An approximate F-test based on the Satterthwaite (1946) approach.

```
ci_satterthwaite(model, ci = 0.95)
dof_satterthwaite(model)
p_value_satterthwaite(model, dof = NULL)
se_satterthwaite(model)
```

## Arguments

model |
A statistical model. |

ci |
Confidence Interval (CI) level. Default to `0.95` (`95%` ). |

dof |
Degrees of Freedom. |

## Value

A data frame.

## Details

Inferential statistics (like p-values, confidence intervals and
standard errors) may be biased in mixed models when the number of clusters
is small (even if the sample size of level-1 units is high). In such cases
it is recommended to approximate a more accurate number of degrees of freedom
for such inferential statitics. Unlike simpler approximation heuristics
like the "m-l-1" rule (`dof_ml1`

), the Satterthwaite approximation is
also applicable in more complex multilevel designs. However, the "m-l-1"
heuristic also applies to generalized mixed models, while approaches like
Kenward-Roger or Satterthwaite are limited to linear mixed models only.

## References

Satterthwaite FE (1946) An approximate distribution of estimates of variance components. Biometrics Bulletin 2 (6):110–4.

## See also

`dof_satterthwaite()`

and `se_satterthwaite()`

are small helper-functions
to calculate approximated degrees of freedom and standard errors for model
parameters, based on the Satterthwaite (1946) approach.

`dof_kenward()`

and `dof_ml1()`

approximate degrees of freedom based on Kenward-Roger's method or the "m-l-1" rule.

## Examples

```
# \donttest{
if (require("lme4", quietly = TRUE)) {
model <- lmer(Petal.Length ~ Sepal.Length + (1 | Species), data = iris)
p_value_satterthwaite(model)
}
#> Parameter p
#> 1 (Intercept) 9.605145e-01
#> 2 Sepal.Length 7.882014e-29
# }
```