correlation. definition shows the direction and the strength of the relationship between two...
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Correlation
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DefinitionDefinition
Shows the direction and the strength of the relationship
between two variables.
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Scatter plot for correlational data
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Examples of positive and negative relationships
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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
6543210
Aggre
ssiv
e b
ehavio
r
12
10
8
6
4
2
0
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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
PS
120
110
100
90
80
70
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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
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example
WEIGHT
200190180170160150140
ST
RE
NG
TH
100
90
80
70
David
Peter
Mark
Jim
Ken
A perfect correlation
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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?
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WEIGHT
220210200190180170160150140
ST
RE
NG
TH
120
110
100
90
80
70
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Zero correlation: when there is no association between two variables.
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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
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WEIGHT
220210200190180170160150140
IQ
120
110
100
90
80
70
20
19
18
17
16
15
14
13
12
11
10
9
87
6
5
4
3
2
1
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Three degrees of relationship
Zero Positive Perfect
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Examples of different values for relationships
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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
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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.
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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
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Changing TogetherChanging Together
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ConclusionIf A correlates with B, three possible causal relationship existA causes B,B causes A, or C causes both A and B/
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Restricted range
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Cognitive Development
Fearof Death
r = -.40
r =.52
r = .10
First graders Sixth Graders
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Correlation of sample and population
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Influence of outlier on correlation
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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
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Other types of correlationOther types of correlation