1. Correlation

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

3. Scatter plot for correlational data

4. 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 .

5. 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
220
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PULLUPS
120
110
100 90 80 70

6. Examples of positive and negative relationships
Beer
Coffee

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

8. STRENGTH WEIGHT example A perfect correlation David Peter Mark Jim Ken
200
190
180
170
160
150
140
STRENGTH
100 90 80 70
David
Peter
Mark
Jim
Ken
A perfect correlation

9. Is this
correlation
perfect?

11. 120
110
100 90 80
STRENGTH 70
140
150
160
170
180
190
200
210
220
WEIGHT

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

13. Example
A zero
correlation

14. 4
120 15 7 8 13 10 17
110 9 5 20
100 19 IQ 2 90 12 1 14 80 6 18 11 16 3 70
140
150
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220
WEIGHT

15. Three degrees of relationship
Zero
weak
Perfect

16. Examples of different values for relationships

17. practice
For each pair, tell whether r is high, moderate, low or zero.±
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
The number of cars and the number of accidents.
The height and age of k-12 students.
k-12 students’ scores on a math test and a science test
k-12 students’ scores on a math test and a PE test
The birthrate and social economic level
The length of the base of a square and the length of its diagonal.

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

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

20. Real examples Correlation Confusion
Eating chocolate, number of acnes.
Drug use and income
Crime rate and the number of death penalties
Number of youth Joining terrorists and unemployment

21. Changing Together

22. Changing Together

23. Factors affecting correlation

24. Restricted range

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

27. Correlation of small sample and population

28. Influence of outlier on correlation

29. Types of correlation index

30. Types of correlation index

31. The Correlational Research Strategy
Chapter 12

32. Correlational Research
The goal of correlational research is to describe the relationship between variables and to measure the strength of the relationship.

33. 3 characteristics
A correlation describes three characteristics of a relationship.
The direction (positive / negative)of the relationship.
The form (linear/ nonlinear) of the relationship.
The consistency or strength (magnitude) of the relationship.

34. Direction
In a positive relationship, there is a tendency for two variables to change in the same direction.
In a negative relationship, there is a tendency for two variables to change in opposite directions.

35. 3 forms of correlation Linear correlation
Data points in the scatter plot tend to cluster around a straight line. The size of increase in Y is consistently predictable (not accurately).
(height and age)- Pearson
Monotonic correlation
The relationship is consistent and predictable, but not linear.
(practice & Performance) Spearman
Nonlinear correlation
When all the points on the scatter diagram tend to lie near a smooth curve.

36. 2 forms of correlation

37. 2 forms of correlation
Example?

38. chi- square
If both variables are non- numerical, the relationship is typically evaluated by organizing the data in a matrix.
The matrix shows the frequency or number of individuals in that cell and the data are evaluated using a chi- square hypothesis test

39. Chi- Square
Drama
Action
Comedy
Latino 4 12 10
Asian 8
White 19 18 14

40. APPLICATIONS OF THE CORRELATIONAL STRATEGY
Prediction (SAT & GPA)
Reliability and Validity (Test & Retest)
Evaluating Theories (IQ and Math)

41. coefficient of determination
The squared value of a correlation is called the coefficient of determination and measures the percentage of variability in one variable that is determined, or predicted, by its relationship with the other variable.

42. Sample size
With a sample of two individuals, you will always obtain a perfect correlation of 1.00
As the sample size increases, it becomes increasingly more likely that the sample correlation accurately represents the real relationship that exists in the population.

43. Advantages
Can identify variables and describe relationships between variables that might suggest further investigation using the experimental strategy to determine cause- and- effect relationships.
Allow researchers an opportunity to investigate variables that would be impossible or unethical to manipulate.
Correlational studies tend to have high external validity.

44. Weaknesses - Internal Validity
Correlational studies tend to have low internal validity.
A correlational study does not determine which variable is the cause and which is the effect.
The third- variable & Directionality problems .

45. RELATIONSHIPS WITH MORE THAN TWO VARIABLES
For studying multivariate relationships we use a statistical procedure known as multiple regression.