Correlation

Question 1

What is Correlation?

Answer 1

A measure of the degree of relationship between two measures (e.g. weight and height), and can be anywhere between -1 and +1. How strongly related the two variables are.

Question 2

In regard to human measurement techniques, how is correlation used?

Answer 2

Used for evaluating the reliability and validity of tests.

Question 3

What is a Correlation Coefficient?

Answer 3

A number between +1 and −1 calculated so as to represent the linear interdependence of two variables or sets of data. This number can be regarded as both a descriptive statistic (describing the strength and direction of a relationship) and a measure of effect size.

Question 4

What does a Correlation Coefficient of +1 mean?

Answer 4

Perfect relationship. As one measure increases, the other also increases. One predicts the other reliably (not independent).

Question 5

What does a Correlation Coefficient of 0 mean?

Answer 5

No relationship. The two measures are completely independent of one another.

Question 6

What does a Correlation Coefficient of -1 mean?

Answer 6

Perfect inverse relationship. As one measure increases, the other decreases.

Question 7

What is the best way to visualise a correlation?

Answer 7

Using a scatterplot.

Question 8

What does it mean when we say that there is a high correlation or they are highly correlated?

Answer 8

It means that the variables are NOT independent. One predicts the other very reliably.

Question 9

What is an outlier?

Answer 9

A value that lies outside most of the other values in a set data.

Question 10

How would a test to measure electrician ability (performance of tasks) be useful in the real world?

Answer 10

1. It could be used as a selection tool if you’re looking to hire electricians
2. For electricians to advertise to customers
3. To help trainees evaluate and choose electrician training courses

Question 11

How would you find out if your test to measure electrician ability was any good (the validity of the test)?

Answer 11

You need to see whether the test correlates with real job performance. The higher the correlation the more valid the test.

Question 12

How do you calculate validity coefficient in regards to electricians?

Answer 12

Calculate correlation between participant’s test scores and their actual job performance ratings. This correlation would be a validity coefficient for the test.

Question 13

What is a perfect correlation?

Answer 13

Correlation coefficient of 1. You can draw a straight line through all the people.

Question 14

What is a pretty good correlation?

Answer 14

Correlation would be about 0.8. The further each person is from the best fit line, the lower the correlation (the less accurate the test score is at predicting job performance).

Question 15

What is an ok correlation?

Answer 15

Correlation would be about 0.4 (not great but probably better than not using the test and hiring at chance).

Question 16

What is a disastrous correlation?

Answer 16

Correlation would be about 0. Test score and job performance completely independent. Test score gives you no information about job performance.

Question 17

What does it mean when someone gets a high test score but a low job performance rating?

Answer 17

Correlation would be about 0. Test score and job performance completely independent. Test score gives you no information about job performance.

Question 18

What is the magnitude of the correlation coefficient dependent on?

Answer 18

The amount of “noise” or scatter in the relationship (the less noise, the stronger the relationship). Also the direction of the correlation coefficient.

Question 19

If you were given perfect correlations with varying slopes, would this still be considered a correlation of 1? Why?

Answer 19

Yes. Because correlation involves standardising both variables (both variables turn into Z scores), meaning correlation is independent of the scale you are using.

Question 20

Is correlation only a linear relationship?

Answer 20

Yes

Question 21

Why must both measures have some decent variability (variance / standard deviation) in their scores?

Answer 21

Because the variation is all that is being measured.

Question 22

In regards to correlation, it is important to design a measure that yields a decent range of scores. T/F

Answer 22

True

Question 23

Why is it important to have decent variability in your scores?

Answer 23

If the spread is truncated (restriction of range) then the correlation magnitude may be reduced (i.e. it will give a false impression that the underlying relationship is smaller than it actually is).

Question 24

Using electricians as an example, how would you ensure variability with their scores?

Answer 24

For the electrician’s test, you would need to ensure that you have tasks of appropriate difficulty so you can tell apart electricians of different levels. Also, recruit participants with an appropriate range of skill levels to evaluate the validity and reliability of your test.

Question 25

In regards to the Electrician’s test, what would happen if there was a restriction of range through test items with variance?

Answer 25

This will suppress the correlation between test score and job performance (or any correlation involving the test). No variability.

If we only simulated easy tasks in our test rather than more difficult tasks, then this will restrict the range as novice electricians are also able to get the maximum score resulting in a “ceiling effect”.

Question 26

When does a ceiling effect occur?

Answer 26

It occurs when most of your data is clustered toward the top of your scale. So he scores of the two groups would be “squashed” together.

Question 27

In regards to the Electrician’s test, what would happen if there was a restriction of range through sampling?

Answer 27

If only novices and not experts were recruited then the range of scores will be restricted to the low end of the test scale. This will suppress the correlation between test score and job performance.

Question 28

Restriction of range does not suppress the size of correlation coefficient. T/F

Answer 28

False. They do suppress the size of correlation coefficient.

Question 29

What are two ways to restrict the range?

Answer 29

Through test tasks with variance (easy/difficulty) and sampling (novice/expert)

Question 30

Absolute values of scores are relevant in correlations. T/F

Answer 30

False. They are irrelevant.

Question 31

Why are absolute values of scores irrelevant in correlations?

Answer 31

Calculating a correlation coefficient you are effectively standardising both measures to z scores (the original raw means and standard deviations of your measures are effectively discarded). Meaning that the absolute raw scores (the original scales used in the measures) are irrelevant.

Question 32

From a sample of seven people, if person’s 1 to 3 score high on Measure 1 and Measure 2, and person’s 5 to 7 score low on both measures, what does that mean?

Answer 32

Measure 1 is highly predictive of Measure 2.

Question 33

If Measure 1 raw scores remained the same, and Measure 2 raw scores were multiplied by 1000, would this change the correlation? Why?

Answer 33

Correlation between the two measures would remain the same because you’re standardising both scales.

Question 34

If you do any linear transformation on either measures, would the correlation change?

Answer 34

No. It would remain the same.

Question 35

Correlations only represent linear (straight line) relationships where two measures vary in directly proportional way to one another. T/F

Answer 35

True

Question 36

What will a correlation coefficient be if the underlying relationship is not a straight line?

Answer 36

It will be an inaccurate estimate of that relationship.

Question 37

What is the significance test you get when you run a correlation? And what does it do?

Answer 37

This is a t-test. It checks whether the correlation coefficient that you obtained is significantly different from zero.

Question 38

How do you get a test of statistical significance?

Answer 38

When you calculate a correlation in SPSS (or whatever).

Question 39

Why do you need a test of statistical significance (t-test)?

Answer 39

You need this because we’re only estimating the correlation of interest via sampling (we only test a tiny proportion of the people to whom the correlation is supposed to apply).

Question 40

Why is the correlation shown by SPSS only an estimate?

Answer 40

Because you can’t test the whole population. There is always going to be a margin of error. The more people we include in our testing sample, the smaller the margin of error will be.

Question 41

Statistics taken from a relatively small sample are surprisingly good surrogates for the statistics of the entire population (e.g. a relatively small number of people from the population can give us a surprisingly accurate estimate of the TRUE population correlation). T/F

Answer 41

True.