DQ 2 : Discuss the errors which can be made by failing to understand the proper use of measurement variables based on level and type of comparison.

Define the four levels by what operations each permits, since that is what generates the errors. Nominal variables are labels — insurance type, unit, diagnosis category — and the only legitimate operations are counting and comparing frequencies. Ordinal variables have order but unequal or unknown intervals: pain scores, Likert agreement, triage acuity, pressure injury stage. Interval variables have equal intervals and an arbitrary zero, so differences are meaningful and ratios are not, which is why 40 degrees Celsius is not twice as hot as 20. Ratio variables have equal intervals and a true zero — weight, length of stay, dose, count of falls — and support the full range of arithmetic. The rule is that the permitted operations run upward: anything you can do at a lower level you can do at a higher one, and not the reverse. State the permitted operations for each level and the errors become obvious.

Now the errors, which is what the prompt actually asks for. Averaging ordinal data is the commonest: a mean pain score of 4.7 treats the distance from 3 to 4 as equal to the distance from 8 to 9, which nobody believes about pain, and the same objection applies to the mean of a Likert item. Treating a coded nominal variable as numeric is worse and is usually a software artefact: coding units as 1 to 5 and reporting a mean of 3.2 produces a number with no referent at all. Choosing the wrong test follows directly — a t-test on ordinal data where a Mann-Whitney was needed, or a Pearson correlation where Spearman was appropriate. In reverse, collapsing a ratio variable into categories throws away information and power for no reason beyond convenience. In a DPI Project the level at which you record your outcome decides which comparisons exist afterwards.