Spearman's rank correllation __inbound8748924990758398835.pptx

it's the study of spearman's rank corellation

1. PRESENTATION SPEARMAN’S RANK CORELLATION Presented by Jefferson Tabano

2. The Spearman's rank-order correlation is the nonparametric counterpart of the Pearson product-moment correlation. Spearman's correlation coefficient, (p or r₃) measures the strength and direction of association between two ranked variables. Examples: Mathematics achievement scores of students in math and music. The number of movie releases that a motion picture studio put out and its gross receipts for the year. The number of hospitals and pharmacies in each of ten randomly selected provinces.

3. ASSUMPTIONS FOR THE TEST The two variables should be ordinal, interval or ratio. The scores on one variable must be monotonically related to the other variable.

4. Spearman’s Rank Correlation Formula Where di = difference in paired ranks and n = number of cases. No tied ranks Where Rs = coefficient and n = number of pairs/cases. To test the significance of the coefficient.

5. Textbook Teacher’s 1 Rating Teacher’s 2 Rating A 14 14 B 20 16 C 28 30 D 30 24 E 22 26 F 12 18 G 15 21 H 19 17 Two teachers were asked to rate eight different textbooks for a specific subject on an ascending scale from 0 to 30 points. Points were assigned for each of several criteria, such as content, illustrative examples, and readability. Is there a correlation between the two teachers' ratings? The data are shown in the table below.

6. 1. State the Null and Alternative Hypothesis Null hypothesis (Ho): There is a significant correlation between the two teachers' ratings. Alternative hypothesis (Ha): There is no significant correlation between the two teachers' ratings. 2. State the level of significance a = 0.05

7. Textbook Techer’s 1 Rating Teacher’s 2 Rating Rank T1 Rank T2 Rank Difference (Rank Difference)^2 A 14 14 7 8 -1 1 B 20 16 4 7 -3 9 C 28 30 2 1 1 1 D 30 24 1 3 -2 4 E 22 26 3 2 1 1 F 12 18 8 5 3 9 G 15 21 6 4 2 4 H 19 17 5 6 -1 1 n = 8 = 30

8. 3. Calculate the Degree of Freedom df = n - 2 = 8 - 2 = 6

9. Strong Positive Correlation tcrit = 2.447

10. t = 2.04 tcrit = 2.447 Non - Critical Region

11. 4. Make a Decision t > tcrit , we reject Ho t < tcrit , we accept Ho 5. Interpret the Results Reject (Ho): There is correlation between the two teachers' ratings. Accept (Ha): There is no correlation between the two teachers' ratings.

12. Since t ( 2.04 ) is lesser than tcrit ( 2.447 ), we accept the null hypothesis. Therfore, There is no significant correlation between the two teachers' ratings.

13. THANK YOU!