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Statistics · Hypothesis testing

Critical Value Calculator

Find normal, t, chi-square, or F cutoffs for a selected significance level and tail convention.

Statistics · Hypothesis testing

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
A test statistic is located on its null reference distribution. The selected tail rule defines results at least as extreme.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand the hypothesis test

Read the test as a model-based comparison

Critical Value. The observed effect is scaled by its null-model uncertainty and located on a reference distribution selected before looking at the result.

Test statistic and reference model

Critical values are quantiles of the selected null reference distribution.

A critical value defines a rejection region chosen before analyzing the observed statistic.

Responsible interpretation

A p-value is not the probability that the null is true, the chance the result occurred ‘by luck,’ or a measure of effect size, importance, replication, bias, or causation.

Required assumption: Degrees of freedom and tail direction must match the underlying test; an F cutoff also needs numerator and denominator degrees of freedom.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the critical value calculator works

Critical values are quantiles of the selected null reference distribution.

A critical value defines a rejection region chosen before analyzing the observed statistic.

Worked example

Critical Value example

The two-sided standard-normal critical values at α=0.05 are approximately ±1.96.

Critical values are quantiles of the selected null reference distribution.

Supported inputs

Precision and limits

Model and design

Degrees of freedom and tail direction must match the underlying test; an F cutoff also needs numerator and denominator degrees of freedom.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

A critical value defines a rejection region chosen before analyzing the observed statistic.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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