Download Two Related Samples t Test

Two Related Samples t Test
In this example 10 students saw five pictures of attractive people and five pictures of unattractive
people. For each picture, the students rated the friendliness of the person on a 10 point scale
(where 1 was very unfriendly and 10 was very friendly.) The mean friendliness rating for the
attractive and unattractive pictures was calculated. The researcher wants to know whether the
attractiveness of the picture affects the perceived friendliness of the person.
1. Step 1: Write the null and alternative hypotheses and specify the probability of making a
Type I error:
H0: µD = 0
H1: µD ≠ 0
α = .05
2. Step 2: Sketch and determine the critical regions:
Critical region
-6
-4
Critical region
-2
0
2
4
6
df = n – 1 = 10 – 1 = 9
From a table of critical t scores with α= .05, two-tailed, tcritical(9) = ± 2.262
(The critical t is both positive and negative because we can reject H0 if μ is either > 0 or < 0.)
3. Step 3: Calculate the test statistic:
a. Open SPSS
b. Either type the data (see the last page for the data) or open a data set. The class
data set (for homework) is available from
<http://academic.udayton.edu/gregelvers/psy216/SPSS/216dataS11.sav> . Save the
data file somewhere and open it with SPSS.
c. Analyze | Compare Means | Paired-Samples T Test
d. Move the two dependent variables (that correspond to the control and treatment
conditions) into the Paired Variables box. You can either drag the variable names
into the box, or select the variables by clicking on them and then clicking on the
arrow button between the two boxes.
e. Click the OK button
f.
The SPSS output viewer will open
g. The first part of the output gives descriptive statistics for the dependent variable for
each condition (level of the independent variable):
Paired Samples Statistics
Mean
Pair 1
N
Std. Deviation
Std. Error Mean
attractive
7.1000
10
1.66333
.52599
unattractive
5.9000
10
1.96921
.62272
h. This tells us that for the mean friendliness rating for the attractive faces is 7.100
(mean column and attractive row), the sample standard deviation (s) is 1.663, and
the standard error of the means (sM) is 0.5265 (which should and does equal s / √N =
1.663 / √10). Likewise, this tells us that for the unattractive faces there were 10
scores (in the N column of the unattractive row), that the sample mean ( ) is 5.900
(mean column and the unattractive row), the sample standard deviation (s) is 1.969,
and the standard error of the means (sm) is 0.623 (which should and does equal s /
√N = 1.969 / √10).
i.
The last part of the output gives us the value of the t-test:
Paired Samples Test
Paired Differences
95% Confidence
Mean
Pair 1
attractive - unattractive
1.20000
Std.
Interval of the
Std.
Error
Difference
Deviation
Mean
Lower
.46667
.14433 2.25567
1.47573
Upper
Sig. (2t
2.571
df
tailed)
9
.030
n. This tells us the mean of the difference scores (1.200), the standard deviation of the
difference scores (1.476), the standard error of the mean of the difference scores
(0.467), the 95% confidence interval of the difference scores (from 0.144 to 2.256),
the value of tobserved = 2.571, df = 9 and p = .030.
4. Step 4: Make a decision: Find the p value for the t-test (in the column labeled Sig. (2tailed)). For this output, that value is .030. If the p value is less than or equal to the α level,
then you should reject H0. Otherwise, you should fail to reject H0. Because p = .030 and α =
.05, we reject H0 and conclude that it is likely the case that the perceived friendliness differs
for attractive and unattractive pictures of people.
5. Cohen’s d must be calculated by hand. Some of the values are from the SPSS output:
Estimated value of Cohen’s d = MD / sD
= 1.200 / 1.476
= 0.813
This is a large effect (greater than .8)
6. r2 must be calculated by hand. Both values for the formula can be gotten from the SPSS
output:
r2 = t2 / (t2 + df) = 2.5712 / (2.5712 + 9) = .423
This is a large effect (greater than .25).
Steps 1 and 2 are identical to those used with SPSS.
Step 3: Calculate the test statistic:
Attractive
9
8
7
8
6
9
5
7
8
4
Unattractive
7
8
8
8
6
5
4
5
6
2
Σ
n
Attractive - Unattractive
2
0
-1
0
0
4
1
2
2
2
12
10
SS
1.2
19.6
sD2 = SSD / df = 19.6 / 9 = 2.178
sMD = √(SD2 / n) = √(2.178 / 10) = 0.467
t = MD / sMD
= 1.2 / 0.467
= 2.570
Step 4: Decide:
If the observed or calculated value of t (= 2.570) is in one off the tails cut off by the critical t (from a
table, ±2.262; see step 2 above), then reject H0, otherwise, fail to reject H0. Reject H0. It is likely the
case that the perceived friendliness differs for attractive and unattractive pictures of people.