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Critical Value Calculator

Math Calculators

Z/t/χ² inverse lookup, two or one tail, rejection region

Quick Answer

Critical Value Calculator: Z/t/χ² inverse lookup, two or one tail, rejection region. Critical Value Calculator uses standard math formulas to compute accurate results instantly.

Distribution

Tail direction

Critical value
±1.9600
Reject H₀ when |Z| > 1.9600
Critical value±1.9600
Rejection region|Z| > 1.9600
Verify sf = α2 × P(Z > 1.9600) = 0.0500 = α
α (per tail)0.025

Calculation steps

  1. 1标准正态分布，双尾检验，α = 0.05，每侧 0.025
  2. 2解 P(Z > z) = 0.025 → z = 1.9600
  3. 3拒绝域：|Z| > 1.9600，即 Z < -1.9600 或 Z > 1.9600

Common critical values

Distributionα 0.10α 0.05α 0.025α 0.01α 0.005
Z two-tail1.64491.96002.24142.57582.8070
Z one-tail (upper)1.28161.64491.96002.32632.5758
t two-tail (df=10)1.81252.22812.63383.16933.5814
χ² (df=1)2.70553.84155.02396.63497.8794
χ² (df=5)9.236411.070512.832515.086316.7496
  • Critical value and p-value are two sides of the same coin: given the statistic, compute p; given α, find the cutoff. Both reach the same decision.
  • Two-tailed α splits evenly: α = 0.05 means each tail holds 0.025, hence the ±1.9600 cutoff.
  • χ² is non-negative and right-skewed, so its test always uses the right tail only — the tail selector is hidden for χ².
  • t approaches Z as df grows: df = 30 gives 2.0423 vs 1.9600; use Z when df ≥ 120 in practice.
  • The table above is computed live by the same engine (no hand-copied tables), values match standard tables to 4 decimals.

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How to Use

  1. Enter values or expressions: type directly into the Critical Value Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Critical Value Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Z/t/χ² inverse lookup, two or one tail, rejection region.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Critical Value Calculator formula

Critical Value Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Critical Value Calculator?
Open the page and fill in the input fields — results update automatically. Z/t/χ² inverse lookup, two or one tail, rejection region.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

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Results provided by this tool are for reference only and do not constitute professional advice.