Correlation and partial correlation

Define correlation

• Looking for the relationship between variables

• A way of measuring the extent to which two variables are related

• Measures pattern of responses across variables

• Should generally have 100+ participants

How can you measure correlation

• Pearson correlation coefficient ‘r’

• r= -1, perfect linear negative correlation

• r= +1, perfect linear positive correlation

• r= 0, no correlation

How can we measure relationships?

• See whether one variable increases and then if the other increases, decreases or stays the same

• Can be done by calculating covariance:

• We look at how much each score deviates from the mean

• If both variables deviate by the same amount, they are likely to be related

What is variance

• Tells us by how much scores deviate from the mean for a single variable

• Linked to sum of squares

What is co variance

• Tells us by how much scores on two variables differ from their respective means

• For the first variable, we calculate the error (difference) between the mean and each subjects score.

• For the second variable, calculate the error (difference) between the mean and their score

• Multiply these error values

• Add these values and you get the cross product deviations

Problems with co variance ?

• Depends upon units of measurement

• Eg, covariance of two variables measured in miles might be 4.25 but if the same scores are converted to Km, covariance is 11

• To standardise it, divide the standard deviations of both variables

What is correlation coefficient

• The standardised version of covariance

Correlation and causality?

• 3rd variable problem,

• In any correlation, causality between 2 variables cannot be assumed because there may be other measured or unmeasured variables affecting the results

• Direction of causality,

• Correlation co efficient say nothing about which variable causes the other to change

What is partial correlation

• The correlation between variables 1+2 when the effects of variable 3 have been partialled out

• Correlation with more than 2 variables

Partial correlation example ?

• We can control for age effects in two ways

• Experimentally, selecting groups according to age

• Statistically, partial out effects of age

What is regression

• Examining how one or more variables (X) can predict another variable (Y)