 . .          .           .           .
"TH:A"     2004 1 . .   .3615133    .6278349           .
"TH:A"     2005 1 . .  .06726224   .06726224    .1704067
"TH:A"     2006 1 . .   .1024842   -.1024842   .06795144
"TH:A"     2007 1 . .  .09083974   .09083974   .22764696
"TH:A"     2008 1 . .  .02267651  -.02267651    .3380715
"TH:A"     2009 1 . .  .15725097  -.15725097  -.20699245
"TH:A"     2010 1 . .   .0957468    .0957468  -.05928836
"TH:A"     2011 1 . . .032091457  .032091457  -.05133688
"TH:A"     2012 1 . .   .1184249    .1184249   .15424915
"TH:A"     2013 1 . .   .2663026    .2663026   .22670837
"TH:A"     2014 1 . .   .2288631    .2288631    .4384329
"TH:ABICO" 2003 . 1 .   .1509448   -.1509448    .3181181
"TH:ABICO" 2004 . 1 .   .3615133   -.7443731   .14622998
"TH:ABICO" 2005 . 1 .   .3615133    .6278349   .26379138
"TH:ABICO" 2006 . 1 . .013820863 -.013820863    .0930719
"TH:ABICO" 2007 . 1 . .066848315  .066848315   .14633332
"TH:ABICO" 2008 . 1 .   .1630021   -.1630021  -.12510586
"TH:ABICO" 2009 . 1 .   .1760944    .1760944   -.0877411
"TH:ABICO" 2010 . 1 . .027172344  .027172344   .02623787
"TH:ABICO" 2011 . 1 .   .1821229    .1821229   .11709617
"TH:ABICO" 2012 . 1 .   .2805742    .2805742  -.09107255
"TH:ABICO" 2013 . 1 .  .04285799   .04285799 -.026736926
"TH:ABICO" 2014 . 1 .  .06678031   .06678031   .15781155
"TH:ACC"   2003 . 1 .  .13844515   .13844515    .3412211
"TH:ACC"   2004 . 1 .  .23043732  -.23043732   .03835598
"TH:ACC"   2005 . 1 .   .1565992   -.1565992  -.18647528
"TH:ACC"   2006 . 1 .  .09132891  -.09132891 -.035536867
"TH:ACC"   2007 . 1 .  .04345912   .04345912   .26724613
"TH:ACC"   2008 . 1 .  .18008757   .18008757   .28804305
"TH:ACC"   2009 . 1 .          .           .           .
"TH:ACC"   2010 . 1 .          .           .           .
"TH:ACC"   2011 . 1 .    .213304     .213304    .3812846
"TH:ACC"   2012 . 1 .  .05535654   .05535654   .15247422
"TH:ACC"   2013 . 1 .  .17010236  -.17010236  -.12541376
"TH:ACC"   2014 . 1 .          .           .   -.1588971
"TH:AFC"   2003 . 1 .  .04718301   .04718301   .19753388
"TH:AFC"   2004 . 1 .  .05981214   .05981214    .2972218
"TH:AFC"   2005 . 1 .  .23442598   .23442598    .8077127
"TH:AFC"   2006 . 1 .   .1069364   -.1069364   .13844872
"TH:AFC"   2007 . 1 .  .04298536  -.04298536   .34691975
"TH:AFC"   2008 . 1 .  .05517821   .05517821     .654694
"TH:AFC"   2009 . 1 . .006168552 -.006168552    .3436305
"TH:AFC"   2010 . 1 .  .01499469   .01499469     .432837
"TH:AFC"   2011 . 1 . .012949838  .012949838   .58664113
"TH:AFC"   2012 . 1 .  .04469505   .04469505    .6833286
"TH:AFC"   2013 . 1 .  .05154819   .05154819    .5198638
"TH:AFC"   2014 . 1 .          .           .     .671021
"TH:AGE"   2003 . 1 .          .           .           .
"TH:AGE"   2004 . 1 .          .           .           .
"TH:AGE"   2005 . 1 .          .           .           .
"TH:AGE"   2006 . 1 .          .           .           .
