James W. Grice, Ph.D.
Oklahoma State University, 2018
Dependent t-test
Use when...
1 2
Use this inferential statistical test when you wish to compare two population means, ì and ì,
and the observations are dependent (or systematically paired). You do not know the population
means nor either population standard deviation (or variance). By “dependent” we mean that the
observations come in pairs; e.g., IQ scores might be obtained from the same sample of persons
on two different occasions (as in a repeated measures design), or observations regarding marital
satisfaction might be obtained form husband and wife pairs.
This test is also known by different names, such as correlated t-test, matched-pairs t-test, and
paired samples t-test.
Assumptions
• Random sampling
• Sampled pairs of observations are independent
• Population distribution for difference scores is normal
• Variable for which means are computed is continuous
o
• H is true
Hypotheses
Usual Form Alternative Form
o 1 2 o diff
H : ì = ì H : ì = 0
A 1 2 A diff
H : ì > ì H : ì > 0
1 2 diff
or ì < ì or ì < 0
Sampling Distribution and Critical Values
The t distribution is the sampling
crit
distribution from which t is
determined. The darkened area in
the distribution to the right is the
obs
“rejection region.” When t falls
in the rejection region, the result is
crit
“statistically significant”, which means that the null hypothesis is rejected. The t value is taken
from a table of such values or determined using an online calculator. The shape of the t
distribution changes depending upon the number of people (observations) in the sampling
process. As the sample size grows larger, the distribution approaches a normal curve. For
crit
smaller sample sizes, it is somewhat platykurtic. To obtain the correct t value, the degrees of
pairs
freedom value is used. For the dependent t-test, df = n - 1.
