Lecture 13 – Correlation – summary page
Correlation: -are two continuous variables related,
-in what way they are related.
-e.g., if one thing increases, does the other increase, decrease, or stay the same?
positive - as iv increases, dv also increases
negative – as iv increases, dv decreases
-normality – of both variables.
-continuous – both have to be continuous.
These are the two you have to figure out ^
-independence – independence of cases
there’s more but these are the ones you need to check for
• Variance = spread of data
• Covariance = do both variables vary in the same direction?
-measures the extent that the spread of two variables matches.
- if people are above mean in one variable and above in another, they have a positive relationship
-ranges from +1 to -1;zero means there is no relationship
perfect positive relationship: r = 1
no relationship: r = 0
perfect negative relationship: r = (-1)
r -> t score -> p value
-always check these
-If most people’s scores are close to the line that best describes the relationship between the two
variables, then the correlation will be large.
Despite the different slopes, the correlations are all +1.0 because there is no deviation from the line.
Changes in one variable perfectly predict changes in the other variable.
When the line does not perfectly describe all data points, the correlation will be less than perfect 3
- two lines, with very similar slopes. But the black dots are much closer to that line than the red x’s. Spread is
larger for x’s. So they have a lower correlation. Can’t be sure than an increase in the x variable results in an
increase in the y variable. Certainty that we can have that as one thing goes up the other does too.
-you CANNOT say that one thing causes another based on a correlation.
-you can only say that there is a relationship.
-Third Variable Issue
-it’s also possible that a third variable that is not accounted for is responsible for the relationship
between the variables that you are finding.
- ie weather being the third variable responsible for the correlation of ice cream sales and murder
-you can determine how much of the variation in one variable is explained by the other variable.
-simply square the