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Chapter 12: Q. 12.39 (page 499)

Identify three ways in which the total number of observations of bivariate data can be obtained from the frequencies in a contingency table.

Short Answer

Expert verified

Three ways in which the total number of observations of bivariate data can be obtained from the frequencies in a contingency table are as follows :-

1. Summing the row totals

2. Summing the column totals

3. Summing the frequencies in the cells

Step by step solution

01

Step 1. Given information

A contingency table is a tabular representation of categorical data.

02

Step 3. Three ways

Three ways in which the total number of observations of bivariate data can be obtained from the frequencies in a contingency table are as follows :-

1. Summing the row totals

2. Summing the column totals

3. Summing the frequencies in the cells

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Most popular questions from this chapter

Scoliosis is a condition involving curvature of the spine. In a study by A. Nachemson and L. Peterson, reported in the Journal of Bone and Joing Surgery, 286girls aged 10to 15years were followed to determine the effects of observation only (129patients), an underarm plastic brace (111patients), and nighttime surface electrical stimulation (46 patients). A treatment was deemed to have failed if the curvature of the spine increased by 6 on two successive examinations. The following table summarizes the results obtained by the researchers.

At the 5%significance level, do the data provide sufficient evidence to conclude that a difference in failure rate exists among the three types of treatments?

We have presented a contingency table that gives a cross-classification of a random sample of values for two variables x and y, of a population.

Perform the following tasks

a. Find the expected frequencies Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

For a χ2-curve with df=4, determine

a. χ0.0052

b.χ0.012

In each case, decide whether Assumptions 1and 2for using chi-square goodness-of-fit test are satisfied.

Sample size n=50.

Relative frequencies0.65,0.30,0.05.

If a variable of two populations has only two possible values, the chi-square homogeneity test is equivalent to a two-tailed test that we discussed in an earlier chapter. What test is that?
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