## Independent Samples T-Test

The Student’s Independent samples t-test (sometimes called a two-samples t-test) is used to test the null hypothesis that two groups have the same mean. A low p-value suggests that the null hypothesis is not true, and therefore the group means are different.

The Student’s independent t-test assumes that the data from each group are from a normal distribution, and that the variances of these groups are equal. If unwilling to assume the groups have equal variances, the Welch’s t-test can be used in it’s place. If one is additionally unwilling to assume the data from each group are from a normal distribution, the non-parametric Mann-Whitney U test can be used instead (However, note that the Mann-Whitney U test has a slightly different null hypothesis; that the distributions of each group is equal).

### Example usage

### Arguments

data | the data as a data frame |

vars | the dependent variables (not necessary when using a formula, see the examples) |

group | the grouping variable with two levels (not necessary when using a formula, see the examples) |

students | TRUE (default) or FALSE, perform Student's t-tests |

bf | TRUE or FALSE (default), provide Bayes factors |

bfPrior | a number between 0.5 and 2 (default 0.707), the prior width to use in calculating Bayes factors |

welchs | TRUE or FALSE (default), perform Welch's t-tests |

mann | TRUE or FALSE (default), perform Mann-Whitney U tests |

hypothesis | 'different' (default), 'oneGreater' or 'twoGreater', the alternative hypothesis; group 1 different to group 2, group 1 greater than group 2, and group 2 greater than group 1 respectively |

norm | TRUE or FALSE (default), perform Shapiro-Wilk tests of normality |

TRUE or FALSE (default), provide Q-Q plots of residuals | |

eqv | TRUE or FALSE (default), perform Levene's tests for homogeneity of variances |

meanDiff | TRUE or FALSE (default), provide means and standard errors |

ci | TRUE or FALSE (default), provide confidence intervals |

ciWidth | a number between 50 and 99.9 (default: 95), the width of confidence intervals |

effectSize | TRUE or FALSE (default), provide effect sizes |

ciES | TRUE or FALSE (default), provide confidence intervals for the effect-sizes |

ciWidthES | a number between 50 and 99.9 (default: 95), the width of confidence intervals for the effect sizes |

desc | TRUE or FALSE (default), provide descriptive statistics |

plots | TRUE or FALSE (default), provide descriptive plots |

miss | 'perAnalysis' or 'listwise', how to handle missing values; 'perAnalysis' excludes missing values for individual dependent variables, 'listwise' excludes a row from all analyses if one of its entries is missing. |

### Returns

A results object containing:

results$ttest | a table |

results$assum$norm | a table |

results$assum$eqv | a table |

results$desc | a table |

results$plots | an array of groups |

Tables can be converted to data frames with asDF or as.data.frame(). For example:

results$ttest$asDF

as.data.frame(results$ttest)

Elements in arrays can be accessed with [[n]]. For example:

results$plots[[1]] # accesses the first element