2. Correlation

Question 1

Correlation

Answer 1

A statistical method for measuring the extent to which two variables are related It measures the pattern of responses across variables

Question 2

Correlation: measuring relationships

Answer 2

As one variable increases does the other increase, decrease, or stay the same

Question 3

Variance

Answer 3

Calculated by subtracting all scores by the mean score. Add this and then sum it.

Question 4

Covariance

Answer 4

We look at how much each score deviates from the mean. If both variables deviate from the mean by the same amount, they are likely to be related.

Question 5

How to determine the relationship between two variables

Answer 5

Visual inspection > scatterplot Numerical calculation > correlation coefficient

Question 6

Covariance Equation

Answer 6

Question 7

Problems with covariance

Answer 7

Depends upon the unit of measurement Solution: standardise it (divide by the standard deviation)

Question 8

Correlation Coefficient

Answer 8

Standardised covariance

Question 9

Correlation Assumptions

Answer 9

Linearity Normality Check: scatterplots, Q-Q/P-P plots, histograms

Question 10

Correlation - assumptions violated

Answer 10

Bootstrap, Spearmans r, Kendall’s tau

Question 11

Pearson’s R

Answer 11

To get the Pearson’s R correlation co-efficient we do the above but times the bottom by the standard deviation for both. This gives us a standardized r value. R values range between -1 to +1.Definition

Question 12

Correlation Effect Sizes

Answer 12

1 = small effect 3 = medium effect 5 = large effect

Question 13

Coefficient of Determination

Answer 13

R2 By squaring the value of r you get the proportion of variance in one variable shared by the other

Question 14

Correlation significance testing

Answer 14

Significant for r tells us whether a sample with a correlation of r = .86 could come from a population where r = 0. Alpha = 0.05 - probability of 5% or less that there is a correlation significantly different from 0 when in reality there is no correlation

Question 15

Factors affecting correlations

Answer 15

Non-linear relationships between variables Restrictions of range Outliers

Question 16

Correlation and Causality

Answer 16

The third variable problem Direction of causality

Question 17

The third variable problem

Answer 17

Causality between two variables cannot be assumed because there may be other measured or unmeasured variables affecting the results

Question 18

Direction of causality

Answer 18

Correlation coefficients say nothing about which variable causes the other to change

Question 19

Nonparametric correlation: Spearman’s Rho (Rs)

Answer 19

Pearson’s correlation on the ranked data Minimises the effects of extreme scores or effects of violations of assumptions

Question 20

Nonparametric correlation: Kendall’s Tau (t)

Answer 20

Better than spearmans for small samples with large number of tied ranks Better estimate of correlation in population

Question 21

Partial Correlations

Answer 21

Measures the relationship between two variables, controlling for the effect that a third variable has on them both

Question 22

Semi-partial Correlation

Answer 22

Measures the relationship between two variables controlling for the effect that a third variable has on only one of the other variables

Question 23

Point-biserial correlation

Answer 23

categorical/dichotomous data E.g. being dead (can’t be a bit dead) Can be dummy coded

Question 24

Biserial Correlation

Answer 24

Continuum underlying dichotomy e.g. passing or failing a test Cannot be run in SPSS

Question 25

Answer 25

Interperet