Gosset_Welch {DanielBiostatistics10th} | R Documentation |

## Two-Sample Student's `t`

-statistic and Welch–Satterthwaite Equation

### Description

To determine the degree of freedom, as well as the standard error,
of two-sample `t`

-statistic, with or without the equal-variance assumption.

### Usage

```
Gosset_Welch(s1, s0, v1 = s1^2, v0 = s0^2, n1, n0, var.equal = FALSE)
```

### Arguments

`s1` , `s0` |
(optional) double scalars or vectors,
sample standard deviations |

`v1` , `v0` |
double scalars or vectors,
sample variances of the treatment and control sample, respectively.
Default |

`n1` , `n0` |
integer scalars or vectors, sample sizes of the treatment and control sample, respectively |

`var.equal` |
logical scalar,
whether to treat the two variances |

### Value

Function Gosset_Welch returns a numeric scalar of the degree of freedom,
with a numeric scalar attribute `'stderr'`

of the standard error of the mean-difference.

### References

Student's `t`

-test by William Sealy Gosset, doi:10.1093/biomet/6.1.1.

Welch–Satterthwaite equation by Bernard Lewis Welch and F. E. Satterthwaite, doi:10.2307/3002019 and doi:10.1093/biomet/34.1-2.28.

### See Also

### Examples

```
x = rnorm(32L, sd = 1.6); y = rnorm(57L, sd = 2.1)
vx = var(x); vy = var(y); nx = length(x); ny = length(y)
t.test(x, y, var.equal = FALSE)[c('parameter', 'stderr')]
Gosset_Welch(v1 = vx, v0 = vy, n1 = nx, n0 = ny, var.equal = FALSE)
t.test(x, y, var.equal = TRUE)[c('parameter', 'stderr')]
Gosset_Welch(v1 = vx, v0 = vy, n1 = nx, n0 = ny, var.equal = TRUE)
```

*DanielBiostatistics10th*version 0.2.2 Index]