## 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).

### 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 qq 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[] # accesses the first element