We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for another randomly sampled 50 items.

Question

We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for another randomly sampled 50 items.

BlackTom AI · Accepted Answer

We start by restating the scenario to ensure clarity: 50 items are randomly sampled from Target stores to record prices, and then another 50 items are randomly sampled from Walmart to record prices. The key question is whether these two samples constitute a paired or unpaired (independent) design.
Option 1: Paired. Interpreting this as a paired design would require that each price from Target be directly matched to a specific price from Walmart, typically by sampling the same item across both stores or by some natural pairing. In this case, there is no indication that the same item was observed in both stores, nor that the data were collected as matched pairs. Without a one-to-one correspondence between Target items and Walmart items, treating the data as paired would be inappropriate. Consequently, this option mischaracterizes the study design.
Option 2: Not Paired. The description shows two independent sampling events completed sequentially but without an explicit linkage between the items from Target and the items from Walmart. Each sample concerns a different set of items, and there is no natural pairing that aligns each Target price with a specific Walmart price. In statistics, when two samples are drawn independently and there is no matching by item, the correct designation is an unpaired or independent samples design. This option accurately describes the study setup.
Additional nuance: If one were to attempt a paired analysis, one would need the same items priced at both stores or a predefined matching criterion that creates pairs. Absent that, the analysis should proceed with methods appropriate for independent samples, such as comparing mean prices using a two-sample t-test or nonparametric equivalents. Conversely, applying paired-test assumptions to these data would artificially impose linkage and potentially distort inference.
In summary, the reasoning supports interpreting the situation as Not Paired because there is no item-level pairing between Target and Walmart price observations, and the data arise from two independent samples rather than from matched pairs.

FA25_QTM_100_3 7.18: Paired or not? Part II.

We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for another randomly sampled 50 items.

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