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| '''`-test-`''' performs [[Statistics/WaldTest|Wald tests]]. | '''`-test-`''' performs [[Statistics/WaldTest|Wald tests]] on regression coefficients. |
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| As a demonstration: | Consider this test on one coefficient: |
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| . test 3.region=0 | . test 3.region = 0 |
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| Note that the [[Statistics/FDistribution|F distribution]] with 1 numerator degree of freedom is the [[Statistics/HotelingsTSquaredDistribution|t-squared distribution]], so the F-statistic can be double-checked by squaring the previously-estimated t-statistic on the corresponding coefficient. | Consider this joint test on a parameter: |
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| . test (2.region=0) (3.region=0) (4.region=0) | . test (2.region = 0) (3.region = 0) (4.region = 0) |
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=== 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 }}} |
Stata test
-test- performs Wald tests on regression coefficients.
See also -testparm-.
Contents
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 = 0.0691The 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 = 0.0001The 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.