One Sample T-Test
The Student’s One-sample t-test is used to test the null hypothesis that the true mean is equal to a particular value (typically zero). A low p-value suggests that the null hypothesis is not true, and therefore the true mean must be different from the test value.
The Student’s One-sample t-test assumes that the data are from 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 median is equal to the test value).
Example usage
data('ToothGrowth')
ttestOneS(ToothGrowth, vars = vars(len, dose))
#
# ONE SAMPLE T-TEST
#
# One Sample T-Test
# ──────────────────────────────────────────────────────
# statistic df p
# ──────────────────────────────────────────────────────
# len Student's t 19.1 59.0 < .001
# dose Student's t 14.4 59.0 < .001
# ──────────────────────────────────────────────────────
#
Arguments
| data | the data as a data frame |
| vars | a vector of strings naming the variables of interest 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 2.0 (default 0.707), the prior width to use in calculating Bayes factors |
| wilcoxon | TRUE or FALSE (default), perform Wilcoxon signed rank tests |
| testValue | a number specifying the value of the null hypothesis |
| hypothesis | 'dt' (default), 'gt' or 'lt', the alternative hypothesis; different to testValue, greater than testValue, and less than testValue respectively |
| norm | TRUE or FALSE (default), perform Shapiro-wilk tests of normality |
| TRUE or FALSE (default), provide a Q-Q plot of residuals | |
| meanDiff | TRUE or FALSE (default), provide means and standard deviations |
| ci | TRUE or FALSE (default), provide confidence intervals for the mean difference |
| ciWidth | a number between 50 and 99.9 (default: 95), the width of confidence intervals |
| effectSize | TRUE or FALSE (default), provide Cohen's d 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. |
| mann |
Returns
A results object containing:
| results$ttest | a table |
| results$normality | a table |
| results$descriptives | a table |
| results$plots | an image |
| results$qq | an array of images |
Tables can be converted to data frames with asDF or as.data.frame(). For example:
results$ttest$asDF
as.data.frame(results$ttest)
Elements in arrays can be accessed with [[n]]. For example:
results$qq[[1]] # accesses the first element