Irkutsk State Medical University Department of Faculty Therapy

Correlations

Khamaeva A. A.

Irkutsk, 2009

Correlation is a measure of the

relation between two or more

variables Correlat ions (E 1 рабочая папкаW ork Ф ЫВ А Ф ЫФ В Ф В Ф Ы 1002v*997c )

Sex

Ag e

Growth

Weig ht

Correlations

• Correlation - a relationship between two quantitative or qualitative and quantitative ordinal variables;

• Association - a relationship between two qualitative variables;

The term correlation was first used by Galton in 1888.

Relationships

between

variables

The most frequently used correlation coefficient

• Parametric - Pearson r (simple Linear correlation or product-moment correlation)

• Nonparametric - Spearman R

Pearson r correlationcorrelation

- measure the degree of

• linear relationship between two variables;

• the relationship normally distributed quantitative variables;

The term was first used by Pearson in 1896.

Pearson r correlationcorrelation

1. Determines the extent to which values of the two variables are "proportional" to each other

2.2. Proportional means linearly related;Proportional means linearly related;S c atterplot (E 1 рабочая папкаW ork Ф ЫВ А Ф ЫФ В Ф В Ф Ы 1002v*997c )

W eight = -97,3131+ 1,0544*x

145 150 155 160 165 170 175 180 185 190

G rowth

40

50

60

70

80

90

100

110

120

130

140W

eig

ht

r = 0.54p < 0.05

Pearson r correlationcorrelation

3. C3. Correlation coefficientorrelation coefficient doesdoes nnoot t depend on the specific measurement depend on the specific measurement units usedunits used

4. Pearson correlation assumes that the two variables are measured on interval scales

Interval scale – a scale of measurement allows you to not only rank order the items that are measured, but also to quantify and compare the sizes of differences between them

A rank - a consecutive number assigned to a specific observation in a sample of observations sorted by their values, and thus reflecting the ordinal relation of the observation to others in the sample

Property of correlation coefficient

1. Correlation coefficients can range from

-1.00 to +1.00

2. A value of 0.00 represents a lack of correlation r = 0

0

0,5

1

1,5

2

2,5

3

3,5

0 1 2 3 4 5

r = 0p < 0.05

Y

X

Properties of correlation coefficient

3. The value of +1.00 represents a perfect positive correlation

4. The value of -1.00 represents a perfect negative correlation

0

1

2

3

4

5

6

0 1 2 3 4 5 6

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Positive correlation coefficient Negative correlation coefficientr = +0.85 r = -0.85

X

Y

X

Y

Properties of correlation coefficient

5. X and Y are interchangeable without affecting the value of r

6. The correlation between X and Y does not necessarily imply cause-and-effect relationship

• X influences on Y• Y influences on X• X and Y are influenced by the third factor

yxxy rr

Evaluation of connection tightness

Connection rNo connection 0

Weak ± 0; 0,3

Moderate ± 0,3; 0,5

Significant ± 0,5; 0,7

Strong ± 0,7; 0,9

Very strong ± 0,9; 1A value of -1.00 and +1.00 represents very strong correlation, or in other words, functional connection

How to Interpret the Value of Correlations

The coefficient of determination – is the square of the correlation between the two variables – it expresses the amount of common variation between the two variables

If r=0.5 coefficient =

0.5 x 0.5 x 100% = 25%

Spearman R correlation

• computed from ranks

• measured on an ordinal scale - the ranks of a variable's values contain information

about their relationship to other values only in terms of whether they are "greater than" or "less than" other values but not in terms of "how much greater" or "how much smaller"

This correlation is used in a case when:

• The number of observation is less that 30• Distribution is abnormal• The type of distribution is unknown• Ratio of variables is non-linear• Applied qualitative variable• Applied qualitative and quantitative

variables

Thank You for your kind attention!