1. Correlation

2. Definition Shows the direction and the strength of the relationship between two variables.

3. Scatter plot for correlational data

4. Examples of positive and negative relationships

5. Positive correlation: when a small amount of one variable is associated with a small amount of another variable, and a large amount of one variable is associated with a large amount of the other.

6. Negative correlation: when a small amount of one variable is associated with a large amount of another variable, and a large amount of one variable is associated with a small amount of the other. WEIGHT 220210200190180170160150140 PULLUPS 120 110 100 90 80 70

7. Perfect Correlation As X changes a unit, Y changes a specific increment.

8. example WEIGHT 200190180170160150140 STRENGTH 100 90 80 70 David Peter Mark Jim Ken A perfect correlation

9. Not always the correlation is perfect. Guess?

11. WEIGHT 220210200190180170160150140 STRENGTH 120 110 100 90 80 70

12. Zero correlation: when there is no association between two variables.

13. Example A zero correlation

14. WEIGHT 220210200190180170160150140 IQ 120 110 100 90 80 70 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

15. Three degrees of relationship ZeroPositivePerfect

16. Examples of different values for relationships

17. For each pair, tell whether r is high, moderate, low or zero. ± practice 1- The number of cars on different highways and the number of accidents. 2- The height and age of k-12 students. 3- k-12 students’ scores on a math test and a science test 4- k-12 students’ scores on a math test and a PE test 5- The birthrate and social economic level 6- The length of the base of a square and the length of its diagonal. 1- Correlation between math ability and shoe size in K-12 2- Height and intelligence in adult population 3- Crime rate and the number of churches 4- The academic degree and income

18. Interpreting correlations Correlation does not demonstrate causation 1.Number of books at home and students’ academic achievement 2.The faster windmills are observed to rotate, the more wind is observed to be 3. The number of storks and birth rate in Denmark 4.Earlier wake- up times are consistently related to higher GPA.

19. Real examples Correlation Confusion Eating chocolate, number of acnes. Drug use and income Crime rate and the number of death penalties Joining terrorists and job loss

20. Changing Together

21. Conclusion If A correlates with B, three possible causal relationship exist A causes B, B causes A, or C causes both A and B/

22. Restricted range

24. Cognitive Development Fear of Death r = -.40 r =.52 r =.10 First graders Sixth Graders

25. Correlation of sample and population

26. Influence of outlier on correlation

29. Spearman correlation Spearman correlation formula is used with data from an ordinal scale (ranks) –Used when both variables are measured on an ordinal scale StudentsRank in MathRank in science Jim13 Jennifer22 Abdul41 Ross34 Kate55 Tara76 Mike67

30. Other types of correlation