A data scientist is investigating the relationship between two categorical variables: 'User Segment' (with 4 levels: 'Free Trial', 'Basic', 'Pro', 'Enterprise') and 'Feature Adoption Rate' (with 3 levels: 'Low', 'Medium', 'High'). They construct a 4x3 contingency table to perform a Chi-squared test of independence. After calculating the expected frequencies, they discover that two cells have an expected frequency below 5. Given this situation, what is the most appropriate immediate action to ensure the validity of the analysis?
Remove the rows or columns containing the cells with low expected frequencies from the analysis.
Immediately apply Fisher's Exact Test, as it is more accurate for small sample sizes and low expected frequencies.
Combine adjacent or logically similar categories in one or both variables to increase the expected frequencies in the cells.
Perform an independent samples t-test for each pair of user segments to compare their feature adoption.
The correct action is to combine adjacent or logically similar categories. The Chi-squared test of independence operates under the assumption that the expected frequency in each cell of the contingency table should be at least 5. When this assumption is violated, as in this scenario, the Chi-squared distribution may not accurately approximate the test statistic, potentially leading to unreliable p-values and an increased risk of a Type I error. The most common and appropriate first step to address this is to combine logically related categories. For instance, the 'Pro' and 'Enterprise' segments could be combined into a 'Paid' category, or the 'Low' and 'Medium' adoption rates could be merged. This action increases the cell counts, helping to meet the test's assumption while retaining most of the data.
Applying Fisher's Exact Test is a plausible alternative, as it is designed for small sample sizes and does not rely on the same large-sample approximation. However, for contingency tables larger than 2x2, combining categories is often the more practical and interpretable first step. Fisher's test can also be computationally intensive for larger tables.
Performing an independent samples t-test is incorrect because a t-test is used to compare the means of a continuous variable between two groups. Both variables in this scenario are categorical.
Removing rows or columns with low expected frequencies is inappropriate as it results in a loss of valuable data and can introduce bias into the analysis.
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