HLTH200 - Correlations

When do you use correlations?

- correlations are used for testing relationships between interval variables.

- the null hypothesis of the correlation test is that no relationship exists between the interval variables in the population; they are independent.

Scatterplots

- direction

- form

- strength

- outliers

Direction

positive relationship - goes upwards

negative relationship - goes downwards

Form

- linear (strong)

- curved (moderate)

- no pattern (weak)

Outliers

Data points significantly different from others. It does no fit the typical pattern or trend of the rest of the group.

Correlations

a measure of how strong of a linear relationship between two variables - gives a correlation coefficient. The two variables must be INTERVAL variables.

*Don't apply correlation to categorical data masquerading as quantitative

*Check that you know the variables' units and what they measure.

Outlier Conditions

- outliers can distort the correlation dramatically

- an outlier can. make an otherwise small correlation look big, or hide a large correlation

- it can even give an otherwise positive association a negative correlation coefficient (and vice versa)

- when you see an outlier, it's often a good idea to report the correlations with and without that point

Correlation Properties

the sign of a correlation coefficient gives the direction of the association

Correlation is always between -1 and +1

strong correlation: close to -1 or +1

weak correlation: near zero

Correlation does not equal causation

whenever we have a strong correlation, it is tempting to explain it by imagining that the predictor variable has caused the response to help.

- scatterplots and correlation coefficient never prove causation

- a hidden variable that stands behind a relationship and determines it by simultaneously affecting the other two variables is called a lurking variable.

Lurking variable example

Observed association:

- # of firefighters (X)

- amount of damage (Y)

Lurking variable:

- seriousness of the fire which can affect both X and Y

When there's a correlation between A&B, There are usually 5 possibilities

- A causes B

- B causes A

- A and B both partly cause each other

- A and B are both caused by a third factor, C

- The observed correlation was due purely to chance