Under a stated hypothesis test and its assumptions, what does statistical significance at a specified alpha mean?
Correct Answer
D) The result meets the stated rejection criterion for the null hypothesis
Under a stated null hypothesis and test assumptions, a p-value measures how incompatible the observed statistic is with that null, using results at least as extreme. A result called significant at a specified alpha meets the test’s rejection criterion. This does not give the probability that the null is true, prove causation or establish practical importance or applicability to every property.
Why This Is the Correct Answer
Option D is correct because statistical significance at a specified alpha means the test result meets the stated rejection criterion for the null hypothesis. Under the null and the test assumptions, the observed statistic is incompatible enough with the null to cross that threshold. It says nothing directly about effect size or the probability that the null is true.
Why the Other Options Are Wrong
Option A: The effect is large enough to matter in practice for valuation decisions
Option A, that the effect is large enough to matter in practice for valuation decisions, confuses statistical significance with practical importance. A tiny effect can be statistically significant with enough data, so significance does not establish practical relevance.
Option B: A second party has independently verified the result
Option B, that a second party has independently verified the result, is unrelated to significance. Significance comes from the test calculation, not from outside review or replication.
Option C: The conclusion applies to each property in the market that was sampled
Option C, that the conclusion applies to each property in the sampled market, overstates what a test shows. Significance concerns the tested hypothesis about the population parameter, not a guarantee that each individual property behaves the same way.
Significant means past the line
Significant just means the result crossed the test's rejection line at the chosen alpha. It does not mean big, verified or universal.
How to use: Use this to reject choices that read extra meaning into significance.
Exam Tip
Pick the choice that restates the rejection criterion; be wary of choices that equate significance with importance or broad applicability.
Common Mistakes to Avoid
- -Equating statistical significance with practical importance
- -Treating significance as the probability that the null is true
- -Applying a significant result to every individual property
Concept Deep Dive
Analysis
This question tests the precise meaning of statistical significance. A result significant at a specified alpha meets the test's rejection criterion for the null hypothesis; it does not establish practical importance, independent verification or applicability to each property.
Background Knowledge
In hypothesis testing, the p-value measures how incompatible the data are with a stated null hypothesis, based on results at least as extreme as those observed. A result is called significant when it falls within the rejection region at the chosen alpha. Significance does not give the probability that the null is true, prove causation or measure practical importance.
Real-World Application
A regression shows a pool adds a statistically significant amount to sale price. The appraiser still evaluates whether the dollar amount is meaningful in the market and whether it fits the subject property before relying on it.
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