Correlation Redux Flashcards
what is Pearson’s r?
tells you the relationship between two variables: strength (‘size of effect’) or direction [+ or -]
what the p value tell us?
if it’s sig diff from 0
what is a ‘small effect’ size?
± 0.1
what is a ‘medium effect’ size?
± 0.3
what is a ‘large effect’ size?
± 0.5
what is significance?
testing the null hypothesis that r = 0 (correlation value is zero)
when can we reject the null hypothesis? / suggest there’s a significant different
when p < 0.05 we can reject the null hypothesis
what is a positive correlation?
both variables increase together
the interpretation of correlation and causality:
- correlation = not sufficient evidence for causality between variables
- does not imply causation
- gives no indication of the direct of causality
what is a negative correlation?
one goes up, the other goes down
what does a correlation coefficient give you?
- How much the two variables vary together
- The further the score from zero, the stronger the relationship
Why can’t we infer causation from a correlation?
The relation between the two variables is often due to the each’s variables relation to the third
what can happen if we take account of this relationship with the third variable (‘control for’)?
the original relatonship disappears as it was spurious (not genuine)
what may the third variable be?
a cofounding variable
how can we examine third variables?
partial correlations
what are some issues with correlation?
- shape of the relationship
- outlier
- restricted ranges
- sample size
- reliability of measures
what should relationships be like?
linear relationship (similar to regression)
what does Pearson’s Correlation Coefficient measure?
linear relationships
what doesn’t Pearson’s Correlation Coefficient measure?
non-linear relationships
* correlations be non-linear but Pearson’s r can not pick this up/do anything about it
non-linear correlations
will reduce the correlation
* still a relationship, just a different shape
Outliers
Individual scores can reduce or enhance the ‘r’
* i.e. if you add a pair of scores -> ‘no relationship’ is turned in a small/medium relationship by one data point
* i.e. if you add a different pair of scores to the data set -> a weak but significant relationship may be removed by one data point
outliers can cut both ways, what does this mean?
can artificially enhance the relationship or reduce it
what do we do about outliers?
we tend to remove them from the data set
how can we fixed stunted relationship?
by having a wide range of scores on all variables to get a clear view of the relationship between your variables
what is stunted relationships?
when there is a restricted range in our scores collected (aka. may be a specific demographic), we fall into the danger of a stunted relationship
what is an example of a stunted relationship?
in our original data, we collect students from across the board - medium relationship (r = 0.353, - < 0.001)
BUT say we only collect data from students who turn up to lectures (most conscientious) - no conscientiousness score below 3.5 (while main was 2.5 in usual student sample)
^ there is a restricted range of the variable conscientiousness due to the scores
This reduces our correlation to 0.043 (p = 0.778)
what is sample size?
- determines significance
- bigger, the better
- lower correlation need large samples to achieve significance
- .3 need around 50 to 60 participants
- .10 needs close to 300
- .10 is small but could be meaningful (important and may be the result you were looking for)
what happens if we have a larger correlation?
more likely to achieve a significance and gain credible findings
what is reliability?
- internal consistency of a measure
- how much can rely on a score from a test, sub scale etc.
- how good is your measure at measuring something (reliability doesn’t tell you that something is
- says nothing about what something is
what are three ways in which we can measure reliability?
- Test-Retest Method
- Split-Half Method
- Cronbach’s Alpha
Test-Retest Reliability Method
Test once and then test later after a certain time
Split-Half Reliability Method
Splits the questionnaire into two random halves, calculates scores and correlates them.
Cronbach’s Alpha
Measures internal reliability using individual items
* Ranges from 0 (no reliability) to 1 (complete reliability)
what is Cronbach’s Alpha?
measure of reliability for set scores
[Kilne, 1999] When is the scale reliable?
