Explain why a person would be wrong to claim, “My correlation coefficient is positive, therefore the two variables are highly correlated.”

 

1.A student is analyzing how two variables are correlated: size of committee and “efficiency” of committee. He reports to his friends that he had a correlation coefficient (r) of -0.85. What does the negative sign on the “r” tell us? (Hint: Don’t just say that the relationship is negative – explain what that means!!)

2. Consider again the r = -0.85. How strong does this appear to be, based on the textbook’s description of how to qualitatively interpret the size of “r”?

3. Think about the two variables and the “r” of -0.85. Why might his friends or colleagues think this researcher is lying about the correlation between group size and efficiency? Hint: think about both the strength AND direction of the correlation!

4. It is discovered that the Pearson correlation coefficient (r) for the correlation of education and income is .5, but for the correlation of education and support for wealth redistribution, it is only .2. Why would it not surprise us to find that the strength of the correlation is stronger in the first scenario than in the second?

5. Thinking back to the scenarios in the previous question, why aren’t either of the correlation coefficients closer to 1?

6. Explain why a person would be wrong to claim, “My correlation coefficient is positive, therefore the two variables are highly correlated.”

7. A student wishes to find the correlation between gender and income. Why is this not going to work, to try to compute “r” for assessing the relationship between these two variables? (HINT: think about what kind of variable each is!)

8. We didn’t cover this in the tutorial, but it’s possible for a “r” to be statistically insignificant even if it appears large (such as .65 or .70). This is impacted by sample size. Why would you trust an “r” based on 50 cases more than you would trust an “r” based on 5 cases?

9. Click on the .jpg file attached to this question. It is a scatterplot.

What does this scatterplot reveal about the relationship of states’ percentage of single parenthood and the violent crime rate? (r = .65)

10. If Mississippi (ms) was removed from the data set, the correlation coefficient would:

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