Exam 11: The Hypothesis of Association: Correlation

Whenever measures are in interval form, regardless of the shape of the distribution, the Pearson r may be used.

When two variables, A and B, are strongly correlated, it means that

Whenever a correlation is significant, then a cause-and-effect relationship must be present.

A researcher wishes to find out whether there is a dependable relationship between the severity of earthquakes and temperature for the 7 days immediately preceding the quake. A sample of 10 measured earthquakes was randomly selected from those recorded since 1965. For each area both the Richter value (higher value meaning more severe quakes) and the mean temperature for the 7 days preceding the quakes were recorded. The data follow: Area Richter Scale Value Mean Temperature A 8.0 65 B 7.0 67 C 4.9 70 D 6.5 66 E 5.0 65 F 5.5 60 G 5.0 63 H 4.5 64 I 5.0 65 J 2.0 65 Neither distribution appears to be skewed. -How many degrees of freedom should be assigned?

For the Pearson r, a non-significant correlation

A significant correlation of -.40

For the Spearman r, in order to establish a significant correlation in the population

Should Ho be rejected or accepted?

A significant Pearson r

A researcher is interested in testing the hypothesis that income is negatively related to family size. A random sample of 10 families was selected from the population of a large mid-western city. All families were assessed on both their per-family income and their numbers of children Family Per-family income Number of children A \ 190,000 2 B \ 30,000 6 C \ 19,000 7 D \ 40,000 3 E \ 23,000 6 F \ 40,000 4 G \ 25,000 5 H \ 40,000 3 I \ 28,000 1 J \ 30,000 5 Since the income distribution was badly skewed, it was decided not to use the Pearson r. -Should Ho be rejected or accepted? If Ho is rejected, state the level of significance.

The Pearson r assumes that

A researcher is interested in whether a correlation exists between Alcohol scores and Drug Abuse scores on the MAQ (Maryland Acquisition Questionnaire). A group of inmates, all of whom had at least two previous incarcerations, were given the MAQ and their Drug and Alcohol scores were compared. Subj\# Drug Alcohol 1 34 40 2 75 60 3 48 53 4 55 47 5 40 50 6 42 48 7 56 52 8 44 54 9 54 44 10 52 56 11 48 51 12 50 41 13 47 38 14 53 55 15 60 40 16 40 60 17 48 58 18 52 60 19 50 48 20 53 47 -Find the Mean for each set of scores

Of the following correlation coefficients, which expresses the weakest association?

The Spearman r may be appropriately used whenever

A researcher is using a standardized test of AP (Anger Potential) and selects 16 subjects to take the test which has a population mean of 20 and an SD of 6.00. The test scores were then converted into both z scores and T scores (See Chapter 5). The scores are as follows: Subj\# X (raw scores) z T 1 5 -2.50 25.00 2 14 -1.00 40.00 3 14 -1.00 40.30 4 17 -0.50 45.00 5 17 -0.50 45.00 6 17 -0.50 45.00 7 20 0.00 50.00 8 20 0.00 50.00 9 20 0.00 50.00 10 20 0.00 50.00 11 23 0.50 55.00 12 23 0.50 55.00 13 23 0.50 55.00 14 26 1.00 60.00 15 26 1.00 60.00 16 35 2.50 75.00 -Find the Pearson r correlation matrix for all three variables.

When high scores on the first variable associate with high scores on the second, and low scores on the first associate with low scores on the second, then the correlation is

If the researcher uses these data to predict GPA, then the scatter plot's abscissa would represent

When portraying a correlation on a scatter plot, the array of data points usually forms an elliptical shape.

A Pearson r of .80 means that 80% of the information about Y being contained in X.

Homoscedasticity refers to the