# coeftest

Linear hypothesis test on coefficients of repeated measures model

## Syntax

``tbl = coeftest(rm,A,C,D)``

## Description

example

````tbl = coeftest(rm,A,C,D)` returns a table `tbl` containing the multivariate analysis of variance (manova) for the repeated measures model `rm`.```

## Input Arguments

expand all

Repeated measures model, returned as a `RepeatedMeasuresModel` object.

For properties and methods of this object, see `RepeatedMeasuresModel`.

Specification representing the between-subjects model, specified as an a-by-p numeric matrix, with rank ap.

Data Types: `single` | `double`

Specification representing the within-subjects (within time) hypotheses, specified as an r-by-c numeric matrix, with rank crnp.

Data Types: `single` | `double`

Hypothesized value, specified as a scalar value or an a-by-c matrix.

Data Types: `single` | `double`

## Output Arguments

expand all

Results of multivariate analysis of variance for the repeated measures model `rm`, returned as a table containing the following columns.

 `Statistic` Type of test statistic used `Value` Value of the corresponding test statistic `F` F-statistic value `RSquare` Measure of variance explained `df1` Numerator degrees of freedom for the F-statistic `df2` Denominator degrees of freedom for the F-statistic `pValue` p-value associated with the test statistic value

## Examples

expand all

`load repeatedmeas`

The table `between` includes the between-subject variables age, IQ, group, gender, and eight repeated measures `y1` through `y8` as responses. The table `within` includes the within-subject variables `w1` and `w2`. This is simulated data.

Fit a repeated measures model, where the repeated measures `y1` through `y8` are the responses, and age, IQ, group, gender, and the group-gender interaction are the predictor variables. Also specify the within-subject design matrix.

`rm = fitrm(between,'y1-y8 ~ Group*Gender + Age + IQ','WithinDesign',within);`

Test that the coefficients of all terms in the between-subjects model are the same for the first and last repeated measurement variable.

`coeftest(rm,eye(8),[1 0 0 0 0 0 0 -1]')`
```ans=4×7 table Statistic Value F RSquare df1 df2 pValue _________ _______ ______ _______ ___ ___ _______ Pillai 0.3355 1.3884 0.3355 8 22 0.25567 Wilks 0.6645 1.3884 0.3355 8 22 0.25567 Hotelling 0.50488 1.3884 0.3355 8 22 0.25567 Roy 0.50488 1.3884 0.3355 8 22 0.25567 ```

The $p$-value of 0.25567 indicates that there is not enough statistical evidence to conclude that the coefficients of all terms in the between-subjects model for the first and last repeated measures variable are different.

## Tips

• This test is defined as `A*B*C = D`, where `B` is the matrix of coefficients in the repeated measures model. `A` and `C` are numeric matrices of the proper size for this multiplication. `D` is a scalar or numeric matrix of the proper size. The default is ```D = 0```.