Exam 18: Determining and Interpreting Associations Among Variables

Michelle Steward is a marketing professor at Wake Forest University. Michelle had been asked by the administration to study a sample of classes at Wake to help the university understand the student population better, particularly in terms of factors that differentiate students with high versus low GPAs. One of the questions asked was: "Did you pass or fail the last test you took?" and another question in the study asked "Did you study or not study for the last test you took?" Michelle decided to run a cross-tabulation analysis on these two questions. When she did she also ran the chi-square test. The result was a Pearson Chi-Square Value of 8.64 and a p value reported as a "Sig." in SPSS of .03. Michelle knew that this meant:

The Pearson Product Moment correlation measures the linear relationship between two nominal and/or ordinal scaled variables.

Strength of association might be described as:

If we were to graph two variables, let's say, height (in inches)and GPA, and the graph showed points scattered about in a formless shape, we could say there is:

The chi-square test is useful for determining:

We would use the Pearson correlation table if we wanted to visualize the nonmonotonic relationship between two nominal scaled variables.

The SPSS command used to execute the Pearson product moment correlation is: ANALYZE; CORRELATE; BIVARIATE.

It is more difficult for a chi-square value with high degrees of freedom (i.e., there are more cells)to achieve "significance" than for a chi-square value with fewer degrees of freedom (i.e., there are fewer cells).

With the information used to construct a cross-tabulation table, a column percentages table can also be constructed, but a row percentages table cannot.

In chi-square analysis, the greater the number of cells, the larger the degrees of freedom. The greater the number of cells, the more opportunity exists to calculate a large chi-square value. In other words, the chi-square value can be "inflated" not due to a real association but simply due to the fact that there are more cells in the analysis. This is why degrees of freedom are used to:

Assume that a researcher and client determine that a p value of .05 or less determines significance. Listed below are several correlation coefficients and their respective significance levels. Which correlation coefficient demonstrates an association not likely due to chance; that is, is it significant?

Associative analyses determine whether stable relationships exist between two variables.

Michelle Steward is a marketing professor at Wake Forest University. Michelle had been asked by the administration to study a sample of classes at Wake to help the university understand the student population better particularly in terms of factors that differentiate students with high versus low GPAs. One of the questions asked was: "What score did you earn (0 to 100)on the last test that you took?" and another question in the study asked "How much time, estimated in numbers of minutes, did you study for the last test you took?" Michelle decided to run a cross-tabulation analysis on these two questions. When she did, she also ran the chi-square test. The result was a Pearson Chi-Square Value of 8.64 and a p value reported as a "Sig." in SPSS of .03. Michelle knew that this meant:

We know that McDonald's customers drink coffee for breakfast and soft drinks at lunch. This is an example of what type of relationship?

Which of the following were discussed by the authors as being ways that we may characterize relationships?

When we present findings on cross-tabulations with chi-square analysis, graphical presentations such as bar or stacked bar charts are often useful.

Which of the following refers to the finding that a systematic relationship exists between the two variables of interest in the population?

If you are examining the SPSS output for Pearson correlation, you will find the value of "1" along the diagonal of the correlation matrix indicating that each variable is perfectly correlated with itself.

The product life-cycle curve that describes the sales pattern of a new product over time (growing slowly during its introduction and then spurting upward rapidly during its growth stage and finally plateauing or slowing down considerably as the market becomes saturated)is an example of which type of relationship?

The manager of the city's professional hockey team conducted a large survey. He wanted to know if there was an association between fans being "season ticket holders" versus "nonseason ticket holders" and whether they "bought" versus "didn't buy" hockey team merchandise at the game. Because his survey included these measurements, he used SPSS to run a Pearson Product Moment correlation coefficient that turned out to be .88 with a Sig. value of .001. This meant: