Correlation Flashcards
What is Correlation?
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.
In regard to human measurement techniques, how is correlation used?
Used for evaluating the reliability and validity of tests.
What is a Correlation Coefficient?
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.
What does a Correlation Coefficient of +1 mean?
Perfect relationship. As one measure increases, the other also increases. One predicts the other reliably (not independent).
What does a Correlation Coefficient of 0 mean?
No relationship. The two measures are completely independent of one another.
What does a Correlation Coefficient of -1 mean?
Perfect inverse relationship. As one measure increases, the other decreases.
What is the best way to visualise a correlation?
Using a scatterplot.
What does it mean when we say that there is a high correlation or they are highly correlated?
It means that the variables are NOT independent. One predicts the other very reliably.
What is an outlier?
A value that lies outside most of the other values in a set data.
How would a test to measure electrician ability (performance of tasks) be useful in the real world?
- It could be used as a selection tool if you’re looking to hire electricians
- For electricians to advertise to customers
- To help trainees evaluate and choose electrician training courses
How would you find out if your test to measure electrician ability was any good (the validity of the test)?
You need to see whether the test correlates with real job performance. The higher the correlation the more valid the test.
How do you calculate validity coefficient in regards to electricians?
Calculate correlation between participant’s test scores and their actual job performance ratings. This correlation would be a validity coefficient for the test.
What is a perfect correlation?
Correlation coefficient of 1. You can draw a straight line through all the people.
What is a pretty good correlation?
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).
What is an ok correlation?
Correlation would be about 0.4 (not great but probably better than not using the test and hiring at chance).
What is a disastrous correlation?
Correlation would be about 0. Test score and job performance completely independent. Test score gives you no information about job performance.
What does it mean when someone gets a high test score but a low job performance rating?
Correlation would be about 0. Test score and job performance completely independent. Test score gives you no information about job performance.
What is the magnitude of the correlation coefficient dependent on?
The amount of “noise” or scatter in the relationship (the less noise, the stronger the relationship). Also the direction of the correlation coefficient.
If you were given perfect correlations with varying slopes, would this still be considered a correlation of 1? Why?
Yes. Because correlation involves standardising both variables (both variables turn into Z scores), meaning correlation is independent of the scale you are using.
Is correlation only a linear relationship?
Yes
Why must both measures have some decent variability (variance / standard deviation) in their scores?
Because the variation is all that is being measured.
In regards to correlation, it is important to design a measure that yields a decent range of scores. T/F
True
Why is it important to have decent variability in your scores?
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).
Using electricians as an example, how would you ensure variability with their scores?
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.
In regards to the Electrician’s test, what would happen if there was a restriction of range through test items with variance?
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”.
When does a ceiling effect occur?
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.
In regards to the Electrician’s test, what would happen if there was a restriction of range through sampling?
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.
Restriction of range does not suppress the size of correlation coefficient. T/F
False. They do suppress the size of correlation coefficient.
What are two ways to restrict the range?
Through test tasks with variance (easy/difficulty) and sampling (novice/expert)
Absolute values of scores are relevant in correlations. T/F
False. They are irrelevant.
Why are absolute values of scores irrelevant in correlations?
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.
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?
Measure 1 is highly predictive of Measure 2.
If Measure 1 raw scores remained the same, and Measure 2 raw scores were multiplied by 1000, would this change the correlation? Why?
Correlation between the two measures would remain the same because you’re standardising both scales.
If you do any linear transformation on either measures, would the correlation change?
No. It would remain the same.
Correlations only represent linear (straight line) relationships where two measures vary in directly proportional way to one another. T/F
True
What will a correlation coefficient be if the underlying relationship is not a straight line?
It will be an inaccurate estimate of that relationship.
What is the significance test you get when you run a correlation? And what does it do?
This is a t-test. It checks whether the correlation coefficient that you obtained is significantly different from zero.
How do you get a test of statistical significance?
When you calculate a correlation in SPSS (or whatever).
Why do you need a test of statistical significance (t-test)?
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).
Why is the correlation shown by SPSS only an estimate?
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.
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
True.
