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
data('ToothGrowth')
ttestIS(formula = len ~ supp, data = ToothGrowth)
#
# INDEPENDENT SAMPLES T-TEST
#
# Independent Samples T-Test
# ────────────────────────────────────────────────────
# statistic df p
# ────────────────────────────────────────────────────
# len Student's t 1.92 58.0 0.060
# ────────────────────────────────────────────────────
#
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