Question

1. Psychology majors at Towson University ranked the psychology faculty on X= favorite teacher and Y= demanding teacher and the results are presented below:

Teacher                                         Favorite                      Demanding

                                                          Rank                            Rank           

A                                                       5                                    4

B                                                       2                                    3

C                                                       8                                    6

D                                                       1                                    1

E                                                       7                                    8

F                                                       3                                    2

G                                                      4                                    5

H                                                       6                                    7

1. Draw a scatterplot (10 pts)
2. Calculate a Spearman rank order correlation on the back of the page (20 pts)
3. Describe the direction and magnitude of the correlation labeling its effect size (small to strong) (2 pts)
4. What is the critical value of the Spearman rank order correlation? (2 pts)
5. Is the obtained value of the Spearman correlation significant? (1 pt)

Answer 1

Solution-A:

In excel select the data

Go to Insert>scatter

Solution-b:

	Favourite rank(X)	Demanding rank(Y)	d=X-Y	d^2
A	5	4	1	1
B	2	3	-1	1
C	8	6	2	4
D	1	1	0	0
E	7	8	-1	1
F	3	2	1	1
G	4	5	-1	1
H	6	7	-1	1
			total	10

spearman rank correlaton coefficient(rho)=

d is the difference between paired ranks

n -no of pairs

rho=1-6*10/(8*8^2-1)

=1-60/8*63

=0.880952

Describe the direction and magnitude of the correlation labeling its effect size (small to strong) (2 pts)

r=0.880952

there exists a strong relationship between  favorite teacher and demanding teacher

What is the critical value of the Spearman rank order correlation?

n=8

df=n-2=8-2=6

critical value is 0.738

Is the obtained value of the Spearman correlation significant? (1 pt)

Ho:rho=0

Ha:rho not =0

calculated rho=0.880952

critical rho=0.738

calculated rho>critical rho

Reject Ho

Accept Ha

Conclusion:

There is suffcient statistical evidence at 5% level of significance to conclude that relationship between  favorite teacher and demanding teacher is statistically significant