"TH:AGE"   2007 . 1 .          .           .    .8584644
"TH:AGE"   2008 . 1 .  .26367554   .26367554   .53351235
"TH:AGE"   2009 . 1 .  .08931428   .08931428    .1910975
"TH:AGE"   2010 . 1 .  .25956905   .25956905   .41588455
"TH:AGE"   2011 . 1 .  .09252103  -.09252103   -.2183907
"TH:AGE"   2012 . 1 .  .04484579   .04484579   .23026714
"TH:AGE"   2013 . 1 .  .13395208   .13395208    .3339454
"TH:AGE"   2014 . 1 .  .27340496  -.27340496  -.14310192
"TH:AH"    2003 1 . .   .2078416   -.2078416   -.3924506
"TH:AH"    2004 1 . .   .1830832   -.1830832   -.2504793
"TH:AH"    2005 1 . . .005306605 .0010229541    -.138877
"TH:AH"    2006 1 . . .016149808  .016149808    .0647247
"TH:AH"    2007 1 . .   .0128961   -.0128961 -.018031029
"TH:AH"    2008 1 . .  .04499222  -.04499222   .02317033
"TH:AH"    2009 1 . .   .0351702   -.0351702   .12964162
"TH:AH"    2010 1 . .  .04360331  -.04360331   .04850768
"TH:AH"    2011 1 . . .005306605 -.005175362   .16721784
"TH:AH"    2012 1 . . .030353934  .030353934   .13856235
"TH:AH"    2013 1 . .  .05105714  -.05105714   .04331774
"TH:AH"    2014 1 . .  .07181978  -.07181978   .01027975
"TH:AHC"   2003 . 1 .  .04777425  -.04777425   .03497014
"TH:AHC"   2004 . 1 . .019984696 -.019984696   .04635291
"TH:AHC"   2005 . 1 .  .04643552   .04643552   .06004512
"TH:AHC"   2006 . 1 . .005306605 -.003667239    .1944249
"TH:AHC"   2007 . 1 .  .01884266   .01884266    .3248635
"TH:AHC"   2008 . 1 .  .01925189  -.01925189   .18949486
"TH:AHC"   2009 . 1 . .027770244  .027770244    .2180857
"TH:AHC"   2010 . 1 . .013661582 -.013661582   .17859873
"TH:AHC"   2011 . 1 .  .03151839  -.03151839   .16725425
"TH:AHC"   2012 . 1 .  .02424605  -.02424605    .1528288
"TH:AHC"   2013 . 1 .  .02805965   .02805965    .1449769
"TH:AHC"   2014 . 1 . .018061165  .018061165   .13083534
"TH:AI"    2003 . 1 . .072685905  .072685905  -.55078727
"TH:AI"    2004 . 1 .  .10123187  -.10123187   -.7373347
"TH:AI"    2005 . 1 . .012330643  .012330643  -.02708403
"TH:AI"    2006 . 1 .  .04343369   .04343369   .29519606
end

[Farhan Hasnat]

Sorry maybe my questions were not clear.

I was wandering if anyone could show some direction on how to structure the data in this case and clue on commands to runt the tests.

Thank you in advance

[Nick Cox]

t tests here seem artificial and partial. If you have three groups, I recommend regression.

[Farhan Hasnat]

Nick Cox Thank you Nick for your useful advice. Unfortunately this is not an option for me as my thesis committee has put forward this request to make it more comparable to the similar studies I am doing

[Leonardo Guizzetti]

What I presume Nick was getting at was to estimated one regression model with group as your only indicator variable. Then, use margins or test to look at pairwise differences between groups, possibly adjusting for multiplicity. The pairwise statistics are what should go in the table.