Null hypothesis for a test of independence
1. Describe the (Ho) null hypothesis for a test of independence.
2. An investigator was interested in the relationship between color preference and number of siblings. A test of independence produced a 2 that allowed the null hypothesis to be rejected. Write a proper conclusion for this test result.
3. Explain the short cut method of calculating 2 and give a numerical example
4. Describe Phi and the odds ratio
5. A social psychologist hypothesized that a factor in juvenile delinquency was the presence or absence of a strong father-figure in the home. He examined the folders of 100 inmates in the federal reformatory and found that only 50 of these young men grew up with a strong father-figure in the home. He also examined the records of 100 randomly selected male college students and found that 70 of them had strong father-figures in their boyhood homes.
Use the chi square method to test the psychologist’s hypothesis.
Chapter-14
1. A labor official predicted that the following percentages of makes of cars would be seen passing a picket line at an automobile plant where a strike was in progress.
General Motors Ford Chrysler Foreign Brand
38% 28% 24% 10%
The following numbers of cars were counted. Analyze the data and write a conclusion about the official’s prediction.
General Motors Ford Chrysler Foreign Brand
114 72 75 41
2. On a test of independence between alcoholism and early toilet training, a clinical researcher found a 2 = 6.48. With df = 1 and = .05, write a conclusion about the relationship between the two variables.
Sample Solution
The null hypothesis for a test of independence is that there is no association between the two variables being tested. In other words, the null hypothesis states that the probability of observing a particular outcome in one variable is not influenced by the value of the other variable. For example, if we are testing the relationship between color preference and number of siblings, the null hypothesis would be that there is no association between these two variables. This means that the probability of a person preferring a particular color would be the same regardless of how many siblings they have.Full Answer Section
The conclusion for this test result would be that there is a significant association between color preference and number of siblings. This means that the probability of a person preferring a particular color is influenced by the number of siblings they have. For example, if the investigator found that people with more siblings were more likely to prefer the color blue, the conclusion would be that there is a positive association between color preference and number of siblings. This means that as the number of siblings increases, the probability of a person preferring blue also increases. 3. Explain the short cut method of calculating 2 and give a numerical example The short cut method of calculating 2 is a simplified version of the standard formula for calculating 2. The short cut method can be used when the expected frequencies in each cell are all equal. The formula for the short cut method is:2 = (observed - expected)^2 / expected
| Color Preference | Number of Siblings |
|---|---|
| Blue | 30 |
| Green | 30 |
| Red | 40 |
2 = (30 - 33.33)^2 / 33.33 + (30 - 33.33)^2 / 33.33 + (40 - 33.33)^2 / 33.33
= 0.72 + 0.72 + 1.98
= 3.42