The analysis of variance is used to compare the mean between two related samples.

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The statement concerns analysis of variance (ANOVA) and its use for comparing means.
Option 1: True. This would claim ANOVA is used for two related samples. In general, one-way ANOVA compares means across three or more independent groups, not specifically two related samples, so this is an oversimplification and generally inaccurate for paired data.
Option 2: False. For two related (paired) samples, the appropriate test is typically a paired t-test (for two related groups) or a repeated measures/within-subjects ANOVA when there are more than two time points or conditions. Standard one-way ANOVA assumes independence between groups and is not designed for related samples. Since the question specifies two related samples, using ANOVA in its standard form is not correct; the paired t-test is the conventional approach, and ANOVA would be reserved for scenarios with more groups or repeated-measures designs with more than two conditions.
Option 3: True or False variants often hinge on the interpretation of ANOVA’s scope. If one interprets ANOVA as a general framework for comparing means that can be extended to various designs, including related samples via repeated-measures ANOVA, then it could be seen as applicable in some contexts. However, the plain statement about two related samples is misleading because the standard ANOVA (one-way) is not the typical method for two related samples.
Option 4: The core misconception is conflating the dependency structure with the method. Independence of observations is a key assumption of one-way ANOVA, which is violated by related samples, thus making the direct use of ANOVA inappropriate in that specific scenario.
In summary, the assertion that ANOVA is used to compare the mean between two related samples is not accurate in the conventional statistical practice, where a paired t-test is the standard choice for two related samples and ANOVA is reserved for comparing means across three or more groups or within-subject designs with more than two conditions.

MKF5912 - S1 2025 Week 10 - Quiz

The analysis of variance is used to compare the mean between two related samples.

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