A data scientist is tasked with evaluating the effectiveness of different marketing strategies on customer conversion. They design an experiment with two categorical independent variables: Campaign_Type (with levels: 'Email', 'Social Media', 'PPC') and Customer_Segment (with levels: 'New', 'Returning'). The dependent variable is the Conversion_Rate. After running a two-way ANOVA, the analysis yields a statistically significant p-value (p < 0.05) for the interaction effect between Campaign_Type and Customer_Segment. What is the most appropriate interpretation and subsequent action for the data scientist to take based specifically on this finding?
Disregard the interaction effect because the main effects are the primary interest. Proceed to analyze post-hoc tests on any significant main effects to determine which group means are different.
Conclude that the assumption of homoscedasticity has been violated due to the interaction. The data should be transformed, and the ANOVA should be re-run on the transformed data.
Interpret that the effect of Campaign_Type on Conversion_Rate is dependent on the Customer_Segment. The next step is to examine the simple main effects by comparing the mean conversion rates of the campaign types for new and returning customers separately.
Switch to running multiple independent t-tests comparing each level of Campaign_Type, collapsing the data across Customer_Segment to increase statistical power.
The correct interpretation of a statistically significant interaction effect in a two-way ANOVA is that the effect of one independent variable on the dependent variable depends on the level of the other independent variable. In this scenario, it means the effectiveness of a Campaign_Type is different for New versus Returning customers. Therefore, analyzing the main effects of Campaign_Type or Customer_Segment in isolation would be incomplete and potentially misleading. The appropriate next step is to conduct a simple main effects analysis. This involves examining the effect of Campaign_Type at each level of Customer_Segment separately (and vice versa) to understand the nature of the interaction. For example, one might find that 'Email' campaigns are most effective for 'Returning' customers, while 'Social Media' campaigns are superior for 'New' customers-an insight that would be lost by only looking at the main effects. The other options are incorrect because they either misinterpret the interaction effect or suggest statistically inappropriate follow-up actions. Disregarding the interaction to focus on main effects is a common but serious error. A significant interaction does not imply that other ANOVA assumptions (like homoscedasticity) are violated. Finally, switching to multiple t-tests would ignore the interaction that was found and would also inflate the family-wise error rate.
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What does a statistically significant interaction mean in a two-way ANOVA?
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Why is focusing solely on main effects inappropriate when a significant interaction is found?