makePaired: Synthesise a dataset from paired-sample t-test summary...

In LikertMakeR: Synthesise and Correlate Likert Scale and Rating-Scale Data Based on Summary Statistics

Synthesise a dataset from paired-sample t-test summary statistics

Description

Generates a dataset from paired-sample t-test summary statistics.

Usage

makePaired(
  n,
  means,
  sds,
  t_value,
  lowerbound,
  upperbound,
  items = 1,
  precision = 0
)

Arguments

n	(positive, integer) sample size
means	(real) 1:2 vector of target means for two before/after measures
sds	(real) 1:2 vector of target standard deviations
t_value	(real) desired paired t-statistic
lowerbound	(integer) lower bound (e.g. '1' for a 1-5 rating scale)
upperbound	(integer) upper bound (e.g. '5' for a 1-5 rating scale)
items	(positive, integer) number of items in the rating scale. Default = 1
precision	(positive, real) relaxes the level of accuracy required. Default = 0

Details

makePaired() generates correlated values so the data replicate rating scales taken, for example, in a before and after experimental design.

The function is effectively a wrapper function for lfast() and lcor() with the addition of a t-statistic from which the between-column correlation is inferred.

Paired t-tests apply to observations that are associated with each other. For example: the same people before and after a treatment; the same people rating two different objects; ratings by husband & wife; etc.

The paired-samples t-test is defined as:

t = \frac{\mathrm{mean}(D)}{\mathrm{sd}(D) / \sqrt{n}}

where:

• D = differences in values

• \mathrm{mean}(D) = mean of the differences

• \mathrm{sd}(D) = standard deviation of the differences, where

\mathrm{sd}(D)^2 = \mathrm{sd}(X_{\text{before}})^2 + \mathrm{sd}(X_{\text{after}})^2 - 2\,\mathrm{cov}(X_{\text{before}}, X_{\text{after}})

A paired-sample t-test thus requires an estimate of the covariance between the two sets of observations. makePaired() rearranges these formulae so that the covariance is inferred from the t-statistic.

Value

a dataframe approximating user-specified conditions.

Note

Larger sample sizes usually result in higher t-statistics, and correspondingly small p-values.

Small sample sizes with relatively large standard deviations and relatively high t-statistics can result in impossible correlation values.

Similarly, large sample sizes with low t-statistics can result in impossible correlations. That is, a correlation outside of the -1:+1 range.

If this happens, the function will fail with an ERROR message. The user should review the input parameters and insert more realistic values.

See Also

lfast, lcor

Examples

n <- 20
pair_m <- c(2.5, 3.0)
pair_s <- c(1.0, 1.5)
lower <- 1
upper <- 5
k <- 6
t <- -2.5

pairedDat <- makePaired(
  n = n, means = pair_m, sds = pair_s,
  t_value = t,
  lowerbound = lower, upperbound = upper, items = k
)

str(pairedDat)
cor(pairedDat) |> round(2)

t.test(pairedDat$X1, pairedDat$X2, paired = TRUE)

LikertMakeR documentation built on March 23, 2026, 9:07 a.m.