A price-related differential above 1.03 in a ratio study suggests which pattern?
Correct Answer
A) Higher-value properties are assessed relatively lower
Why this is correct: The price-related differential (PRD) detects assessment regressivity or progressivity. A PRD significantly above 1.03 indicates regressivity, meaning higher-value properties are assessed at a lower proportion of their value (relatively lower) compared to lower-value properties. Why the other choices are wrong: A PRD above 1.03 suggests the opposite of lower-value properties being assessed relatively lower. It indicates non-uniformity, not uniformity. The PRD calculation itself does not comment on sample size adequacy. Exam tip: PRD > 1.03 = Regressive (high-value properties under-assessed). PRD < 0.98 = Progressive (high-value properties over-assessed).
Why This Is the Correct Answer
Option A is correct because a PRD above 1.03 indicates regressivity, which by definition means higher-value properties carry relatively lower assessment ratios. The arithmetic follows directly: low ratios on the high-value properties pull the value-weighted mean down while leaving the unweighted mean comparatively high, and the quotient of the two exceeds one. Recognizing the direction is the entire task, since both this option and its mirror image are offered. The practical implication is an equity problem that an assessing jurisdiction would need to correct.
Why the Other Options Are Wrong
Option B: Lower-value properties are assessed relatively lower
This describes progressivity, the opposite condition, in which lower-value properties are assessed at lower ratios and higher-value properties at higher ones. That pattern pushes the weighted mean above the unweighted mean and drives the PRD below 1.00, generally flagged below 0.98. The two conditions are symmetric, which is why reversing them is the most likely error on this item.
Option C: All properties in the group are assessed uniformly
Uniform assessment would place the PRD close to 1.00, within the accepted band, because the ratios would not vary systematically with property value. A reading above 1.03 is by definition evidence that uniformity has failed in a value-related way. Note also that the PRD addresses only value-related bias; overall dispersion is measured separately by the coefficient of dispersion.
Option D: The sample contained too few sales to evaluate
The PRD is a computed statistic and says nothing about whether the sample was large enough; adequacy of sample size is judged separately, and a small sample simply makes any resulting statistic less reliable. A ratio study can produce a PRD from very few sales, and the number will be meaningful only to the extent the sample represents the stratum. The option confuses a diagnostic result with a data sufficiency question.
PRD High, Rich Ratios Low
PRD high means the rich pay a lower ratio. Push the big properties' ratios down and the value-weighted mean drops, so dividing the plain mean by that smaller weighted mean gives a number above one. High PRD, high-value properties under-assessed, and that is what regressive means here.
How to use: Fix the direction with the band: below 0.98 is progressive, 0.98 to 1.03 is acceptable, above 1.03 is regressive. Then translate regressive into plain language, meaning expensive properties assessed at lower ratios. Match that translation to the option, and ignore choices about uniformity or sample size, which are different statistics and different questions.
Exam Tip
Memorize the 0.98 to 1.03 band together with which side is which; questions on this topic almost always turn on direction rather than on computing the statistic.
Common Mistakes to Avoid
- -Reversing regressive and progressive when interpreting the PRD
- -Treating the PRD as a general uniformity measure rather than a value-related bias measure
- -Drawing conclusions from a PRD computed on a thin or unrepresentative sample of sales
Concept Deep Dive
Analysis
This question tests a mass appraisal uniformity statistic used in assessment ratio studies. A ratio study compares each property's assessed value to its sale price, producing an assessment ratio for every observation. The price-related differential is computed by dividing the mean of those ratios by the weighted mean, where the weighted mean is total assessed value divided by total sale price and therefore gives more influence to higher-value properties. When high-value properties are assessed at lower ratios than low-value properties, the weighted mean falls below the simple mean and the PRD rises above one. That pattern is called regressivity, because the effective assessment burden regresses as value increases, and it means owners of modest properties are shouldering a proportionally heavier share of the tax. The generally accepted standard treats a PRD between 0.98 and 1.03 as acceptable uniformity, so a reading above 1.03 signals regressivity worth investigating, and a reading below 0.98 signals progressivity in the opposite direction.
Background Knowledge
You need to know how an assessment ratio study is constructed and the main statistics it produces, including the median ratio as a measure of level, the coefficient of dispersion as a measure of uniformity, and the price-related differential as a measure of value-related bias. You should also know the generally accepted PRD band of 0.98 to 1.03 and the terms regressive and progressive as they apply to assessment, which run opposite to their everyday usage in tax policy.
Real-World Application
A county's ratio study of 480 residential sales returns a median ratio of 0.94 and a PRD of 1.09. The analyst concludes higher-value homes are systematically under-assessed relative to modest ones, recommends re-examining the valuation model's treatment of quality and size, and stratifies the next study by price range to isolate where the bias originates.
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