    # Re: st: calculating df for t and f-statistics in survey linear

 From jpitblado@stata.com (Jeff Pitblado, StataCorp LP) To statalist@hsphsun2.harvard.edu Subject Re: st: calculating df for t and f-statistics in survey linear Date Sat, 09 Sep 2006 15:02:13 -0500

```Jade <ja1@umbc.edu> is analyzing survey data, and wants to know the degrees of
freedom used with the reported t and F tests:

> I'm trying to figure out how to compute the df for t and F in these
> results (below).  I'm not sure what is being used as N?  Any direction
>
> . svyreg  fac_etoh bio_sex age dep_sum
>
> Survey linear regression
>
> pweight:  gswgt1                               Number of obs    =      1348
> Strata:   region                               Number of strata =         4
> PSU:      psuscid                              Number of PSUs   =        92
>                                                Population size  = 1138728.8
>                                                F(   3,     86)  =     11.46
>                                                Prob > F         =    0.0000
>                                                R-squared        =    0.0448
> ------------------------------------------------------------------------------
> fac_etoh |      Coef.    Std. Err.      t    P>|t|    [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> bio_sex |   .3015771    .0693058     4.35   0.000    .1638464    .4393079
> age     |  -.0744264    .0298961    -2.49   0.015   -.1338386   -.0150142
> dep_sum |  -.0153594    .0047195    -3.25   0.002   -.0247383   -.0059805
> _cons   |    .919665    .5149458     1.79   0.078   -.1036815    1.943011

The numerator and denominator df used in the model F test are reported in the
output.

Numerator:	3 = df_m, one for each indepvar in the model
Denominator:	86 = (92 - 4) - (3 - 1) = df_r - (df_m - 1)

Here df_r is the design degrees of freedom, which is documented in the Survey
manual to be N - L; number of PSU's minus number of Strata.

For the individual t-tests, df_r is used to compute the p-values.

--Jeff