Week 4: multiple correlations, shared variance, effect sizes and power

analysing multiple correlations at once

-same as analysing two variables on SPSS → just put more variables into output

degrees of freedom

-still N-2 because we are comparing 2 variables in each correlation

shared variance

-R²

-proportion of variation in scores in one variable that can be explained by the variation in the other variable

-the stronger the relationship between variables, the more variance they share

-the leftover percentage from the shared variance is the variation that can be explained by other factors

shared variance equation

R² = r x r

-squaring the correlation coefficient

effect sizes conceptual introduction

-p value gives us an indication of statistical significance

-but is the difference found between the groups also relevant or psychologically significant?

-effect sizes give an indication of this

statistical significance (measure of effect)

-probability can show when there is a difference that is probably not due to chance

-shows existence of the effect

effect size (measure of effect)

-a standardised measure of how important the difference/effect is that you found in the sample

-shows magnitude of the effect

why is it useful to have an effect size?

-avoids problems with very big sample sizes

• when N is very big, it is almost impossible to not find a statistically significant effect

• but this doesn’t always mean that it is ‘important’

-can interpret the magnitude of an effect, independent of the scale that was used

• comparing studies that use different measures

• often used in meta-analyses or review papers

correlations (different measures of effect size)

-r value is the effect size

t-tests (different measures of effect size)

-Cohen’s d

-both independent and paired t-tests

-can be given as part of the output from SPSS

Cohen’s d

-represents the standardised mean difference (between groups or between conditions)

-specifically, is a measure of size of difference between two means

-the larger the difference, the larger the Cohen’s d → the larger the effect of the IV on the DV

interpretation of Cohen’s d value

• less than 0.20 → trivial effect

• 0.20 - 0.50 → small effect

• 0.50 - 0.80 → medium effect

• more than 0.80 → large effect

-larger value indicates more important/pronounced effect

-can be a negative value and can be larger than 1

effect size independent t-test

-to calculate Cohen’s d for independent t-tests:

• Cohen’s d = (mean of group 2 - mean of group 1) / SD pooled

equation for SD pooled

effect size paired t-test

-to calculate Cohen’s d for paired t-test:

• Cohen’s d = (mean of group 2) - (mean of group 1) / overall SD

power conceptual overview

-null hypothesis testing is related to probability of making a type 1 error → pays little attention to chance of making type 2 error

-the concept of power shifts the focus to type 2 error

power - technical definition

-the probability of correctly rejecting a false H₀

-mathematically works out to 1-β

(β = type 2 error = probability of accepting false H₀)

power - simplified definition

-the degree to which we can detect intervention effects

-emphasis on researcher’s ability to correctly find effects that exist, rather than likelihood of incorrectly finding effects that don’t exist

small effect (power)

-for a small effect → we need more people (larger sample size) to have sufficient ‘power’ to find it

big effect (power)

-for a big effect → we need fewer people (smaller sample size) to have sufficient ‘power’ to find it

good level of power

β = 0.80