8: CORRELATION AND PARTIAL CORRELATION

Question 1

bivariate linear correlation

Answer 1

• examines the relationship between 2 variables
• relationships vary in: form, direction, magnitude / strength

+1 / -1 represent a perfect correlation (positive/negative)

0 represents no correlation

Question 2

correlation: hypothesis testing

Answer 2

• Linear correlation involves measuring the relationship between two variables measured in a sample
• But crucially, we’re interested in whether there’s a relationship between the equivalent population variables
• We use sample statistics to estimate the population parameters
• Always start by assuming the null hypothesis is true: there is no relationship between the population variables
• Once we’ve determined the relationship in our sample, inferential analyses allow us to determine the probability of measuring a relationship of that magnitude when the null hypothesis is true

Question 3

correlation: p-values

Answer 3

what is the chance of measuring a relationship of that magnitude when the null is true?
- answer this in terms of prob
- p-value: the prob of measuring a relationship of that magnitude when the null is true
- we set a threshold level of probability (alpha) where we will be willing to reject null
- if prob is less than our threshold we are prepared to reject null

Question 4

bivariate linear correlation: parametric assumptions

Answer 4

• both variables should be continuous (level of measurement), if one (or both) is ordinal use non-para alternative
• related pairs: each participant should have a pair of values
• absence of outliers
• linearity - points in the scatterplot should be best explained with a straight line
• additional point to note - sensitive to range restrictions (floor and ceiling effects)

if data violates - spearman’s rho (or kendall’s tau if fewer than 20 cases)

Question 5

floor and ceiling

Answer 5

Ceiling and floor effects occur when a considerable proportion of subjects score the best/maximum or worst/minimum score, rendering the measure unable to discriminate between subjects at either extreme of the scale

Question 6

pearson’s correlation coefficient

Answer 6

• investigates the relationship between 2 quanititve, continous variables
• the resulting correlation coefficitent (r) is a measure of the strenght of association between the 2 variables
• r reflects how well a straight line fits the data points (i.e. the strength of the correlation)
• if points cluster around line, r is further from 0
• if points are scattered a distance from the line, r will be closer to 0

Question 7

covariance

Answer 7

• provides a measure of the variance shared between our x and y variables
• the correlation corefficient (r) is a ratio of covaraicne (shared variance0 to separate variances
• if covariance is large relative to the separate variances, r will be further from 0
• if the covariacne is small …, r will be close to 0

Question 8

degrees of freedom for r

Answer 8

N-2

report degrees of freedom when reporting r

Question 9

sampling distribution of correlation coefficients

Answer 9

H0 states there is no relationship between population variables

so under the null the sampling dist of correlation coefficients will have a mean of 0

Question 10

r distribution

Answer 10

• the r distribution has a mean of 0
• the extent to which an individual samples correlation coefficient (r) deviates from 0 can be expressed in standard error units
• using the r-distribution, and what we know about the proportion of scores falling under each area of a sampling list. we can determine the probability of obtaining an r-value of a given magnitude when the null is true ( p-value)

Question 11

confidence intervals around r

Answer 11

really interested in r for the pop.
“we have 95% confidence that the population correlation coefficient falls between ____ and ____”

not done by SPSS
report to 3 d.p

Question 12

shared variance

Answer 12

r^2: expresses the proportion of variance that is shared (between variables)

Question 13

effect size: r

Answer 13

r is another useful measure of effect size, it can be squared to give a measure of shared variance, expressed as a proportion of separate variances (r2)
* It tells us how much of the variance in y can be ‘explained by’ x

Question 14

partial correlation

Answer 14

• allows us to examine the relationship between 2 variables, while removing the influence of a 3rd variable
• we want to control for the effect of this variable: ‘partial out’, “hold ‘variable’ constant”

can use this to find if this 3rd variable actually has an influence