Biostatistics- Pearson Correlation

correlation

Measures the strength and direction of the association between 2 continuous variables (interval or ratio)

correlation examples

-height and weight
-A1c and systolic blood pressure
-Supply and price

What are the 2 different types of correlation

-Pearson Product-Moment correlation
-Spearman Correlation

Pearson product-moment correlation goal

to asses the degree that quantitative variables are linearly related

What kind of variables are used in a Pearson Product-Moment Correlation

2 continuous variables with equal distance between them

effect size statistic

Pearson Correlation coefficient (r)

What is the correlation coefficient of a Pearson Product-Moment Correlation?

r

What is the range of the Pearson Correlation Coefficient (r)? What do these values mean?

Range = +1/-1
0 = no association
+1 = positive association
-1 = negative association
*the higher the number, the stronger the correlation

Assumptions of the Pearson Correlation

-variables are normally distributed (skewness/ kurtosis)
-linear relationship
-cases represent a random sample from the population and the scores on variables of one case are independent of scores on these variable for other cases

Positive correlation graph

Negative correlation graph

no correlation graph

Strength of the correlation coefficient (r) values and what they mean

0 = no association
+/- 0.1= weak association
+/- 0.3= moderate association
+/- 0.5 = strong association

which correlation is stronger?
(-0.75)
(+0.25)

(-0.75)

Pearson null hypothesis

H0: rxy = 0
-population correlation is zero
-there is no relationship between x and y in the population

Pearson Alternative Hypothesis

H1: rxy =/ 0
-population correlation is NOT zero
-there is a relationship between x and y in the population
-could be positive or negative

Pearson write up equation

r (df) = r value, p value

Pearson degrees of freedom

N-2

What does N stand for?

sample size

How to do the full write up for the Pearson correlation

The (strong/moderate/weak) correlation between (variable 1) and variable 2 (was/ was not significant) (equation).

Write Up example: Is there a relationship between age and LDL cholesterol?

The strong positive correlation between age and LDL cholesterol was significant r (49) = .87, p<.001

Correlation does not equal...

causation