# statsmodels.base.model.LikelihoodModelResults.t_test¶

LikelihoodModelResults.t_test(r_matrix, cov_p=None, scale=None, use_t=None)[source]

Compute a t-test for a each linear hypothesis of the form Rb = q

Parameters: r_matrix : array-like, str, tuple array : If an array is given, a p x k 2d array or length k 1d array specifying the linear restrictions. It is assumed that the linear combination is equal to zero. str : The full hypotheses to test can be given as a string. See the examples. tuple : A tuple of arrays in the form (R, q). If q is given, can be either a scalar or a length p row vector. cov_p : array-like, optional An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used. scale : float, optional An optional scale to use. Default is the scale specified by the model fit. use_t : bool, optional If use_t is None, then the default of the model is used. If use_t is True, then the p-values are based on the t distribution. If use_t is False, then the p-values are based on the normal distribution. res : ContrastResults instance The results for the test are attributes of this results instance. The available results have the same elements as the parameter table in summary().

tvalues
individual t statistics
f_test
for F tests

patsy.DesignInfo.linear_constraint

Examples

```>>> import numpy as np
>>> import statsmodels.api as sm
>>> results = sm.OLS(data.endog, data.exog).fit()
>>> r = np.zeros_like(results.params)
>>> r[5:] = [1,-1]
>>> print(r)
[ 0.  0.  0.  0.  0.  1. -1.]
```

r tests that the coefficients on the 5th and 6th independent variable are the same.

```>>> T_test = results.t_test(r)
>>> print(T_test)
<T contrast: effect=-1829.2025687192481, sd=455.39079425193762,
t=-4.0167754636411717, p=0.0015163772380899498, df_denom=9>
>>> T_test.effect
-1829.2025687192481
>>> T_test.sd
455.39079425193762
>>> T_test.tvalue
-4.0167754636411717
>>> T_test.pvalue
0.0015163772380899498
```

Alternatively, you can specify the hypothesis tests using a string

```>>> from statsmodels.formula.api import ols
>>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR'
>>> results = ols(formula, dta).fit()
>>> hypotheses = 'GNPDEFL = GNP, UNEMP = 2, YEAR/1829 = 1'
>>> t_test = results.t_test(hypotheses)
>>> print(t_test)
```

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