Question

determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. stress score where the mean is zero and the increments of measurement are equal choose the correct answer below. a. the ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural starting point. b. the nominal level of measurement is most appropriate because the data cannot be ordered. c. the ordinal level of measurement is most appropriate because the data can be ordered, but differences (obtained by subtraction) cannot be found or are meaningless. d. the interval level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is no natural starting zero point.

Explanation:

1. Recall the definitions of each level of measurement:

• Nominal: Data is categorized, no order. So option B is wrong as stress scores can be ordered.
• Ordinal: Data can be ordered, but differences (subtraction) are not meaningful. Option C says differences are not meaningful, but the problem states "the mean is zero and the increments of measurement are equal" – for ordinal, we don't use mean (since differences aren't meaningful), so C is wrong.
• Ratio: Has a natural zero (where zero means absence of the quantity), and ratios (e.g., twice as much) and differences are meaningful. But the problem says "the mean is zero" and "no natural starting zero point" – ratio has a natural zero, so A is wrong.
• Interval: Data can be ordered, differences (subtraction) are meaningful, but there's no natural zero (zero doesn't mean absence of the quantity). Stress scores (like in some psychological scales) can have a mean of zero (e.g., standardized scores), increments are equal (interval between scores is consistent), and no natural zero (a stress score of zero doesn't mean no stress in an absolute sense). So option D matches the interval level.

Answer:

D. The interval level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is no natural starting zero point.