Lectures and practical lab on Correlation analysis

notes on correlation analysis and practical lab using IBM SPSS statistics

1. Correlation & Regression izyan

2. correlation

3. What is correlation ANALYSIS?

4. What is correlation ANALYSIS?

5. Correlation answer…

6. Correlation - scatter plot Use scatter plot for visual assessment of the linear relationship

7. Correlation - scatter plot Use scatter plot for visual assessment of the linear relationship

8. Correlation coefficient It measures the degree of association Pearson’s correlation coefficient measures only the degree of linear relationship between two numerical variables (remember: it cannot conclude cause and effect relationship) The population correlation coefficient, (rho)  measures the strength of the association between the parameters The sample correlation coefficient, r is an estimate of and is used to measure the strength of the linear relationship in the sample observations   Use 𝜌 if your research involves everyone in the population, use r if there is sampling involved

9. Correlation coefficient

10. Characteristics of 𝜌 and r

11. Examples of the correlation coefficient

12. Examples of the correlation coefficient

13. Guideline in interpreting r or 𝜌

14. Factors affecting r

15. Assumptions for correlation analysis *note  if assumption 3 and/or 4 are not met, use Spearman’s correlation

16. Steps in Hypothesis testing

17. Working Example Situation: A study was conducted among 100 women between age of 20 to 30 years old. The researcher want to know whether there is a significant linear correlation between their height and Reproductive Ambition Score. They also would like to know the strength and direction of the relationship. Dataset: 07 correlation data.SAV Variables: height, reproductive ambition score

18. There are 5 variables in this dataset

19. There are 100 samples in the dataset. There are no cells with missing value

20. To answer this question: Is there a significant linear correlation between their height and Reproductive Ambition Score? What are the strength and direction of the relationship?

21. Step 1: hypotheses

22. Step 2: significance level

23. Step 3: Assumption ?? (checked using scatter plot, “elliptical shape”

24. Step 3: Assumption The variables in X-axis and y-axis can be interchanged

25. FROM SPSS OUTPUT This is the example on how the variables in the x-axis and y-axis can be interchanged The scatter plot is in “elliptical shape” Assumptions No 3 and 4 are MET

26. STEP 4: PERFORM THE STATISTICAL TEST 6 9 10 7 8 11

27. FROM SPSS OUTPUT Correlation coefficient, r P value

28. STEP 5: result presentation & interpretation Variables Mean SD Pearson correlation coefficient, r Height Reproductive ambition score Height 161.4 9.09 1 -0.66* Table 1 Descriptive statistics and correlation of variables * p<0.05 There is a significant linear correlation between height and reproductive ambitious score (p<0.001) among the women aged between 20 to 30 years The observed correlation coefficient, r is -0.66, which suggests negative linear relationship and moderate to good correlation (Colton, 1974)

29. STEP 6: CONCLUSION There is a statistically significant negative correlation between height and reproductive ambitious score among the women. We observed that the taller the woman was, the lower was her reproductive ambition.

30. Results presentation Table 1 Descriptive statistics and correlation of variables * p<0.05 Exercise: conduct correlation analyses and fill in the Mean (SD) and r values as indicated Variables Mean SD Pearson correlation coefficient, r Height Reproductive ambition score Career orientation score Maternal personality score Height 161.4 9.09 1 -0.66* Reproductive ambition score 70.65 12.12 - 1 Career orientation score - - 1 Maternal personality score - - - 1