Assuming all relevant assumptions are met, what statistical test would you run to evaluate the extent to which location and person predict the amount of sleep?

Question

BlackTom AI · Accepted Answer

Because the dependent variable is amount of sleep (continuous) and there are two categorical predictors (location and person), a two-way ANOVA is the appropriate test.

1. Relevant knowledge points and concepts
- Dependent variable: continuous (amount of sleep).
- Independent variables: two categorical factors (location, person).
- Two-way ANOVA tests main effects of each factor and their interaction on the continuous outcome.
- Key assumptions: independent observations, normality of residuals, homogeneity of variances, and additivity (unless interaction is significant).

2. Complete reasoning process step by step
- Identify model: Yijk = μ + αi + βj + (αβ)ij + εijk, where αi = effect of location, βj = effect of person, (αβ)ij = interaction, εijk = error.
- Partition total variability into components attributable to each factor, their interaction, and error.
- Compute sums of squares and mean squares, then F-statistics to test significance of effects.

3. Calculations (symbolic intermediate steps)
- Let a = number of locations, b = number of persons, n = observations per cell, N = abn.
- Grand mean: ȳ...
- SSA = bn Σ_i (ȳ_i.. − ȳ...)^2
- SSB = an Σ_j (ȳ_.j. − ȳ...)^2
- SSAB = n Σ_i Σ_j (ȳ_ij. − ȳ_i.. − ȳ_.j. + ȳ...)^2
- SSE = Σ_i Σ_j Σ_k (y_ijk − ȳ_ij.)^2
- Degrees of freedom: dfA = a−1, dfB = b−1, dfAB = (a−1)(b−1), dfE = ab(n−1)
- Mean squares: MSA = SSA/dfA, etc.
- F_A = MSA/MSE, F_B = MSB/MSE, F_AB = MSAB/MSE; compare to F-critical.

4. Why the correct answer is correct
- Two-way ANOVA matches the situation: continuous outcome and two categorical predictors, allowing tests of each factor’s main effect and their interaction. It explicitly models how location and person jointly influence amount of sleep.

5. Why other options are incorrect
- Chi-squared Test of Independence: for two categorical variables, not for a continuous outcome.
- Independent-samples t-test: compares means between two groups for one factor only.
- One-way ANOVA: handles only a single categorical factor, not two simultaneously.
- Simple linear regression: designed for a continuous predictor or a single predictor (or coded categorical), but does not directly provide the factorial decomposition (main effects and interaction) as two-way ANOVA does.

6. Conclusion
Two-way ANOVA is the correct test. This matches the provided answer: Two-way ANOVA.

Assuming all relevant assumptions are met, what statistical test would you run to evaluate the extent to which location and person predict the amount of sleep?单项选择题

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