α > 0.7
(tells you that you have a reliable measure)
- higher score = more reliable
[Kilne, 1999] Why does α depend on the number of items?
more questions tend to produce a bigger α (more items, produce a bigger alpha)
Conditions of α (in a way)
- Treat Subscales separately (you are measuring reliability of the skill to measure ONE thing)
- test of a measure’s ability to test for one ‘thing’
- All scores should be in the same direction
- reverse code reversed questions
α is a property of a set of test scores, what does this mean?
so α can change across different populations
* do your own reliability measures even for established tests (score you get, you need to check the reliability for)
what does the reliability of a measure put limits on?
strength of any relationship
weaker reliability means..
you’re less likely to find a result / relationship between the variables
weak reliability leads to…
lower correlations
* more random variation in the scores from your measures
* ‘Attenuation’ = more random in your scores if there’s less reliability
Low reliability means…
more random variation
* more error / less true error of what you’re looking for (lower correlation)
Score = True Score + Error
Systematic Variation + Random Variation
SPSS and Cronbach’s Alpha
Item-total statistics TABLE in SPSS is:
* Useful to see which items are troublesome
* Ones with low Item-total correlation
* Ones that if removed increases the Alpha
A student was interested if executive control was related to problem-solving. He used a standardised measure of executitive control (Wisconsin Card Sort) and had participants solve simple sudokus (to measure problem-solving). He found that there was no relation between the measures.
This is a case of restricted ranges
A student wished to see if social media usage was related to mood IRL. She asked students to measure how long they spent on each social media platform over the week. She then designed a 10-item questionnaire that measured participant’s general mood over the past week. When the measure were correlation there was only a weak relationship found
Low Reliability of Measures
What is a Partial Correlation?
- we suspect that a correlation between two variables (X and Y) is due to a third variable (Z)
BUT the real relationship is between each of the two variables and the third seperately
how do we check for the real relationship between each of the two variables and third seperately?
partial correaltions
* examine the relationship between two variables after you have taken into consideration X and Y separate relationship with Z (third variable)
‘control for Z and examine the relationship between X and Y’
what happens when you control for a third factor?
sometimes the relationship between the two (X and Y) variables can disappear
i.e. “When participants’ scores on the Extroversion scale were controlled for, the relationship between Small talk and life satisfaction was not significant (r=0.02)”
what is covariance?
measure of how two variables vary together
* uses the difference between score and sample meal
* multiples these differences together
* we then need to standardised it and the standardised score is the correlation
If there is a relationship between two variables then…
as one variable changes, the other should also change in a consistent way
how do we measure change?
as deviation from the mean for each set of scores
if the deviation from the means are similar for each group then what?
the scores vary together
things that are related should…
show a similar distance from the mean
* and if they do this, this increases the covariance
how to calculate the sums for partial correlation?
- take each score away from the mean for that variable
- will tell us where each score is in relation to the mean (above / below / how far) - we multiple residuals (difference between the scores and the means) for each participants
- if both score above mean (=answer positive); the bigger each score’s differences from the mean the bigger this answer (‘the crossproduct’)
- if one above, one below (=answer negative)
- if both negative (=answer positive) - add up the cross products
- divide by n-1 giving you the covariance for each variable
- bigger one variable, stronger it is
covariance: the larger the covariance
the more the variables co-vary
covariance can be..
positive
- one variable goes up, so does the other
negative
- one variable goes up, other goes down
Covariance
- Affected by unit of measurement / sample size etc
- You can’t compare across samples
- Can’t real say this is a big or small relationship in absolute terms until you standardise it
What can correlation do?
- Standardizes the covariance
- Allows you to compare across samples etc.
- Gives you the standard Pearson “r”
How to Calculate Pearson’s ‘r’?
r=covxy/sxsy
- a standardized measure of the covariance
- you divided the covariance by the product of Standard deviations of the samples (the SD’s multiplied together)
Pearson’s R
correlation coefficient that measures linear correlation between two sets of data
if individuals are scoring below the mean in one condition and above in the other, what type of covariance is this?
high negative
- all cross products would be negative
if there were no consistent pattern between the data in conditions, what type of covariance is this?
low
if participants are scoring either positive in both conditions or negative, what type of covariance is this?
high positive
- consistent parting in the relationship
