Question

A positive correlation (r = 0.52) is found between hours spent playing with other children at age two and sociability in kindergarten. Answer the following questions based on this result.
What does a positive correlation mean in this specific scenario?
If someone concludes that requiring children to play withi others at age 2 will increase sociability, what errors are being made?
What is the coefficient of determination?
If the researcher who made this conclusion was in fact, incorrect in this decision, what type of error in statistical decision making did she make?
If this researcher had a sample size of 15 and started with a nondirectional hypothesis, what was the critical r value (using the table in your textbook)?
Should she accept or reject her null hypothesis?

Answer 1

What does a positive correlation mean in this specific scenario?

A positive correlation means that both the variables (hours spent playing with other children at age two and sociability in kindergarten) move in the same direction. That is, hours spent playing with other children at age two and sociability in kindergarten increase or decrease at the same time.

If someone concludes that requiring children to play withi others at age 2 will increase sociability, what errors are being made?

Correlation does not imply causation. That is, even if children to play with others at age 2 and sociability are positively correlated, it does not mean that requiring children to play withi others at age 2 will increase sociability. There may be a third variable which affects both the variables requiring children to play with others at age 2 and sociability.

What is the coefficient of determination?

Coefficient of determination, = 0.52² = 0.2704

If the researcher who made this conclusion was in fact, incorrect in this decision, what type of error in statistical decision making did she make?

If we are making the conclusion that there was correlation (reject the null hypothesis), but in reality there was no correlation (null hypothesis is true), we make Type I error.

If this researcher had a sample size of 15 and started with a nondirectional hypothesis, what was the critical r value

For nondirectional hypothesis and sample size of 15, the critical r value is 0.482 at significance level of 0.05.

Should she accept or reject her null hypothesis?

As, the observed r (0.52) is greater than the critical value (0.482), we should reject the null hypothesis.