A researcher tightens their significance threshold from α = 0.05 to α = 0.01 without changing anything else about their study. What happens to Type I and Type II error rates?
ABoth Type I and Type II error rates decrease, since a stricter threshold improves the test overall
BType I error rate decreases, but Type II error rate increases (and power falls), since more of the alternative distribution now falls on the fail-to-reject side
CType II error rate decreases because the test is now more conservative
DNeither error rate changes; only the p-value threshold changes
Moving the threshold right (stricter α) puts less of the null distribution in the rejection region — Type I error falls. But simultaneously, more of the alternative distribution falls outside the rejection region — β rises and power falls. Visualize two overlapping curves: the threshold line sits between them. Slide it right: less false-alarm area under the null curve, but more miss-area under the alternative curve. The two error rates are coupled through the shared threshold — you cannot reduce one without enlarging the other, holding all else fixed.
Question 2 Multiple Choice
A medical screening test for a serious disease has α = 0.10 and β = 0.20. A statistician recommends lowering α to 0.01 to make the test more rigorous. A clinician objects. Why might the clinician be right?
AReducing α is always the wrong choice in medical contexts regardless of the disease
BIn screening contexts, missing a true case (Type II error) is often more harmful than a false positive; lowering α raises β, meaning more sick patients go undetected — the cost of the error being minimized may be lower than the cost of the error being inflated
CSignificance levels cannot be changed once a study has been designed
DThe clinician prefers a higher false positive rate because it increases treatment revenue
The choice between error types is a substantive judgment, not a statistical one. In screening for a serious disease, false negatives (missing a case) typically carry catastrophic consequences — the patient goes untreated. False positives (flagging a healthy patient) lead to follow-up tests, which is costly and stressful but usually recoverable. Lowering α from 0.10 to 0.01 reduces false alarms but increases missed cases (β rises). For this application, raising β is likely the worse tradeoff. The relative costs of the two errors depend on what happens downstream.
Question 3 True / False
Increasing sample size is the primary way to simultaneously achieve lower Type I error and higher power, because it narrows both distributions and reduces their overlap.
TTrue
FFalse
Answer: True
This is the key escape from the Type I/Type II tradeoff. With fixed distributions, moving the threshold always trades one error for the other. But a larger sample makes both the null and alternative distributions narrower (by the Central Limit Theorem, standard errors shrink). If the two distributions are narrow enough and far enough apart, the threshold can sit in a gap between them — delivering low α and high power simultaneously. Power analysis before a study asks exactly this question: how large must n be to achieve acceptable error rates on both sides?
Question 4 True / False
A researcher who raises their significance threshold from α = 0.05 to α = 0.10 will thereby increase their Type II error rate.
TTrue
FFalse
Answer: False
Raising α (moving the rejection threshold left) expands the rejection region — more of the alternative distribution now falls on the rejection side. This means fewer misses: β decreases and power increases. The tradeoff runs in both directions: tightening α (moving threshold right) decreases Type I but increases Type II; loosening α (moving threshold left) decreases Type II but increases Type I. The student who memorizes 'strict α is good' without understanding the geometry will get this backwards.
Question 5 Short Answer
Explain the mechanism by which reducing Type I error by tightening α increases Type II error, and describe what must change in a study design to escape this tradeoff.
Think about your answer, then reveal below.
Model answer: Tightening α moves the rejection threshold to a more extreme position, so fewer observations from the null distribution trigger rejection (Type I error falls). But the same threshold shift means more observations from the alternative distribution now fall on the non-rejection side — more true effects are missed (Type II error rises, power falls). The two error rates share one threshold: there is no position that minimizes both simultaneously. The escape is increasing sample size, which narrows both distributions (reducing standard errors), pushing them apart until the threshold can sit in the gap between them rather than in a region of overlap — achieving low α and high power simultaneously.
The geometric picture is essential: two bell curves partially overlapping, with a threshold line. Every threshold position produces a specific (Type I, Type II) pair. Moving the line trades one for the other. The only way to improve both simultaneously is to reduce the overlap itself — which means larger samples. This is why 'we need a bigger study' is a principled statistical claim, not just a hedge.