MLS-C01 Exploratory Data Analysis Practice Question
A data analyst is examining a dataset with a target variable that has three classes: A, B, C. They plot the distribution of a feature 'X' for each class and notice that for classes A and B, the distributions are bimodal, while for class C it is unimodal. They want to assess whether feature 'X' is useful for separating the classes. Which of the following metrics should they compute to quantify the separability?
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
ANOVA F-statistic between feature X and the target.
The ANOVA F-statistic measures the ratio of between-group variance to within-group variance, directly quantifying separability. Option B is wrong because 'variance ratio' is not the standard name; the correct metric is the F-statistic. Option C is wrong because the chi-square test is for categorical features, not continuous ones like feature X. Option D is wrong because mutual information measures dependency but does not specifically test separability in terms of variance between groups.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✓
ANOVA F-statistic between feature X and the target.
Why this is correct
Correct. The ANOVA F-statistic tests whether the means of feature X differ significantly across classes A, B, and C, which is a direct measure of separability.
- ✗
Variance ratio (between-group variance / within-group variance).
Why it's wrong here
Incorrect. While the concept of variance ratio (between-group / within-group) underlies the F-statistic, 'variance ratio' is not a standard metric name; the correct term is ANOVA F-statistic.
- ✗
Chi-square test of independence.
Why it's wrong here
Incorrect. The chi-square test of independence is used for categorical features, but feature X is continuous, so this test is not appropriate.
- ✗
Mutual information between X and the target.
Why it's wrong here
Mutual information quantifies the statistical dependence between feature X and the target, indicating how much knowing X reduces uncertainty about the target. However, it does not directly quantify the degree of overlap or distinctness between the class-conditional distributions of X, which is crucial for assessing separability based on observed unimodal and bimodal patterns. This metric is tempting because it effectively measures feature relevance for classification tasks, making it excellent for general feature selection where the goal is to identify informative attributes, but not specifically for quantifying distributional separation.
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