st: problem with the interpretation of pstest after psmatch2, t-tests and percentage of bias provide conflicting results, which one should I follow?

[simone ferro <simone.ferro88@gmail.com>]

dear Statalist,

I would please need some clarifications about the interpretation of the command pstest after running psmatch2:
I report a random output just as an example.

pstest ebitda_marg asset employees av_age donne_perc laureati_perc bluecollar_perc, both

------------------------------------------------------------------------------
                Unmatched |       Mean               %reduct |     t-test
    Variable      Matched | Treated Control    %bias  |bias| |    t    p>|t|
--------------------------+----------------------------------+----------------
  ebitda_marg   Unmatched | 11.404   8.2304     36.8         |   3.25  0.001
                 Matched  | 10.746   10.555      2.2    94.0 |  -2.33  0.020
                          |                                  |
        asset   Unmatched | 395.52   34.389     28.6         |   2.48  0.014
                 Matched  | 115.36   89.157      2.1    92.7 |  -2.10  0.037
                          |                                  |
    employees   Unmatched | 641.98   508.48      4.6         |   0.42  0.677
                 Matched  | 474.12   704.43     -8.0   -72.5 |   0.18  0.857
                          |                                  |
       av_age   Unmatched | 53.369   56.714    -45.0         |  -4.06  0.000
                 Matched  |  53.39   53.051      4.6    89.9 |   3.84  0.000
                          |                                  |
   donne_perc   Unmatched | .34711   .37372    -11.8         |  -1.06  0.291
                 Matched  | .34805   .33374      6.3    46.2 |   0.16  0.874
                          |                                  |
laureati_perc   Unmatched | .26656   .18165     35.4         |   3.15  0.002
                 Matched  | .26815   .23665     13.2    62.9 |  -1.52  0.129
                          |                                  |
bluecollar_~c   Unmatched | .30019    .3349    -11.2         |  -1.00  0.317
                 Matched  | .30425   .33592    -10.2     8.7 |  -0.28  0.776
                          |                                  |
------------------------------------------------------------------------------
If I understood well, reported t-.tests' null hypothesis is that the two covariates are equal in treated and control group, 
so I should look at t-tests to check if the groups are well balanced,
In some tutorial instead I've read that the right approach is to look at the bias percentage that should be under 10 to be considered ok,

Which one of the two approaches is the right one?it's fundamental for me to understand because they provide totally different interpretations.
indeed if I look at t-tests, I find problems with ebitda_margin, asset and av_age, because they are significantly different in the two groups,
while if I look at the bias percentage, I find problem with laureati_perc and blecollar, because their bias% are bigger than 10.

I also would appreciate your confirmation of the interpretation of the two indicators(%bias and t-tests), because with this interpretation I find the two values contradictory.
looking for example at the variable av_age, I find a very little bias, and the means after matching of treated and control group are almost identical(53.39 and 53.051), by the way the t-test reports a p-value of 0.000!
So it seems like I have misunderstood the meaning of the t.test because I don't think that 53.39 and 53.051 can be statistically different with a t-stat of 3.84, also given the nature of the variable(the average age of the managers of a firm) that should infact be quite variable.
The same happens with the variable ebitda, which reports a bias% of 2.2% and almost identical values(10.746 and 10.555), but t-stat is -2.33 and p-value 2%!
Can you please help me?
thanks in advance for the help,
Regards,
Simone Ferro
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