It has been suggested that the rate of forgetting (coded as normal vs. fast) for word lists
often used in psychological experiments may depend on the type of memory test
employed, either free-recall or recognition. What is the best way to test this hypothesis?
a. regression
b. z-test for population mean
c. ANOVA
d. Chi square test for independence
How about d?
To test the hypothesis that the rate of forgetting for word lists may depend on the type of memory test employed, the best way would be to use a Chi-square test for independence.
The Chi-square test for independence is a statistical test that determines whether there is a relationship between two categorical variables. In this case, the variables would be the rate of forgetting (normal vs. fast) and the type of memory test (free-recall vs. recognition).
Here's how you can conduct the Chi-square test for independence to test this hypothesis:
1. Formulate the null and alternative hypotheses:
- Null hypothesis (H0): There is no relationship between the rate of forgetting and the type of memory test.
- Alternative hypothesis (Ha): There is a relationship between the rate of forgetting and the type of memory test.
2. Collect data: Gather data on the rate of forgetting (normal vs. fast) for word lists and the type of memory test employed (free-recall vs. recognition).
3. Set up a contingency table: Create a contingency table that shows the observed frequencies of the rate of forgetting and the type of memory test.
| | Normal forgetting | Fast forgetting |
|----------------|------------------|----------------|
| Free-recall | | |
| Recognition | | |
4. Calculate expected frequencies: Calculate the expected frequencies for each cell in the contingency table under the assumption of independence.
5. Perform the Chi-square test: Calculate the Chi-square test statistic by comparing the observed and expected frequencies in each cell of the contingency table.
6. Determine the p-value: Find the p-value associated with the calculated Chi-square test statistic. The p-value represents the probability of observing the data if the null hypothesis is true.
7. Make a decision: Compare the p-value to a predetermined significance level (e.g., 0.05). If the p-value is less than the significance level, reject the null hypothesis and conclude that there is a relationship between the rate of forgetting and the type of memory test. If the p-value is greater than the significance level, fail to reject the null hypothesis.
Therefore, the correct answer is (d) Chi-square test for independence.