Question

Question 5 A researcher wants to find out the effect of marriage on the self‐esteem of couples. He measured the average self‐esteem scores of couples before marriage and a year after their wedding day. Their average self‐esteem scores are shown below.

Pair	After one year	Before marriage
A	14	8
B	16	4
C	18	10
D	10	10
E	9	9
F	16	9

Is there a significant difference in the self‐esteem scores before marriage and a year after the couples’ wedding day? Using the 5 steps of hypothesis testing, test at α .05, one‐tailed test. If the difference is significant, test the effect size through Cohen’s d and describe the effect size.   

**** I am specifically stuck on showing the work of the cohen d calculation of effect size!

Answer 1

Answer:

Question 5 A researcher wants to find out the effect of marriage on the self‐esteem of couples. He measured the average self‐esteem scores of couples before marriage and a year after their wedding day. Their average self‐esteem scores are shown below.

Pair	After one year	Before marriage
A	14	8
B	16	4
C	18	10
D	10	10
E	9	9
F	16	9

Is there a significant difference in the self‐esteem scores before marriage and a year after the couples’ wedding day? Using the 5 steps of hypothesis testing, test at α .05, one‐tailed test. If the difference is significant, test the effect size through Cohen’s d and describe the effect size.   

**** I am specifically stuck on showing the work of the cohen d calculation of effect size!

Null hypothesis Ho: d= 0 Alternative hypothesis: H: Md > 0

Upper tail test

Difference = after-before

u /Ps Pr!

5.5 4.7223/6

= 2.8529

DF = n-1 =5

Table value of t with 5 DF at 0.05 level =2.015

Rejection Region: Reject Ho if t > 2.0150

Calculated t = 2.8529 , falls in the rejection region

The null hypothesis is rejected.

There is a significant difference in the self‐esteem scores before marriage and a year after the couples’ wedding day.

Cohen d is (divide the mean of the differences by the SD of the differences)

Cohen d =5.5/ 4.7223=1.164686699

=1.16

Since calculated Cohen d =1.16 which is greater than 0.8, the effect size is large.

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	6
DBar	5.5000
Degrees of Freedom	5
SD	4.7223
Standard Error	1.9279
t Test Statistic	2.8529
Upper-Tail Test
Upper Critical Value	2.0150
p-Value	0.0179
Reject the null hypothesis