Correlation Redux

Question 1

what is Pearson’s r?

Answer 1

tells you the relationship between two variables: strength (‘size of effect’) or direction [+ or -]

Question 2

what the p value tell us?

Answer 2

if it’s sig diff from 0

Question 3

what is a ‘small effect’ size?

Answer 3

± 0.1

Question 4

what is a ‘medium effect’ size?

Answer 4

± 0.3

Question 5

what is a ‘large effect’ size?

Answer 5

± 0.5

Question 6

what is significance?

Answer 6

testing the null hypothesis that r = 0 (correlation value is zero)

Question 7

when can we reject the null hypothesis? / suggest there’s a significant different

Answer 7

when p < 0.05 we can reject the null hypothesis

Question 8

what is a positive correlation?

Answer 8

both variables increase together

Question 9

the interpretation of correlation and causality:

Answer 9

• correlation = not sufficient evidence for causality between variables
• does not imply causation
• gives no indication of the direct of causality

Question 10

what is a negative correlation?

Answer 10

one goes up, the other goes down

Question 11

what does a correlation coefficient give you?

Answer 11

• How much the two variables vary together
• The further the score from zero, the stronger the relationship

Question 12

Why can’t we infer causation from a correlation?

Answer 12

The relation between the two variables is often due to the each’s variables relation to the third

Question 13

what can happen if we take account of this relationship with the third variable (‘control for’)?

Answer 13

the original relatonship disappears as it was spurious (not genuine)

Question 14

what may the third variable be?

Answer 14

a cofounding variable

Question 15

how can we examine third variables?

Answer 15

partial correlations

Question 16

what are some issues with correlation?

Answer 16

• shape of the relationship
• outlier
• restricted ranges
• sample size
• reliability of measures

Question 17

what should relationships be like?

Answer 17

linear relationship (similar to regression)

Question 18

what does Pearson’s Correlation Coefficient measure?

Answer 18

linear relationships

Question 19

what doesn’t Pearson’s Correlation Coefficient measure?

Answer 19

non-linear relationships
* correlations be non-linear but Pearson’s r can not pick this up/do anything about it

Question 20

non-linear correlations

Answer 20

will reduce the correlation
* still a relationship, just a different shape

Question 21

Outliers

Answer 21

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

Question 22

outliers can cut both ways, what does this mean?

Answer 22

can artificially enhance the relationship or reduce it

Question 23

what do we do about outliers?

Answer 23

we tend to remove them from the data set

Question 24

how can we fixed stunted relationship?

Answer 24

by having a wide range of scores on all variables to get a clear view of the relationship between your variables

Question 25

what is stunted relationships?

Answer 25

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

Question 26

what is an example of a stunted relationship?

Answer 26

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)

Question 27

what is sample size?

Answer 27

* 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)

Question 28

what happens if we have a larger correlation?

Answer 28

more likely to achieve a significance and gain credible findings

Question 29

what is reliability?

Answer 29

* 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

Question 30

what are three ways in which we can measure reliability?

Answer 30

* Test-Retest Method * Split-Half Method * Cronbach's Alpha

Question 31

Test-Retest Reliability Method

Answer 31

Test once and then test later after a certain time

Question 32

Split-Half Reliability Method

Answer 32

Splits the questionnaire into two random halves, calculates scores and correlates them.

Question 33

Cronbach's Alpha

Answer 33

Measures internal reliability using individual items * Ranges from 0 (no reliability) to 1 (complete reliability)

Question 34

what is Cronbach's Alpha?

Answer 34

measure of reliability for set scores

Question 35

[Kilne, 1999] When is the scale reliable?

Answer 35

α > 0.7 (tells you that you have a reliable measure) - higher score = more reliable

Question 36

[Kilne, 1999] Why does α depend on the number of items?

Answer 36

more questions tend to produce a bigger α (more items, produce a bigger alpha)

Question 37

Conditions of α (in a way)

Answer 37

* 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

Question 38

α is a property of a set of test scores, what does this mean?

Answer 38

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)

Question 39

what does the reliability of a measure put limits on?

Answer 39

strength of any relationship

Question 40

weaker reliability means..

Answer 40

you're less likely to find a result / relationship between the variables

Question 41

weak reliability leads to...

Answer 41

lower correlations * more random variation in the scores from your measures * 'Attenuation' = more random in your scores if there's less reliability

Question 42

Low reliability means...

Answer 42

more random variation * more error / less true error of what you're looking for (lower correlation)

Question 43

Score = True Score + Error

Answer 43

Systematic Variation + Random Variation

Question 44

SPSS and Cronbach's Alpha

Answer 44

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

Question 45

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.

Answer 45

This is a case of restricted ranges

Question 46

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

Answer 46

Low Reliability of Measures

Question 47

What is a Partial Correlation?

Answer 47

* 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

Question 48

how do we check for the real relationship between each of the two variables and third seperately?

Answer 48

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'

Question 49

what happens when you control for a third factor?

Answer 49

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)”

Question 50

what is covariance?

Answer 50

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

Question 51

If there is a relationship between two variables then...

Answer 51

as one variable changes, the other should also change in a consistent way

Question 52

how do we measure change?

Answer 52

as deviation from the mean for each set of scores

Question 53

if the deviation from the means are similar for each group then what?

Answer 53

the scores vary together

Question 54

things that are related should...

Answer 54

show a similar distance from the mean * and if they do this, this increases the covariance

Question 55

how to calculate the sums for partial correlation?

Answer 55

1. 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) 2. 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) 3. add up the cross products 4. divide by n-1 *giving you the covariance for each variable* - bigger one variable, stronger it is

Question 56

covariance: the larger the covariance

Answer 56

the more the variables co-vary

Question 57

covariance can be..

Answer 57

positive - one variable goes up, so does the other negative - one variable goes up, other goes down

Question 58

Covariance

Answer 58

* 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

Question 59

What can correlation do?

Answer 59

* Standardizes the covariance * Allows you to compare across samples etc. * Gives you the standard Pearson “r”

Question 60

How to Calculate Pearson's 'r'?

Answer 60

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)

Question 61

Pearson's R

Answer 61

correlation coefficient that measures linear correlation between two sets of data

Question 62

if individuals are scoring below the mean in one condition and above in the other, what type of covariance is this?

Answer 62

high negative - all cross products would be negative

Question 63

if there were no consistent pattern between the data in conditions, what type of covariance is this?

Answer 63

low

Question 64

if participants are scoring either positive in both conditions or negative, what type of covariance is this?

Answer 64

high positive - consistent parting in the relationship