Two data sets of different sizes cannot be analyzed as paired data.

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BlackTom AI · Accepted Answer

Question restatement: The claim is that two data sets of different sizes cannot be analyzed as paired data.

Option 1: True. To perform a paired analysis (such as a paired t-test or Wilcoxon signed-rank test), there must be a one-to-one pairing between observations in the two data sets, meaning they share the same number of observations and each observation in one data set is linked to a specific observation in the other. When the data sets have different sizes, you cannot establish a complete one-to-one correspondence for all observations, so a true paired analysis is not appropriate for the full data set. In practice, analysts might either use only the common paired observations if a pairing is still possible after matching, or switch to an unpaired (independent) analysis, such as an independent samples t-test, or apply alternative methods that handle unequal sample sizes.

Option 2: False. This would state that two data sets of different sizes can be analyzed as paired data, which contradicts the fundamental requirement of pairing. A paired analysis relies on each observation in one set being matched with a specific observation in the other set, which cannot be guaranteed when the sizes differ. If someone tries to force a pairing by arbitrary matching or by discarding observations to equalize sizes, that introduces bias and changes the nature of the data, so it is not the standard or correct approach for genuine paired data analysis.

In summary, the correct interpretation is that the statement is true: you cannot properly analyze two data sets of different sizes as paired data without modifying the data or the analysis method. If paired analysis is desired, you must ensure one-to-one correspondence, typically by aligning sizes or rethinking the study design to obtain equal-length paired observations.

FA25_QTM_100_3 7.16: True / False: paired.

Two data sets of different sizes cannot be analyzed as paired data.

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