10.4 Paired Data & Hypothesis Testing

paired t-test

a hypothesis test for the mean of the pairwise differences of two groups

SE(đ) = s_d/√n

the formula for the standard error of a paired t-test - the variable n represents the number of pairs

t = (đ - Δ₀) / [SE(đ)]

the formula for the test statistic for a paired t-test - the test has n-1 degrees of freedom

paired data condition

as a condition of a paired t-test, the data must be paired - each data point in one group has a matching point in the second group

paired data

observations that are collected - data is also paired when the observations in one group are naturally related to the observations in the other

randomization condition

as a condition of a paired t-test, randomness must be present in the scenario - the pairs can be from a random sample, or the order of treatments can be randomly assigned

H₀: μ_d = Δ₀

the null hypothesis for a paired t-test - the hypothesized difference is almost always zero

10% condition

as a condition of a paired t-test, the sample sizes must be less than or equal to 10% of the population

nearly normal condition

as a condition of a paired t-test, the differences between matched pairs of data must follow a normal model and show a nearly normal shape

independence assumption

as an assumption of a paired t-test, the differences between matched pairs must be independent of each other