![]() ![]() Overall, the least popular flavor was strawberry.ġ2. Most preferred flavour was chocolate, while for men, the most preferred flavour Of men prefer strawberry, compared to only 11.765% of women. 35.524% of men prefer coffee compared to only 23.529% of women. You would say: 41.176% of women prefer chocolate compared to only 29.762% In other words, you would work with row percents and you would compare the percentages of men and women that fall into a column. Since you want to compare men with women, you would use percentage across, compare down. In this table, the independent variable is sex. Which method would be more appropriate for interpreting this table - percentage down, compare across or percentage across, compare down? Why? ![]() You know because you have examined the table of critical values of chi-squared and you found that a value of chi-squared of 5.02827 with three degrees of freedom has a probability between 0.1 and 0.2.ġ1. How do you know that is how certain you are? Since chi-squared for this data, 5.02827, is less than the critical value of 7.815, you fail to reject the null hypothesis.īecause your value of chi-squared is between 4.624 and 6.251, the probability of getting a value of chi-squared as large as the one you obtained would be between 10% and 20%, even if the row variable is independent of the column variable.ġ0. So the answer to the question is "Yes, the row variable is independent of the column variable." In other words, the data does not convince you that sex is related to preferred flavor. The data shown in this table could have come from a population in which sex is not related to preferred flavor of ice cream. Since chi-squared for this data, 5.02827, is less than the critical value of 7.815, you fail to reject the null hypothesis. The 95% critical value for chi-squared with 3 degrees of freedom is 7.815. Is the row variable independent of the column variable? H ALT : "Sex is related to preference of ice cream flavor."ħ. H Ø : "Sex is not related to preference of ice cream flavor." The value of chi-squared for the table is the sum of the values in each cell: The cell contributions are calculated according to the formula in the answer to question 4. ![]() This table shows the difference between observed and expected (the top number in each cell) and the cell's contribution to chi-squared (the bottom number in each cell). This table shows the observed and expected counts for each cell in the table. What is the value of chi-squared for this table? ![]() Therefore, the female strawberry cell's contribution to chi-squared is:ĥ. The expected for the female strawberry cell is 85 × 25 ÷ 169 = 12.57396. What is the contribution of the female strawberry cell to the value of chi-squared?Įach cell contributes an amount to chi-squared: Thus 84 × 35 ÷ 169 = 17.3964, the number of males you would expect to prefer vanilla.Ĥ. To calculate the expecteds for the male vanilla cell, multiply the number of cases in the male row by the number in the vanilla column and divide the result by the total number in the table. The second method of calculating the expecteds is a bit more straightforward and is likely to result in slightly more accurate results because it reduces rounding error. So you'd expect 17.3964 males and 17.6035 females to prefer vanilla. You would also expect 20.71% of the females to prefer vanilla, which is 17.6035. Now, 20.71% of 84 people is 17.3964, so this is how many males you would expect to prefer vanilla. Since overall 20.71% prefer vanilla, you would expect 20.71% of males to prefer vanilla. If sex is not related to flavor preference, you would expect the same percentages of males to prefer the same flavors as females. The first way to calculate the expecteds uses the marginal percentages. You can see that 62.5% of all people passed the test and 50% took the drug. The marginal percentages have been added in the table below. You need the marginal counts and percentages, often called "the marginals." The counts are already present in the "Totals" row and column. For both, you need to add a few more numbers to the table. There are two ways to calculate the expecteds. What would the expected number be for the male vanilla cell? (How many men would you expect to prefer vanilla?) You calculate degrees of freedom by multiplying the number of rows minus one times the number of columns minus one: df = (rows - 1) × (cols - 1) = (4 - 1) × (2 - 1) = 3ģ. If you were going to perform a chi-square test on this table, what would your degrees of freedom be? ![]()
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