High t statistic with high p value for same variable?

Question

I am trying to do a difference in difference model to compare two cities' police departments' uses of force after treatment from a consent decree. When I run the model with clustered standard errors, I get a significant t statistic for the treatment variable, but also a very high p value. I am newer to statistics, so I am wondering how this can be interpreted? I thought that a high t statistic should coincide with a very low p value.

Here is the code I used: reg UOF10000 SEATTLE TIME TREATED MIN_POP FEM_POP DEG_POP officerspop, cluster(SEATTLE)

SEATTLE indicates whether the department is Seattle, the treated department. TIME indicates whether it is past 2015, when the treatment starts. TREATED is the interaction of these two. The rest are demographic controls. Is there something I'm doing that might generate such results? Here is the output:

`Linear regression                               Number of obs     =         72
                                            F(0, 1)           =          .
                                            Prob > F          =          .
                                            R-squared         =     0.1521
                                            Root MSE          =     1.0831

                                (Std. err. adjusted for 2 clusters in SEATTLE)
------------------------------------------------------------------------------
         |               Robust
UOF10000 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
 SEATTLE |  -1.031602   3.427315    -0.30   0.814    -44.57976    42.51656
    TIME |  -.4138573   .0758693    -5.45   0.115    -1.377869    .5501542
 TREATED |  -.5722371   .0901167    -6.35   0.099    -1.717278    .5728041
 MIN_POP |  -.0000302   .0000286    -1.06   0.483    -.0003941    .0003337
 FEM_POP |   9.04e-06   .0000499     0.18   0.886    -.0006255    .0006436
 DEG_POP |   .0000166   .0000146     1.14   0.458    -.0001687     .000202
 officerspop |   892.6141   2162.243     0.41   0.751    -26581.29    28366.52
   _cons |  -3.155234   5.075511    -0.62   0.646    -67.64571    61.33524`
------------------------------------------------------------------------------

Answer 1

Your standard error is adjusted for only 2 clusters. That doesn't look right. It's hard to find a definitive answer to the minimum number of clusters (the book 'Mostly Harmless Econometrics' suggests 42. Which is (a bit of) a joke.

Your t-statistic has very (very!) few degrees of freedom, which is why the p-value and the t-value look inconsistent, but they're not. I'm not sure if it's possible to request the df from Stata, but the value is <1.

It's unusual to use a predictor as a cluster variable as well.