Correlation

1. Correlation

2. Correlation Correlation refers to a relationship that exists between pairs of measures. Knowledge of the strength and direction of the relationship allows us to predict one variable from the other with an accuracy greater than chance.

3. Correlation For example, you can guess someone’s weight more accurately if you know how tall they are because height and weight are positively correlated.

4. Correlation For example, you can guess someone’s weight more accurately if you know how tall they are because height and weight are positively correlated. When two variables are positively correlated that means they tend to both move higher or both move lower at the same time.

5. Correlation For example, you can guess someone’s weight more accurately if you know how tall they are because height and weight are positively correlated. When two variables are positively correlated that means they tend to both move higher or both move lower at the same time. Generally, taller people weigh more than shorted people.

6. Correlation When two variable are negatively correlatedthat means that they change in value inversely. Higher scores on one generally go with lower scores on the other.

7. Correlation When two variable are negatively correlatedthat means that they change in value inversely. Higher scores on one generally go with lower scores on the other. For example, the outdoor temperature and the weight of one’s clothing are negatively correlated. The higher the temperature is, the less clothing we wear. The lower the outdoor temperature, the more clothing we wear.

8. Correlation When two variable are negatively correlatedthat means that they change in value inversely. Higher scores on one generally go with lower scores on the other. For example, the outdoor temperature and the weight of one’s clothing are negatively correlated. The higher the temperature is, the less clothing we wear. The lower the outdoor temperature, the more clothing we wear. Another example: How old you are and how much longer you will live are negatively correlated.

9. Correlation When two variable are negatively correlatedthat means that they change in value inversely. Higher scores on one generally go with lower scores on the other. For example, the outdoor temperature and the weight of one’s clothing are negatively correlated. The higher the temperature is, the less clothing we wear. The lower the outdoor temperature, the more clothing we wear. Another example: How old you are and how much longer you will live are negatively correlated. The existence of a negative correlation does not mean the absence of a relationship. It means that the variables tend to move in opposite directions, not that the variables are unrelated.

10. Correlation A near zero correlationis said to exist when scores on the two variables are unrelated. Higher scores on one variable are just as likely to be accompanied by higher scores as by lower scores on the other variable.

11. Correlation A near zero correlationis said to exist when scores on the two variables are unrelated. Higher scores on one variable are just as likely to be accompanied by higher scores as by lower scores on the other variable. An example: The street number on your house and the odometer reading of your car.

12. Correlation For Each of the Following Examples, State From Your General Knowledge Whether the Correlation Between the Two Variables is Likely to be Positive, Negative, or Near Zero, and Explain Why

13. Average Number of Calories Eaten Per Day and Body Weight

14. Average Number of Calories Eaten Per Day and Body Weight Positive – Caloric Intake is One of the Major Determinants of Body Weight

15. Golf Scores and the Number of Years of Golfing Experience

16. Golf Scores and the Number of Years of Golfing Experience Negative – Golfers Improve with Experience and Hence Would Be Expected to Get Better (Lower) Scores

17. Length of Hair and Shoe Size in Adult Males

18. Length of Hair and Shoe Size in Adult Males Near Zero – It’s Doubtful That These Two Measures Could Be Influenced By Common Factors

19. Amount of Formal Education One Has Received and the Time Spent Collecting Public Assistance (Welfare)

20. Amount of Formal Education One Has Received and the Time Spent Collecting Public Assistance (Welfare) Negative – Educated Individuals Are More Likely to Be Employable and Hence Less Likely to Need Welfare

21. Per Capita Consumption of Alcohol in a Group of Cites and Suicide Rates in Those Cities

22. Per Capita Consumption of Alcohol in a Group of Cites and Suicide Rates in Those Cities Positive – A Common Set of Stresses and Other Factors Are Likely to Influence Rates of Both Alcoholism and Suicide in a Given Community

23. Number Correct on a Current Events Test and Time Spent Reading the Newspaper

24. Number Correct on a Current Events Test and Time Spent Reading the Newspaper Positive – The Newspapers Are Full of Stories Concerning Current Events Around the World

25. Strength of Traditional Religious Beliefs and Favorableness of Attitude Toward Abortion on Demand

26. Strength of Traditional Religious Beliefs and Favorableness of Attitude Toward Abortion on Demand Negative – Members of Traditional Religious Groups Are More Likely to Regard Abortion as Immoral Than Others

27. Height and Political Conservatism

28. Height and Political Conservatism Near Zero

29. Correlation Correlations can be represented either graphically by the construction of a special type of graph called a scatter-plot diagram or through the computation of an index called a coefficient of correlation.

30. Correlation Correlations can be represented either graphically by the construction of a special type of graph called a scatter-plot diagram or through the computation of an index called a coefficient of correlation. Most of the seminal work that went into the development of these representation was done by the early statistician Karl Pearson, employed by the Guinness Brewery.

31. Correlation Construction of a scatter-plot diagram requires acquiring pairs of scores from each subject. For example, suppose we wanted to look at the relationship between height and self esteem in men. Perhaps we have a hypothesis that how tall you are effects your level of self esteem. So we collect pairs of scores from twenty male individuals. Height, measured in inches, and Self Esteem based on a self-rating scale (where higher scores mean higher self esteem).

37. Linear Regression

38. Linear Regression Best Fitting Line Line of Prediction

39. Coefficient of Correlation

40. Coefficient of Correlation A statistical computation that indicates the strength and direction of an underlying correlation

41. Coefficient of Correlation A statistical computation that indicates the strength and direction of an underlying correlation

42. Coefficient of Correlation A statistical computation that indicates the strength and direction of an underlying correlation Always results in a signed number in the range from -1.00 to +1.00 If the sign is positive, that indicates the underlying relationship is a positive correlation. If the sign is negative, it indicates an underlying negative correlation. The closer the value is to “1” (either positive or negative) the stronger is the indicated underlying relationship.

43. Coefficient of Correlation A statistical computation that indicates the strength and direction of an underlying correlation Always results in a signed number in the range from -1.00 to +1.00 If the sign is positive, that indicates the underlying relationship is a positive correlation. If the sign is negative, it indicates an underlying negative correlation. The closer the value is to “1” (either positive or negative) the stronger is the indicated underlying relationship.

44. Coefficient of Correlation A statistical computation that indicates the strength and direction of an underlying correlation Always results in a signed number in the range from -1.00 to +1.00 If the sign is positive, that indicates the underlying relationship is a positive correlation. If the sign is negative, it indicates an underlying negative correlation. The closer the value is to “1” (either positive or negative) the stronger is the indicated underlying relationship.

45. Coefficient of Correlation r = +.86

46. Coefficient of Correlation Sign r = +.86

47. Coefficient of Correlation Magnitude Sign r = +.86

48. Coefficient of Correlation Magnitude Sign r = +.86 Direction

49. Coefficient of Correlation Magnitude Sign r = +.86 Direction Strength

50. Coefficient of Correlation r = +.86 r = +.31 r = -.96 r = +.04 r = +1.02