P-Value Calculator

P-Value is evaluated from Test Statistic, Test Type and Significance Level. The calculation reports P-Value, Decision and Interpretation.

Results

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About the P-Value Calculator

P-Value is treated here as a quantitative relation between Test Statistic, Test Type and Significance Level and P-Value, Decision, Interpretation and Critical Value z*.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Two-tailed: p = 2 x (1 - Phi(|z|))
Right-tailed: p = 1 - Phi(z)
Left-tailed: p = Phi(z)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Two-tailed: p = 2 x (1 - Phi(|z|))
Right-tailed: p = 1 - Phi(z)
Left-tailed: p = Phi(z)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Drug Trial — Mean BP Reduction

Inputs

test_stat: 2.35 test_type: two alpha: 0.05

P-Value: 0.018773. Decision: Reject H0. Interpretation: Statistically significant at alpha = 0.05. Critical Value z*: 1.96

With Test Statistic = 2.35, Test Type = two and Significance Level = 0.05 as the stated inputs, the result is P-Value = 0.018773, Decision = Reject H0 and Interpretation = Statistically significant at alpha = 0.05. Each value corresponds to the declared output fields.

Example 2: Website A/B Test — Conversion Rate

Inputs

test_stat: 1.87 test_type: right alpha: 0.05

P-Value: 0.030742. Decision: Reject H0. Interpretation: Statistically significant at alpha = 0.05. Critical Value z*: 1.645

With Test Statistic = 1.87, Test Type = right and Significance Level = 0.05 as the stated inputs, the result is P-Value = 0.030742, Decision = Reject H0 and Interpretation = Statistically significant at alpha = 0.05. Each value corresponds to the declared output fields.

Example 3: Quality Control — Underfilling

Inputs

test_stat: -2.58 test_type: left alpha: 0.01

P-Value: 0.00494. Decision: Reject H0. Interpretation: Statistically significant at alpha = 0.01. Critical Value z*: 2.326

With Test Statistic = -2.58, Test Type = left and Significance Level = 0.01 as the stated inputs, the result is P-Value = 0.00494, Decision = Reject H0 and Interpretation = Statistically significant at alpha = 0.01. Each value corresponds to the declared output fields.

Example 4: Fail to Reject — Education Study

Inputs

test_stat: 1.42 test_type: two alpha: 0.05

P-Value: 0.155608. Decision: Fail to Reject H0. Interpretation: Not statistically significant at alpha = 0.05. Critical Value z*: 1.96

With Test Statistic = 1.42, Test Type = two and Significance Level = 0.05 as the stated inputs, the result is P-Value = 0.155608, Decision = Fail to Reject H0 and Interpretation = Not statistically significant at alpha = 0.05. Each value corresponds to the declared output fields.

Common Use Cases

Test if a sample mean differs significantly from a target
Determine statistical significance of an experiment
Calculate p-value from test statistic
Compare means in A/B testing