Correlations

Question 1

What two things can a correlation coefficient be regarded as?

Answer 1

A descriptive statistic (describing the strength and direction of a relationship {between -1 and +1}) and a
measure of effect size

Question 2

What does the magnitude of the correlation coefficient depend on?

Answer 2

The amount of noise or scatter in the relationship; the less noise, the stronger the relationship

Question 3

Why is variation in scores critical to correlations?

Answer 3

Both measures must have some decent variability in their scores because the variation is all that’s being measured (it’s all about how people score relative to each other)

Question 4

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

Answer 4

If everyone scores the same then any correlation will be meaningless (if variance/standard deviation is zero, you can’t even calculate a correlation)

Question 5

What if the spread of scores is truncated (i.e. restriction of range)?

Answer 5

Then the correlation magnitude may be reduced (i.e.

will seem that the underlying relationship is smaller than it actually is)

Question 6

If testing the ability of a sample of electricians, what would you need to ensure?

Answer 6

That you include tasks of appropriate difficulty so you can tell apart electricians of different levels; recruit participants with an appropriate range of skill levels to evaluate the validity and reliability of your test

Question 7

What would happen if we only simulated very easy tasks in a test?

Answer 7

It will restrict the range, as the worst novices could get the maximum score (ceiling effect) and the scores would be squashed together and suppress the correlation

Question 8

What would happen if we only recruit novices and not experts?

Answer 8

The range of scores will be restricted to the low end of the scale, suppressing the correlation

Question 9

Why are absolute values of scores irrelevant in correlations, and why are the raw scores discarded?

Answer 9

Because we’re evaluating scores relative to other scores in the sample; when calculating a correlation coefficient, both measures are standardised to z scores

Question 10

What if the underlying relationship is not a linear/straight line?

Answer 10

Then a correlation coefficient will be an inaccurate estimate of that relationship; correlations only
represent linear relationships where two measures vary in a directly proportional way to one another

Question 11

What is the significance test you get when you run a correlation and why do you need this?

Answer 11

A t-test that checks whether the correlation coefficient you obtained is significantly different from
zero; because we’re generally only ESTIMATING the correlation of interest from a sample

Question 12

Why is the correlation shown by SPSS only an estimate?

Answer 12

In psychology we’re usually only interested in how much two measures correlate in general across the
population, then we can use this to predict outcomes

Question 13

If we only have a small sample size, can we be confident that it’ll be a reasonable approximation of
the true population correlation?

Answer 13

Yes, but there will be a margin of error (confidence interval), and this will get smaller the more people
we include in our testing sample

Question 14

What does sample size determine about the accuracy of the correlation estimate?

Answer 14

If it’s a big sample, the estimated correlation is more likely to be accurate and stable, and therefore
closer to the population

Question 15

What does the p value you get with a correlation determine?

Answer 15

How likely it is that you’ll get this correlation coefficient if the “real” population correlation was actually zero (can it be reasonably discriminated from zero?)

Question 16

If you get a p value of .05 with your correlation coefficient of .80, what does this mean?

Answer 16

There’s only a 1 in 20 (5%) chance that the population correlation you’re trying to estimate is actually zero rather than something bigger than zero

Question 17

In what situation do you not need so much sensitivity and can get away with smaller samples?

Answer 17

If you have a really large correlation, as it’s easier to detect as being different from zero (a small correlation requires more sensitivity/larger sample to detect as statistically significant)

Question 18

What if our margin of error includes zero?

Answer 18

Then our sample correlation is not significantly greater than zero (p>.05, ns), so we can’t conclude that the population correlation is likely to be greater than zero.

Question 19

What does a power analysis tell you?

Answer 19

Exactly how many people you need to test to be able to detect a particular size of correlation as significant

Question 20

In a power analysis, what correlations are considered small, medium and large?

Answer 20

Small = .10; medium = .30; large = .50

Question 21

How is clinical significance differentiated from statistical significance?

Answer 21

It’s about whether the level of correlation is of practical importance, which depends entirely on the context

Question 22

What kind of test is a Pearson’s r correlation coefficient, and when would it be used?

Answer 22

Parametric test; when variables are normally distributed and on an interval scale of measurement (more sensitive)

Question 23

Under what conditions would a Spearman’s Rho correlation coefficient be used?

Answer 23

For non-parametric data; variables don’t need to be normal and can be ordinal scale of measurement; it’s less sensitive (uses rank order of the data rather than raw scores)

Question 24

If your data are not appropriate for a parametric test, what do you do?

Answer 24

Try fixing it up first using non-linear transformations, and if this doesn’t work, use Spearman’s Rho