Question

Using the "Example Dataset" and SPSS, apply the t-test to assess the following statement: "Men and women have different incomes in this city."

1. Describe what t-test is the most appropriate and explain why. Discuss whether you used a one-tailed or two-tailed test and explain why.
2. Using SPSS, calculate the t-test and provide the test statistic and critical value assuming an alpha of .05.
3. Calculate the effect size using r².

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

Answer 1

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) ⁄ SD_pooled

SD_pooled = √((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