t Test for Two Related Samples (Repeated Measures)
Repeated measures?Whenever the same subject is measured
more than once.
Two related samples occur whenever each observation in one sample is paired, on a one-to-one basis, with a single observation in the other sample.
What is compared?The mean difference scores between the two
groups.
D = Σ D n
The sign of D is crucial.
Problems with repeated measures:Enough time must pass between measures to
ensure no bias or lingering effects.Counterbalancing – half of the subjects
experience the conditions in the opposite order. A then B or B then A.
HypothesesNull Hypothesis
H0: μD = 0
Alternative HypothesisDirectional
H1: μD > 0 or H1: μD < 0
Non Directional H1: μD ≠ 0
t ratio for two population means(two related samples)
t = sample mean difference – hypothesized population mean difference
estimated standard error
or D - µDhyp
sD
Calculations1. Assign a value to n, the number of
difference scores2. Subtract X2 from X1 to obtain D3. Sum all D scores4. Calculate mean of D5. Calculate SS for D6. Find standard error SD
7. Solve for t
Use the EPO dataScores for Two EPO Experiments
X1 X2 D
12 7 5
5 3 2
11 4 7
11 6 5
9 3 6
18 13 5
Use the EPO data (p 323)
Scores for Two EPO Experiments
X1 X2 D D2
12 7 5 25
5 3 2 4
11 4 7 49
11 6 5 5
9 3 6 36
18 13 5 25
30 164
Calculations
SSD = ΣD2 –
SD =
SD =
(ΣD) 2
n
√SSD
n - 1
SD
√ n
Calculations
t = D – µDhyp
SD
Confidence interval (p 319)
D ± (tconf)(sD)
Find value of tconf in Table B
Standardized Effect Size, Cohen’s d
d = D sD
Progress Check 15.2Days Ill Due to Colds
Pair Number Vitamin C (X1) Fake Vitamin C (X2)
1 2 3
2 5 4
3 7 9
4 0 3
5 3 5
6 7 7
7 4 6
8 5 8
9 1 2
10 3 5
t test for population correlation (p329)
t =
ρhyp = 0
r - ρhyp
√1 – r2
n - 2
Progress Check 15.6 (p 331)A random sample of 27 California taxpayers
reveals an r = .43 between years of education and annual income. Use t to test the null hypothesis at the .05 level of significance that there is no relationship between educational level and annual income for the population of California taxpayers.
Answer on 511.
Top Related