Prepared by: Assoc. Prof. Dr Bahaman Abu Samah Department of Professional Development and Continuing Education Faculty of Educational Studies
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1 Prepared by: Assoc. Prof. Dr Bahaman Abu Samah Department of Professional Development and Continuing Education Faculty of Educational Studies Universiti Putra Malaysia Serdang
2 Participants to be able to: 1. Understand when to apply Spearman/Rank Ordered Correlation 2. Run the analysis 3. Interpret the results
3 Determine relationship between two ranked ordered variables DV Ordinal IV Ordinal DV Interval/Ratio IV Interval/Ratio OR
4 Describe Strength Direction Determine r s Hypothesis Test
5 X Y X X Y Y Positive Relationship Negative Relationship No Relationship
6 Range of -1 r s 1
7 r Strength of Relationship <.2 Negligible Relationship Low relationship Moderate relationship High relationship >.9 Very high relationship
8 Alpha (α) Criteria p < α p α Decision Reject H O Fail to reject H O State H O and H A Decision Conclusion sig-value (p)
9 Step 1: Hypotheses H O : ρ s = 0 H A : ρ s 0 ρ s < 0 ρ s > 0 Step 2: Significance level Set the significance level (alpha) Generally in social science α=.05 Step 3: Significance value Report the significance value (p)
10 Step 4: Decision Criteria Decision Whether to Reject OR Fail to reject H O Step 5: Conclusion p < α p α Reject H O Fail to reject H O Reject H O : There is a significant relationship between IV and DV Fail to reject H O : There is no sig. relationship between the IV and DV
11 working Examples
12 Example 1: Pearson Correlation In the recent research poster competition, 10 posters were short listed. Two selected judges were asked to rank the posters according to the prescribed criteria. Data solicited from the two judges are presented in the table below: 1. Determine Spearman rho correlation coefficient 2. Describe the nature of relationship between the two judges 3. Test the hypothesis on the relationship at.01 level of significance ranking of Data set: Judge Poster Data: Spearman 1
13 Procedures Define Variables
14 Procedures Enter Data
15 Procedures Spearman Rho Correlation
16 Results
17 Answer: 1. Correlation coefficient r s =.964 Correlati ons Spearman's rho X Y Correlation Coef ficient Sig. (2-t ailed) N Correlation Coef ficient Sig. (2-t ailed) N **. Correlation is signif icant at the 0.01 level (2-tailed). 2. Nature of relationship X Y ** ** There is a positive and high relationship between ratings of the two judges
18 Cont. 3. Hypothesis test, α =.01 H O : ρ s = 0 H A : ρ s 0 Since p (.000) < α (.01) Reject H O There is a significant relationship between rating of the two judges at.01 level of significance Correlati ons X Y Spearman's rho X Correlation Coef ficient ** Sig. (2-t ailed)..000 N Y Correlation Coef ficient.964** Sig. (2-t ailed).000. N **. Correlation is signif icant at the 0.01 level (2-tailed).
19 Data solicited from a randomly selected sample were used to measure relationship between working environment (X) and work commitment (Y). EDA revealed the work commitment data did not meet the assumption of normality. 1. Determine the appropriate correlation coefficient 2. Describe the nature of relationship between the two variables 3. Test the hypothesis on the relationship at.05 level of significance Data set: ID X Y Data: Spearman 2
20 Cont. 1. Correlation coefficient r =.134 Correlati ons Spearman's rho X Y Correlation Coef ficient Sig. (2-t ailed) N Correlation Coef ficient Sig. (2-t ailed) N X Y Nature of relationship There is a positive and negligible relationship between working environment (X) and work commitment (Y)
21 3. Hypothesis test, α =.01 H O : ρ = 0 H A : ρ 0 Since p (.678) > α (.05) Fail to reject H O There is no significant relationship between working environment (X) and work commitment (Y) at.05 level of significance Correlati ons Spearman's rho X Y Correlation Coef ficient Sig. (2-t ailed) N Correlation Coef ficient Sig. (2-t ailed) N X Y
22 Application Exercises
23 Exercise 1: Data Set 3: Based on the above data set, identify the appropriate variables to run for Spearman Rho correlation For the test: 1. Determine correlation coefficient and describe the nature of relationship 2. Test the hypothesis on the relationship at.05 level of significance State the null and alternative hypotheses State your decision and conclusion; and justify your answer
24 Answer: 1. Correlation coefficient r s = Nature of relationship: 2. Hypothesis H O : H A : Decision and conclusion (Justify):
25 Exercise 2: Data Set: Hatco Based on the above data set, identify the appropriate variables to run for Pearson Product- Moment correlation For the test: 1. Determine correlation coefficient 2. Test the hypothesis on a positive relationship between the variables at.01 level of significance State the null and alternative hypotheses State your decision and conclusion; and justify your answer
26 Answer: 1. Correlation coefficient r s = Nature of relationship: 2. Hypothesis H O : H A : Decision and conclusion (Justify):
27 Table 1: Spearman Correlation Coefficients between Selected Variables and Job Performance Variables r s p Age Income Years of Service Peer Support Work environment Motivation
28 Exercise 2: Data Set: Hatco Based on the above data set, identify the appropriate variables to run for Spearman correlation For the test: 1. Determine correlation coefficient 2. Test the hypothesis on a positive relationship between the variables at.01 level of significance State the null and alternative hypotheses State your decision and conclusion; and justify your answer
29 Answer: 1. Correlation coefficient r = Nature of relationship: 2. Hypothesis H O : H A : Decision and conclusion (Justify):
30 Table 2: Spearman Correlation Coefficients between Selected Variables and Satisfaction Variables r s p Delivery speed Price level Price flexibility Manufacturer image Service Salesforce image Product quality Usage level
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