Description Usage Arguments Value Author(s) References See Also Examples

In the t test, it is usually the case that the assumption of equal variances on the two groups is violated. The test problem is known as the Behrens-Fisher (BF) problem when no assumption of equal population variances can be made. For the BF problem, the T statistic provides value for a given dataset and its statistical distribution is not easy to characterise.

To our knowledge, the best approximation thus far is due to Welch (1938). The Welch<e2><80><99>s test involves two layers of approximations: approximating the distribution of the statistic by a t-distribution, which in turn depends on an approximate degrees of freedom.

The Monte Carlo based tests improve upon Welch<e2><80><99>s approximate test by avoiding one layer of approximation, resulting in enhancement in statistical power than Welch's t-approximation.

1 | ```
mcBFtest(x, y, method, MC)
``` |

`x` |
a (non-empty) numeric vector of data values |

`y` |
a (non-empty) numeric vector of data values |

`method` |
if "t" is used, we will use t-test assuming equal variance and df=n+m-2. If "W" is used, we assume unequal variance and the Welch approximation is used. If "Monte Carlo", the Monte Carlo procedure is applied. |

`MC` |
a number for Monte Carlo procedure |

The function returns a list including

`p.value` |
the p-value for the test. |

You-Gan Wang, Na Wang

Welch, B.L. (1938). The significance of the difference between two means when the population variances are unequal. Biometrika, 29 (3/4), 350<e2><80><93>362.

Ullah, I., Paul, S., Hong, Z., & Wang, Y-G. (2019). Significance tests for analyzing gene expression data with small sample sizes. Bioinformatics, in press.

`t.test`

function from package `stats`

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