Chapter 11.2, Problem 22BB

Using Yates’s Correction for Continuity The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates's correction for continuity in cells with an expected frequency of less than 10 or in all cells of a contingency table with two rows and two columns. With Yates’s correction, we replace

${\displaystyle \sum \frac{{(\text{O-E)}}^{\text{2}}}{\text{E}}}$ with ${\displaystyle \sum \frac{{\left(|\text{O}-\text{E}\text{| }-\text{ 0}\text{.5}\right)}^2}{\text{E}}}$

Given the contingency table in Exercise 9 “Four Quarters the Same as $1?” find the value of the X² test statistic using Yates’s correction in all cells. What effect does Yates’s correction have?

9. Four Quarters the Same as $1? In a study of the “denomination effect,” 43 college students were each given one dollar in the form of four quarters, while 46 other college students were each given one dollar in the form of a dollar bill. All of the students were then given two choices: (1) keep the money; (2) spend the money on gum. The results are given in the accompanying table (based on ‘The Denomination Effect.” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36.) Use a 0.05 significance level to test the claim that whether students purchased gum or kept the money is independent of whether they were given four quarters or a $1 bill. Is there a “denomination effect”?