= Stata test =

'''`-test-`''' performs [[Statistics/WaldTest|Wald tests]] on regression coefficients.

See also [[Stata/TestParm|-testparm-]].

<<TableOfContents>>

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== Usage ==

Consider this test on one coefficient:

{{{
. use https://www.stata-press.com/data/r18/census3
(1980 Census data by state)

. regress brate medage c.medage#c.medage i.region
[snip]

. test 3.region = 0
 ( 1) 3.region = 0
      F( 1, 44) = 3.47
       Prob > F = 0.0691
}}}

The [[Statistics/FTest|F-statistic]] of the hypothesis is 3.47, corresponding to a significance level of about 0.07. In most settings, this would be considered insufficient to reject the null hypothesis: the factor is not significant.

Consider this joint test on a parameter:

{{{
. test (2.region = 0) (3.region = 0) (4.region = 0)
 ( 1) 2.region = 0
 ( 2) 3.region = 0
 ( 3) 4.region = 0
      F( 3, 44) = 8.85
       Prob > F = 0.0001
}}}

The F-statistic of the joint hypotheses is 8.85, corresponding to a significance level very close to 0. This is a strong basis to reject the joint null hypotheses: the variable is significant.



=== Coefficient Names ===

To list the coefficient names that `-test-` can reference, add the '''`coeflegend`''' option to an estimation command.

{{{
. webuse nhanes2l
(Second National Health and Nutrition Examination Survey)

. regress bpsystol i.diabetes##c.age c.age#c.age i.hlthstat, coeflegend
[snip]
--------------------------------------------------------------------------------
      bpsystol | Coefficient  Legend
---------------+----------------------------------------------------------------
      diabetes |
     Diabetic  |  -2.789364  _b[1.diabetes]
           age |   .0436002  _b[age]
               |
diabetes#c.age |
     Diabetic  |    .158519  _b[1.diabetes#c.age]
               |
   c.age#c.age |   .0060262  _b[c.age#c.age]
               |
      hlthstat |
    Very good  |    .829615  _b[2.hlthstat]
         Good  |   2.438839  _b[3.hlthstat]
         Fair  |   4.179397  _b[4.hlthstat]
         Poor  |   3.100577  _b[5.hlthstat]
               |
         _cons |    111.268  _b[_cons]
--------------------------------------------------------------------------------

. test (_b[age] = 0)  (_b[c.age#c.age] = 0)

 ( 1)  age = 0
 ( 2)  c.age#c.age = 0

       F(  2, 10326) = 1140.12
            Prob > F =    0.0000
}}}



=== Expressions ===

Expressions are interpreted by these patterns, where `a` and `b` represent ''sub-expressions'' and `1` represents a scalar value.

 * `a`: hypothesis that a coefficient is equal to 0
 * `a = 1`: hypothesis that a coefficient is equal to a scalar value
 * `a = b`: hypothesis that coefficients are equal to each other

Expressions can be delimited with parentheses.

Sub-expressions can be variable names, factor indicators, or linear combinations. For example:

 * `x1`: variable `x1`
 * `2.a`: factor indicator 2 of `a`
 * `2*x1`: linear combination of a variable
 * `x1+x2`: linear combination of variables

If a multiple-equation model has been run, use the `[equation]variable` syntax to specify the hypothesis. For example, `test [y1]x1=[y3]x1`.

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== See also ==

[[https://www.stata.com/manuals/rtest.pdf|Stata manual for -test-]]



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CategoryRicottone