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

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

correlation Pearson r correlation - measure the degree of linear relationship between two variables; the relationship normally distributed quantitative variables; The term was first used by Pearson in 1896.

correlation Pearson r correlation 1. Determines the extent to which values of the two variables are "proportional" to each other 2. Proportional means linearly related; r = 0.54 p < 0.05

correlation Pearson r correlation 3. Correlation coefficient does not depend on the specific measurement units 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 to A value of 0.00 represents a lack of correlation r = 0 p < 0.05 Y X

Properties of correlation coefficient 3.The value of represents a perfect positive correlation 4.The value of represents a perfect negative correlation Positive correlation coefficientNegative correlation coefficient r = +0.85r = 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

Evaluation of connection tightness Connectionr No connection0 Weak± 0; 0,3 Moderate± 0,3; 0,5 Significant± 0,5; 0,7 Strong± 0,7; 0,9 Very strong± 0,9; 1 A value of and 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

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