Exam 11: Chi-Square Tests and Strategies When Population Distributions Are Not Normal

The degrees of freedom for the chi-square test for goodness of fit is:

The chi-square test was invented by __________.

Complete the following formula: φ =__________.

A high school principal wanted to know if the racial makeup of her teachers mirrored that of the student body. The student body broke down into 47% White, 28% Latino, 15% African American, and 10% other. Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were Other. Do these results suggest that the racial makeup of the faculty members is different from that of the students? (Use the .05 significance level.) Use the five steps of hypothesis testing and explain your findings.

When a distribution appears to be non-normal based on the scores in the study, one solution is to apply a(n)__________. Then, having met the normal-curve assumption, you can carry out an ordinary parametric test.

The formula for the degrees of freedom for a chi-square test for independence is the number of columns minus one, __________ the number of rows minus one.

When the normal-curve assumption is strongly violated, the ordinary t test:

A lack of relationship between two nominal variables is called __________.

In a study with 100 people, an analysis results in a χ² value of 3.15. What is the phi coefficient?

"A chi-square test for independence indicated that males and females were not evenly distributed across the categories [χ² (3, N = 234)= 56.79, p = .04]." What is the chi-square value in this study?

In general, the t test and the analysis of variance are:

A(n)__________ statistic reflects the overall lack of fit between the expected and observed frequencies.

All of the following are valid conclusions from the study EXCEPT:

A study was conducted on the effects of lack of REM sleep on the ability to recall a list of words. The study found that, of participants deprived of normal REM sleep, 4 scored high on memory recall, 7 scored moderately, and 9 scored low. Of participants who received normal sleep, 10 scored high, 9 moderately, and 1 low. Do these results suggest that REM sleep is related to how people score on the memory recall? (Use the .01 significance level.) a. Use the five steps of hypothesis testing. b. Sketch the chi-square distribution. c. Explain the logic of what you have done. d. Figure a measure of effect size and indicate whether it is small, medium, or large. e. Figure the approximate power.

__________ allow scores from non-normal populations to be analyzed using the standard parametric procedures such as t tests and analyses of variance.

All of the following are steps in figuring the chi-square statistic EXCEPT:

A research article reported that "level of intensity was compared to reaction time using a Wilcoxon rank-sum test." The researcher has conducted a(n)__________ test.

In a chi-square test, the variables are:

In the chi-square test for goodness of fit, the degrees of freedom are __________ minus 1.

For the following question(s): A researcher posed the question: "Does Smith's rehabilitation program decrease the rate of prisoners who reoffend?" A researcher conducted a study and published her findings. Here is an excerpt from which article the following excerpt was taken: A chi-square test for independence was conducted to test whether Smith's rehabilitation program differed from the old system in the number of repeat offenders. Results indicated that a difference did exist, χ² (1, N = 68)= 8.74, p < .01. -Of prisoners under Smith's program, __________% did reoffend.