Correlation

DefinitionDefinition

Shows the direction and the strength of the relationship

between two variables.

Scatter plot for correlational data

Examples of positive and negative relationships

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 .

Time watch TV

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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

220210200190180170160150140PU

LLU

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Perfect CorrelationPerfect Correlation

As X changes a unit, Y changes a specific increment.

Name Weight Strength

Lomba 150.00 75.00

Jim 160.00 80.00

Mark 170.00 85.00

Peter 180.00 90.00

David 190.00 95.00

example

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David

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A perfect correlation

I D W E I G H T S T R E N G T H

1 150 75

2 152 76

3 158 78

4 162 79

5 167 85

6 168 86

7 172 89

8 177 90

9 180 93

10 185 96

11 186 98

12 189 100

13 192 103

14 193 104

15 195 106

16 196 109

17 200 111

18 204 113

19 209 115

20 210 117

Not always the correlation is perfect.

Guess?

WEIGHT

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

I D W E I G H T I Q

1 150 80

2 152 92

3 158 75

4 162 119

5 167 100

6 168 78

7 172 115

8 177 114

9 180 107

10 185 112

11 186 77

12 189 86

13 192 114

14 193 80

15 195 117

16 196 76

17 200 112

18 204 78

19 209 95

20 210 100

Example

A zerocorrelation

WEIGHT

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IQ

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Three degrees of relationship

Zero Positive Perfect

Examples of different values for relationships

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 test4- k-12 students’ scores on a math test and a PE test5- The birthrate and social economic level6- The length of the base of a square and the length of its diagonal.

1- Correlation between math ability and shoe size in K-122- Height and intelligence in adult population3- Crime rate and the number of churches4- The academic degree and income

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.

Real examples Correlation Confusion

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

Changing TogetherChanging Together

ConclusionIf A correlates with B, three possible causal relationship existA causes B,B causes A, or C causes both A and B/

Restricted range

Cognitive Development

Fearof Death

r = -.40

r =.52

r = .10

First graders Sixth Graders

Correlation of sample and population

Influence of outlier on correlation

Spearman correlation

• Spearman correlation formula is used with data from an ordinal scale (ranks)– Used when both variables are measured on

an ordinal scale

Students Rank in Math Rank in scienceJim 1 3Jennifer 2 2Abdul 4 1Ross 3 4Kate 5 5Tara 7 6Mike 6 7

Other types of correlationOther types of correlation