Chapter 16

Question 1

random sampling distribution of r

Answer 1

• Not normally distributed
• • If rho = 0, it’s symmetrical and close to normal
• • If rho =/= 0, it’s skewed because rho can’t exceed +/- 1 -> larger the absolute value of rho, greater skew
• Smaller n = greater skew
• Values of r will vary less from sample to sample when n is large
• Values of r will vary less from sample to sample when rho is strong

Question 2

when is the random sampling distribution of r skewed?

Answer 2

• If rho =/= 0, it’s skewed because rho can’t exceed +/- 1 -> larger the absolute value of rho, greater skew
• Smaller n = greater skew
• If rho = 0, it’s symmetrical and close to normal

Question 3

rho

Answer 3

• Pearson’s correlation coefficient for population of paired scores
• Only absolute value matters (it gets squared, no +/- not important)

Question 4

desirable properties of fisher’s z transformation

Answer 4

• Sampling distribution is normal (regardless of rho or n)
• Standard error of z’ is independent of rho values
• Non-linear transformation that will change the shape of the distribution (and will normalize it)
• Magnitude: if r is negative, zF is also negative (don’t forget to put +/- in your answer!)

Question 5

What can you do with perfect correlations? Why can you do it?

Answer 5

If you have perfect correlations, you can create a formula to convert one value to another (because there’s no variability)

Question 6

why do we prefer the t-test for correlations?

Answer 6

• T-test is better than z-test because it’s more powerful for correlations (so we don’t use the z-test)
• T-test gains its power by using sample estimate of r to estimate standard error

Question 7

H0 for testing correlations

Answer 7

• that they’re 0 -> any significant correlation means that there’s little chance that the correlation is 0
• Remember that H0 can never be true, just a plausible option

Question 8

1-tail vs. 2-tail tests

Answer 8

• 2-tail: detects significant correlations in either the positive or negative direction (if H0 is rejected, we can conclude either that correlation is > or < 0)
• 1-tail: if it’s logical that the correlation won’t be 0 but can’t be negative (or vice versa), can use a 1-tail test (more power -> critical region concentrated in one tail)