You want to draw inferences about whether two samples were drawn from a single population, or from two populations. Which statistical test could potentially be appropriate?

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BlackTom AI · Accepted Answer

The question asks which statistical test could potentially be appropriate for inferring whether two samples come from a single population or from two populations.

Option 1: ANOVA. ANOVA compares means across groups and is not limited to just two groups; when there are two groups, ANOVA and a two-sample t-test yield equivalent results under standard assumptions. Therefore, ANOVA could be used to assess differences between two samples, which makes it potentially appropriate in this context.

Option 2: Independent-samples t-test. This test is designed specifically to compare the means of two independent samples (i.e., two groups assumed to come from possibly different populations). If the two samples are independent, this test is a direct method to assess whether their population means differ, aligning with the goal of determining whether they come from the same or different populations.

Option 3: Paired-samples t-test. This test is used when the two samples are related or matched (e.g., pre-post measurements on the same subjects). If the study design involves paired or matched observations, the paired t-test is appropriate for comparing the means of the two related samples. While not always applicable, it could be appropriate in the right paired-design scenarios, contributing to the possibility that the two samples originate from related populations or conditions.

Option 4: All of the above. Since ANOVA can handle two groups (and is equivalent to a two-sample comparison under certain conditions), the independent-samples t-test directly compares two independent groups, and the paired-samples t-test is appropriate for related samples, all of these tests could potentially be appropriate depending on the exact study design and assumptions.

In light of these points, the reasoning shows that each listed test has a scenario in which it could be appropriate for evaluating whether two samples come from a single population or from two populations, depending on independence, pairing, and the number of groups. Therefore, this set of options supports the notion that all of the above could be appropriate under different conditions.

PSYC20007_2025_SM2 Goals of Statistical Testing III

You want to draw inferences about whether two samples were drawn from a single population, or from two populations. Which statistical test could potentially be appropriate?

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