Mark this question Select the false statement about ANOVA If a researcher wants to compare the mean wages of females in different age groups at a particular company, he or she should not use ANOVA because the population means are unknown. If a researcher wants to study the effectiveness of three brands of nicotine patches, the researcher should use One-Way ANOVA test. If a researcher wants to compare the mean wages of females in different age groups at a particular company to the mean wages of males in different age groups at the same company, the researcher should use Two-Way ANOVA test. A one-way ANOVA hypothesis test considers comparisons between populations based on one characteristic, while a two-way ANOVA hypothesis test considers comparisons between populations based on multiple characteristics.
The Correct Answer and Explanation is:
Correct answer:
The false statement is: “If a researcher wants to compare the mean wages of females in different age groups at a particular company, he or she should not use ANOVA because the population means are unknown.”
Explanation:
This statement is incorrect because ANOVA (Analysis of Variance) is specifically designed to compare sample means to make inferences about population means. In real-world research, the population means are rarely known in advance. That is precisely why statistical methods like ANOVA are used — to estimate whether observed differences in sample means reflect true differences in the population.
In this case, if a researcher wants to compare the mean wages of females across different age groups, they can and should use a One-Way ANOVA. The single factor under consideration here is age group, which makes it a one-way design. ANOVA does not require knowledge of the population means beforehand; it only requires that certain assumptions are met, such as:
- The samples are independent.
- The populations from which the samples are drawn are normally distributed.
- The variances among groups are approximately equal (homogeneity of variance).
The other statements are true:
- Comparing three brands of nicotine patches involves one factor (brand), so a One-Way ANOVA is appropriate.
- Comparing mean wages by gender and age group involves two factors (gender and age group), so a Two-Way ANOVA is the correct approach.
- The final statement correctly describes the difference between One-Way and Two-Way ANOVA.
In summary, ANOVA is used exactly because population means are unknown. The researcher uses sample data to test hypotheses about those means. The first statement is therefore false.
