LECTURE 9 CORRELATION (Pearsons r and t test).pptx
- 1. CORRELATION ANALYSIS WILFREDO P MARINO ASSOCIATE PROFESSSOR
- 2. Correlation Analysis 🞂 Almost all variables measured in a research study are related. 🞂 Correlation analysis used to measure strength of association (linear relationship) between two numerical variables. 🞂 Population correlation coefficient ρ (Rho) is used to measure the strength of relationship between the two variables. 🞂 Sample correlation coefficient r is an estimate of ρ and used to measure the strength of the linear relationship in the sample observations
- 3. Scatter Plot Y X Y X Y X Y Y r = -1 r = -0.6 r = 0 r = 0.6 r = 1
- 4. Features of ρ and r 🞂 Unit free 🞂 Range between -1 and 1 🞂 The closer to -1, the stronger the negative linear relationship 🞂 The closer to 1, the stronger the positive linear relationship 🞂 The closer to 0, the weaker the linear relationship 🞂 Correlation coefficient tells us about the strength and direction of the linear relationship between variables.
- 5. INTERPRETATION Coefficient Verbal Interpretation 0.00-0.20 Weak correlation, almost negligible relationship 0.21-0.40 Slight correlation, definite but small relationship 0.41-0.70 Moderate correlation, substantial relationship 0.71-0.90 High correlation, marked relationship 0.91-1.00 Very high correlation, very
- 6. Pearson’s Product Moment Correlation Coefficient Pearson’s r
- 7. EXAMPLE 🞂A researcher would like determine the degree of relationship between job performance and salary of engineers in a company. Engineers Job Performance Salary in Thousan d Pesos A 75 80 B 70 75 C 65 65 D 90 95 E 85 90 F 85 85 G 80 90 H 70 75 I 65 70 J 90 90
- 8. YOU TRY 🞂 A researcher would like determine the degree of relationship between grade in statistics and research. Statistic s Research 1 2 2 1 2 2 3 1 3 1 2 2 2 3
- 9. Engineers Job Performance x Salary in Thousand Pesos y A 75 80 B 70 75 C 65 65 D 90 95 E 85 90 F 85 85 G 80 90 H 70 75 Assign Variables x and y
- 10. 75 80 6000 5625 6400 70 75 5250 4900 5625 65 65 4225 4225 4225 90 95 8550 8100 9025 85 90 7650 7225 8100 85 85 7225 7225 7225 80 90 7200 6400 8100 70 75 5250 4900 5625 65 70 4550 4225 4900 90 90 8100 8100 8100 Complete the table
- 11. 75 80 6000 5625 6400 70 75 5250 4900 5625 65 65 4225 4225 4225 90 95 8550 8100 9025 85 90 7650 7225 8100 85 85 7225 7225 7225 80 90 7200 6400 8100 70 75 5250 4900 5625 65 70 4550 4225 4900 90 90 8100 8100 8100 775 815 64000 60925 67325 Summation
- 12. Pearson’s r
- 13. Pearson’s r
- 14. Pearson’s r
- 15. Interpretation The obtained correlation coefficient 0.949 shows a very high positive correlation or very dependable relationship between the variables job performance and salary of engineers in a company.
- 16. Significance of the Correlation Coefficient 🞂 Decision whether the linear relationship in the sample data is strong enough to use to model the relationship in the population. 🞂 Hypothesis test decide whether the value of the population coefficient ρ is “close to zero” or “significantly different from zero”.
- 17. Test Statistics
- 18. Test Statistics
- 20. SUMMARY TABLE Variable df r t-value Critical Value Ho Job Performance and Salary 8 0.94 9 7.044 2.306 Rejec t Since the computed t-value (7.044) is greater than the 2.306 critical value, the decision is to reject the null hypothesis. The result shows that there is a sufficient evidence at 0.05 level of significance to show that there is a significant relationship between the job performance and salary of engineers in a company
- 21. DATA ANALYSIS TOOL PAK Correlation
- 22. ENCODE THE DATA
- 23. CLICK DATA THEN DATA ANALYSIS DATA DATA ANALYSIS
- 26. LABELS IN FIRST ROW and ALPHA Check the Label
- 27. OUTPUT RANGE Output Range in $D$1
- 29. ACTIVITY 1
- 30. ACTIVITY 2
- 31. AD MAJOREM DEI GLORIAM “Torture the data, and it will confess to anything.” “Errors using inadequate data are much less than those using no data at all.” Charles Babbage