Lab # 3 — One Sample, Independent, & Paired Samples t-tests (20 points)
1.
Practice computing One Sample t-test (7 points)
Reminder: A sample mean to be compared with a known value.
Scenario:
Suppose you know that the national average on the ABC Attitude Toward Math Scale is 4.0. You draw a random sample of 12th
grade students from a rural school district in Alabama, administer the attitude scale to the sample, and obtain a mean of 3.7 among the students. You want to determine if the sample mean of 3.7 is significantly different from the national average of 4.0. Conduct a one sample
t
test.
a.
State the null (HO) and alternative (HA) hypothesis using statistical notation (1 point)
b.
Create a database in SPSS. Use data provided in Table 1.1.
Use SPSS to perform the appropriate statistical test. (1 point)
c.
Report the mean and the standard deviation. Use APA format. (1 point)
d.
Report the statistical test results. Use APA format. (1 point)
e.
Compute an effect size (Cohen’s d). What is the strength of the effect? (1 point)
f.
Decision about the null hypothesis (reject or fail to reject)? (1 point)
g.
Discuss the results. What verbal conclusions can be made? (1 point)
2.
Practice computing Independent Sample t-test (7 points)
Reminder: Compares two samples that are independent from each other.
Scenario:
Next, supposed you wanted to compare the female and male students’ attitude towards math. To determine if there is a difference in attitude towards math between the two samples, conduct an independent sample t test.
a.
State the null (HO) and alternative (HA) hypothesis using statistical notation (1 point)
b.
Use SPSS to perform the appropriate statistical test. (1 point)
c.
Can we assume equal variances? Report results of Levene’s test. (1 point)
d.
Compute an effect size (Cohen’s d). What is the strength of the effect? (1 point)
e.
Report the mean and the standard deviation. Report the t test results. Use APA format. (2 points)
f.
Discuss the results. What verbal conclusions can be made? Include decision about the null hypothesis (reject or fail to reject)? (1 point)
3.
Practice computing Paired Sample t-test (6 points)
Reminder: Compares two samples that are independent from each other.
Scenario:
Next, suppose you found in your research that overall math attitudes scores were low, indicating that on average, students did not have positive experience with math. So, you design a program to boost positive experiences in math through activities and problem-based learning. All students in your sample enroll in the program. You want to compare their pre-program attitude towards math score to their post-program attitude toward math score. After participating in the new program, you administer the ABC Attitude Toward Math Scale again. To determine if there is an increase in positive attitude towards math from pre-program to post-program, conduct a paired samples t test.
a.
State the null (HO) and alternative (HA) hypothesis using statistical notation (1 point)
b.
You will create a new database. Use data provided in Table 1.2.
(1 point)
c.
Use SPSS to perform the appropriate statistical test. (1 point)
d.
Report the mean and the standard deviation. Report the t test results. Use APA format. (1 point)
h.
Compute an effect size (Cohen’s d). What is the strength of the effect? (1 point)
e.
Discuss the results. What verbal conclusions can be made? Include decision about the null hypothesis (reject or fail to reject)? (1 point)
Table 1.1- Student Sample Scores on
Attitude Toward Math Scale
|
Student ID
|
Math Score
|
Gender
|
1
|
2
|
Male
|
2
|
10
|
Female
|
3
|
6
|
Male
|
4
|
0
|
Female
|
5
|
6
|
Male
|
6
|
4
|
Female
|
7
|
3
|
Male
|
8
|
4
|
Female
|
9
|
5
|
Male
|
10
|
1
|
Female
|
11
|
1
|
Male
|
12
|
5
|
Female
|
13
|
7
|
Male
|
14
|
1
|
Female
|
15
|
1
|
Male
|
16
|
3
|
Female
|
17
|
4
|
Male
|
18
|
4
|
Female
|
19
|
6
|
Male
|
20
|
1
|
Female
|
Table 1.2-
Pre-Program and Post-Program Attitude Toward Math
|
Student ID
|
Pre-Program Math Score
|
Post-Program Math Score
|
1
|
2
|
4
|
2
|
10
|
10
|
3
|
6
|
7
|
4
|
0
|
2
|
5
|
6
|
10
|
6
|
4
|
6
|
7
|
3
|
7
|
8
|
4
|
8
|
9
|
5
|
6
|
10
|
1
|
2
|
11
|
1
|
3
|
12
|
5
|
6
|
13
|
7
|
9
|
14
|
1
|
2
|
15
|
1
|
1
|
16
|
3
|
5
|
17
|
4
|
6
|
18
|
4
|
9
|
19
|
6
|
8
|
20
|
1
|
3
|