## Paired Samples T-Test

The Student’s paired samples t-test (sometimes called a dependent-samples t-test) is used to test the null hypothesis that the difference between pairs of measurements is equal to zero. A low p-value suggests that the null hypothesis is not true, and that the difference between the measurement pairs is not zero.

The Student’s paired samples t-test assumes that pair differences follow a normal distribution – in the case that one is unwilling to assume this, the non-parametric Wilcoxon signed-rank can be used in it’s place (However, note that the Wilcoxon signed-rank has a slightly different null hypothesis; that the two groups of measurements follow the same distribution).

### Example usage

### Arguments

data | the data as a data frame |

pairs | a list of lists specifying the pairs of measurement in data |

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 |

wilcoxon | TRUE or FALSE (default), perform Wilcoxon signed rank tests |

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

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

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

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

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

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

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

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$norm | 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