Using the "Example Dataset" and SPSS, apply the t-test to assess the following statement: "Men and women have different incomes in this city."
Sex |
Female |
Male |
Female |
Male |
Female |
Female |
Female |
Male |
Female |
Male |
Female |
Male |
Female |
Male |
Male |
Male |
Female |
Male |
Male |
Female |
Female |
Female |
Male |
Male |
Female |
Male |
Female |
Female |
Male |
Male |
Annual_Income* |
51000 |
23000 |
35000 |
10000 |
28000 |
5000 |
46000 |
36000 |
51000 |
12000 |
78000 |
34000 |
15000 |
28000 |
28000 |
24000 |
55000 |
62000 |
32000 |
7000 |
17000 |
64000 |
5000 |
14000 |
20000 |
72000 |
85000 |
15000 |
64000 |
27000 |
A t-test for two means with unknown population variances and two independent samples is a hypothesis test that attempts to make a claim about the population means (μ2).
More specifically, a t-test uses sample information to assess how plausible it is for the population means μ1 and μ2 to be equal. The test has two non-overlapping hypotheses, the null and the alternative hypothesis.
The formula for a t-statistic for two population means
Steps to be followed in SPSS
1) Enter the data in Data view with variable named as Annual Income and Gender
2) Go to analyse--> compare means-->independent sample t- test
3) Test variable = Annual_income, Grouping variable = Gender
4) define group as 1 and 2 for male and female.
5) click on ok
Annual_income |
Gender |
51000.00 |
Female |
23000.00 |
Male |
35000.00 |
Female |
10000.00 |
Male |
28000.00 |
Female |
5000.00 |
Female |
46000.00 |
Female |
36000.00 |
Male |
51000.00 |
Female |
12000.00 |
Male |
78000.00 |
Female |
34000.00 |
Male |
15000.00 |
Female |
28000.00 |
Male |
28000.00 |
Male |
24000.00 |
Male |
55000.00 |
Female |
62000.00 |
Male |
32000.00 |
Male |
7000.00 |
Female |
17000.00 |
Female |
64000.00 |
Female |
5000.00 |
Male |
14000.00 |
Male |
20000.00 |
Female |
72000.00 |
Male |
85000.00 |
Female |
15000.00 |
Female |
64000.00 |
Male |
27000.00 |
Male |
Group Statistics |
|||||
Gender |
N |
Mean |
Std. Deviation |
Std. Error Mean |
|
Annual_income |
Male |
15 |
31400.0000 |
20138.09468 |
5199.63369 |
Female |
15 |
38133.3333 |
25575.84426 |
6603.65459 |
Independent Samples Test |
||||||||||
Levene's Test for Equality of Variances |
t-test for Equality of Means |
|||||||||
F |
Sig. |
t |
df |
Sig. (2-tailed) |
Mean Difference |
Std. Error Difference |
95% Confidence Interval of the Difference |
|||
Lower |
Upper |
|||||||||
Annual_income |
Equal variances assumed |
2.236 |
.146 |
-.801 |
28 |
.430 |
-6733.33333 |
8405.02495 |
-23950.24647 |
10483.57981 |
Equal variances not assumed |
-.801 |
26.540 |
.430 |
-6733.33333 |
8405.02495 |
-23993.03136 |
10526.36470 |
From the above table p value for t-test for Equality of Means is 0.430 which is greater than 0.05 (i.e. 5% level of significance ) so we fail to reject the null hypothesis and conclude that there is no significant difference between the annual income of female and male.
Effective size
Cohen's d = (M2 - M1) ⁄ SDpooled
SDpooled = √((SD12 + SD22) ⁄ 2)
Cohen's d = (38133.33 - 31400) ⁄ 23018.104402 = 0.292523.
Gates' delta = (38133.33 - 31400) ⁄ 20138.09 = 0.334358.
Hedges' g = (38133.33 - 31400) ⁄ 23018.104402 = 0.292523.
answer
Using the "Example Dataset" and SPSS, apply the t-test to assess the following statement: "Men and...