biostats lecture 5

correlation

• the relationship between 2 variables: how the 2 variables change together (co-vary)

• measures the association between 2 variables, not necessarily causality

causality

• a directly causes b to happen

cannot

• presence of a correlation between 2 variables alone __ tell us if there is any causal relationship between the 2 variables

tend to change together

• having a correlation tells that 2 variables ___ either in the same direction or opposite direction

the hawthorne efffect

• the idea that participant knowledge of an experiment can influence its results

correlation coefficient

• measure the strength of correlation between 2 variables

• range: -1 to +1

• 0= no correlation

• > 0 postitive correlation

• < 0 negative correlation

• -1 perfect negative correlation

• +1 perfect positive correlation

postitive correlation

• correlation coefficient > 0

negative correlation

• correlation coefficient <0

pearson

• when both variables are continuous and have a normal distribution (not skewed)

pearson correlation coefficient

• calculated based on actual values of the variables

• affected by extreme values

• ex: age, blood pressure

• measures the strength of a linear relationship between 2 continuous variables

• 0 could mean no linear relationship but there amy be a non linear relationship

pearson postitive correlation

• means that as one variable’s value increases, the value of the other variable tends to also increase and vice versa

pearson negative correlation

• means that as one variable’s value increases, the value of the other variable tends to decrease and vice versa

pearson correlation coefficient of 0

• could mean no relationship at all OR

• no linear relationship but there may be a nonlinear relationship

spearman

• when at least one variable is ordinal, or at least one variable is continuous but with a skewed distribution

spearman coefficient

• calculated based on ranks of data values, not actual values

• more appropriate when there extreme values (outliers)

• ex: GPA and summative exam score 1

• measures the strength of a monotonic (in one direction) relationship between 2 ranked variables

spearman positive correlation

• as the rank of one variable’s value increases, the rank of the other variable’s values tends to also increase and vice versa

spearman negative correlation

• means that as rank of one variable’s value increases, the rank of one variable’s value tends to decrease and vice versa

monotonic relationship

• can be monotonically increasing or decreasing but does not have to be linear

tests for statistical significance

• p value

• 95% CI

interpretation of correlation

• direction of correlation

• strength of correlation

p value

• p value < alpha is statistically significant and indicates correlation

95% CI

• if does NOT include 0, there is a statistically significant corrleation at alpha = 0.05

0

• if CI 95% has 0, indicated no correlation

small strength

• 0.1 to < 0.3

medium stength

• 0.3 to < 0.5

large strength

• 0.5 to 1

r

• value to look at for direction and strength of correlation