Visual Tool
BY: Statistics Fundamentals Team
Reviewed By: Minsa A (Senior Statistics Editor)

Rejection Region Diagram Maker

Create publication-ready rejection region diagrams for z-tests and t-tests. Set your significance level, choose the tail direction, and optionally add your test statistic — the tool calculates critical values, shades the rejection region, and renders an SVG diagram you can download instantly.

Rejection Region Diagram Maker

Critical region settings

Result

Alpha (α)0.050
Critical value(s)—
Test statistic—
p-value (approx.)—
Enter a test statistic to see the decision.

Standard normal distribution — two-tailed, α = 0.050

Best for
Hypothesis test reports
Supports
Left, right, and two tails
Output
Editable SVG diagram

Rejection Region Examples

Browse hypothesis testing visuals for reports, slides, and teaching materials

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What Is a Rejection Region Diagram?

A rejection region diagram shows the sampling distribution under the null hypothesis, the significance level (α), and the critical value boundary where the null hypothesis would be rejected. The shaded red area represents values of the test statistic that are so extreme under H₀ that they lead to rejection. It is commonly used in statistics homework, research methods sections, lab reports, and classroom slides.

According to the NIST Engineering Statistics Handbook, the rejection region (also called the critical region) is defined by the critical value — the threshold beyond which the test statistic is considered statistically significant. The choice of tail direction depends entirely on the alternative hypothesis.

When Should You Use This Tool?

Right-tailed diagram: Use when the alternative hypothesis tests whether a value is greater than the null value. H₁: μ > μ₀. The rejection region is in the right tail. Example: testing whether a new drug raises average blood pressure above baseline.
Left-tailed diagram: Use when the alternative hypothesis tests whether a value is smaller than the null value. H₁: μ < μ₀. The rejection region is in the left tail. Example: testing whether a teaching intervention reduces error rates below the historical average.
Two-tailed diagram: Use when the alternative hypothesis tests whether a value is different from the null value in either direction. H₁: μ ≠ μ₀. Alpha is split equally across both tails: α/2 per tail. Example: testing whether a coin is biased (either heads-heavy or tails-heavy).
t-Distribution: Use when the population standard deviation is unknown and your test statistic follows a t-distribution. The t-distribution has heavier tails than the standard normal, making critical values larger in magnitude. The shape depends on the degrees of freedom (df = n − 1 for one-sample t-tests).

How to Read the Diagram

If the test statistic (the vertical red line) falls inside the red shaded region, reject H₀ at the selected alpha level. If it stays outside the shaded region, fail to reject H₀. The decision rule is fully visual — no table look-up needed. For two-tailed tests, alpha is split equally between the left and right tails, so each tail contains α/2 of the total probability.

Critical Value Reference Table

The most commonly used critical values for the standard normal distribution:

α levelTwo-tailed z*Right-tailed z*Left-tailed z*
α = 0.10±1.645+1.282−1.282
α = 0.05±1.960+1.645−1.645
α = 0.025±2.241+1.960−1.960
α = 0.01±2.576+2.326−2.326
α = 0.001±3.291+3.090−3.090

Z-Test vs T-Test: Which Distribution to Use?

FeatureZ-TestT-Test
Population σKnownUnknown (estimated from sample)
Sample sizeLarge (n ≥ 30)Any, but especially small (n < 30)
Distribution shapeStandard normal (fixed)Student's t (depends on df)
Critical valuesFixed for given α and tailLarger magnitude; approach z as df → ∞
Common applicationsProportion tests, large survey samplesOne-sample, two-sample, paired t-tests

Related Topics

Hypothesis Testing Guide T-Test Calculator Z-Score Calculator Normal Distribution Calculator Chi-Square Calculator Bell Curve Generator

Sources & further reading:

Frequently Asked Questions

Yes. Use the Left / Two / Right toggle buttons in the control panel. Left-tailed shades the left tail, right-tailed shades the right tail, and two-tailed shades both tails with α split equally (α/2 per tail). The critical values update automatically based on your choice.

Yes. Select "Z test (standard normal)" for a z-test or "t test (Student's t)" for a t-test. For t-tests, enter the degrees of freedom (df = n − 1 for one-sample tests, df = n₁ + n₂ − 2 for independent two-sample tests). The t critical values are computed using an accurate numerical approximation of the inverse t-CDF.

Yes. Enter your test statistic in the "Test statistic" field. A solid vertical red line will be drawn at that value on the distribution. The result panel will then show "Reject H₀" if the statistic falls in the rejection region, or "Fail to Reject H₀" if it falls outside. Leave the field blank to show only the critical region.

The dropdown includes the five most common significance levels: α = 0.10, 0.05, 0.025, 0.01, and 0.001. You can also select "Custom…" to enter any value between 0.0001 and 0.5. The most common choice in academic research is α = 0.05, which means a 5% chance of rejecting a true null hypothesis (Type I error rate).

Yes. Click "Download SVG" to save the diagram as a scalable vector graphic (SVG) file that can be opened in Illustrator, Inkscape, or any vector editor. SVG files are infinitely scalable and ideal for academic papers, slide decks, and lab reports. "Copy SVG" copies the SVG code to your clipboard for direct pasting into HTML or other applications.

Not exactly. A p-value calculator takes a test statistic and returns the probability of observing a result at least as extreme under H₀. This tool visualizes the critical region approach — it shows the threshold (critical value) and whether your test statistic falls inside it. Both approaches give the same decision, but the critical region method is more visual and easier to explain in presentations. The tool does show an approximate p-value alongside the diagram.