The paired/related t-test Flashcards
We are following a repeated measures design. What t-test do we used to measure differences in means?
Related/paired t-test
Why do we use related/paired t-tests to look for differences in means in repeated subjects design?
Because we can pair the data
It seems sensible to calculate the difference or change in the paired scores within participants
What is the formula for the t-value?
t = (sample mean - pop. mean) / e.s.e
Aliens visiting from the planet Ziltoidia 10 are keen to test the hypothesis that they experience height changes during their stay on earth due to our higher gravity. They tasked you (earth’s premier scientist and statistician) with addressing this question shortly after arrival on Earth. As a good experimenter you had the foresight to measure the heights of 25 Ziltoidians at this point. In line with your research plan you have also now measured the height of the same 25 Ziltoidians one year later, and worked out the change in height (height on arrival minus height one year later) for each ziltoidian.
The sample mean height change m = .25 cm and the sample s.d. height change s = 0.65cm.
a) the research hypothesis is (1 or 2)-tailed
b) The estimated standard error of the mean for height change scores is (…….)
c) Assuming the null hypothesis is true, the t-score associated with the sample mean change score is (……..)
HINT: Use the formula t = (m - 0) / e.s.e.
d) Indicate whether you should reject the null hypothesis (reject or fail to reject)
a) 2-tailed
b) 0.13 (0.65 / SQRT 25)
c) 1.92 (0.25 - 0) / 0.13
d) fail to reject
An educational psychologist wishes to test the 2-tailed hypothesis that a new year-long reading program at a local school will change reading ability. The psychologist obtains reading age scores from a year 2 class (N = 36) that has taken part in the new program for the last academic year. Scores were obtained at the start and end of the school year (note that scores are appropriately transformed to factor out natural age-related improvements in reading ability). The data collected are summarised below:
Pre-program: sample mean = 6.81, sample s.d. = 1.1
Post-program: sample mean = 7.19, sample s.d. = 1.2
sample s.d. for paired reading ability change scores (post-pre) = 1.32
a) the research hypothesis is (1 or 2) -tailed
b) The estimated standard error of the mean for paired reading ability change scores is (……..)
c) Assuming the null hypothesis is true, the t-score associated with the sample mean change score is (……….)
d) Indicate whether you should reject the null hypothesis (select reject or fail to reject)
a) 2-tailed
b) 0.22 (1.32 / SQRT 36)
c) 1.73 (-0.38 - 0) / 0.22
d) fail to reject
