Is it reliable?

Let's think for a minute about a different question:

• If I were to repeat the experiment, how similar would the results be?

Go to the Matlab script CorrelationSim.m

• Select Section 2 and run this section

You have just generated a population of data pairs (x,y) or (attractiveness, trustworthiness) with true correlation coefficient ρ = 0.21

Now we are going to draw lots of samples of size n from that population and work out the sample correlation coefficient r in each sample

• Select and run Section 3 of CorrelationSim.m

• How many samples did you generate? Look at the code!

• Change the number of samples to 10000 and run it again.

You should have a figure containing a histogram of the sample correlation coefficients for each of the 10000 samples.

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So - given that the true correlation ρ = 0.21, you can observe quite a range of sample correlation coefficients.

What do you think you could change to get a narrower range?

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You could increase the number of subjects in each sample.

• Try increasing the number of subjects per sample to 100 and re-running the section

• Compare the histogram for n=100 to n=50. Which sample size gives a more reliable estimate of ρ ?

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