Wald Test Logistic Regression Calculator

Calculator Input Form

The layout stays single-column overall, while the calculator fields use a responsive 3-column, 2-column, and 1-column grid.

Predictor Name

Outcome Name

Estimated Coefficient (β̂)

Standard Error

Null Coefficient (β₀)

Confidence Level (%)

Sample Size (optional)

Number of Events (optional)

Quick Guide

Enter β̂ and its standard error from a fitted logistic model. The calculator then returns the Wald test, p-value, odds ratio, and confidence intervals.

Formula Used

1) Wald z statistic

z = (β̂ - β₀) / SE(β̂)

This compares the estimated logistic coefficient to its hypothesized null value, usually zero.

2) Wald chi-square statistic

W = z²

For one coefficient, the Wald chi-square has 1 degree of freedom.

3) Two-tailed p-value

p = 2 × [1 - Φ(|z|)]

Here, Φ is the cumulative distribution function of the standard normal distribution.

4) Odds ratio

OR = exp(β̂)

A positive coefficient gives an odds ratio above one, while a negative coefficient gives an odds ratio below one.

5) Confidence interval

β̂ ± z* × SE(β̂)

The calculator also exponentiates the coefficient limits to produce the confidence interval for the odds ratio.

How to Use This Calculator

Enter the predictor name and the binary outcome label.
Paste the estimated logistic regression coefficient into the β̂ field.
Enter the coefficient’s standard error from your regression output.
Keep β₀ at zero for the usual null test, or change it if needed.
Select your preferred confidence level.
Optionally enter sample size and event count for extra context.
Click Calculate Wald Test to show the result above the form.
Use the CSV and PDF buttons to export your calculated output.

Example Data Table

These rows demonstrate how typical coefficient tests may look in practice.

Predictor	Coefficient (β̂)	SE	Wald z	p-Value	Odds Ratio	95% OR CI
Age (years)	0.42	0.15	2.80	0.0051	1.52	[1.13, 2.04]
Current smoker	1.10	0.32	3.44	0.0006	3.00	[1.60, 5.62]
Exercise hours	-0.28	0.11	-2.55	0.0109	0.76	[0.61, 0.94]

Frequently Asked Questions

1) What does the Wald test check in logistic regression?

It tests whether a specific coefficient differs from its hypothesized value, usually zero. In practice, it asks whether the predictor contributes evidence about the outcome after accounting for the coefficient’s estimated uncertainty.

2) What inputs do I need for this calculator?

You need the estimated logistic coefficient and its standard error. Predictor name, outcome label, confidence level, sample size, and event count improve readability and reporting, but the coefficient and standard error drive the core Wald calculations.

3) How is the Wald z statistic calculated?

The calculator subtracts the null coefficient from the estimated coefficient and divides that difference by the standard error. A larger absolute z value indicates stronger evidence against the null hypothesis.

4) What does the odds ratio tell me?

The odds ratio is the exponentiated coefficient. Values above one indicate higher odds as the predictor increases, while values below one indicate lower odds, assuming other variables in the model stay fixed.

5) Why can Wald tests be unreliable sometimes?

Wald tests can behave poorly with small samples, rare events, large standard errors, or separation problems. In those situations, likelihood ratio tests or profile likelihood intervals often provide more stable inference.

6) What p-value usually indicates significance?

Many analysts compare the p-value to 0.05, but the best threshold depends on the study design and error tolerance. This calculator automatically compares the p-value with the alpha implied by your chosen confidence level.

7) Can I test a null coefficient other than zero?

Yes. Enter a different β₀ value when your hypothesis tests a specific nonzero effect. The calculator then evaluates whether the estimated coefficient differs meaningfully from that alternative null target.

8) Is the Wald test better than the likelihood ratio test?

Not always. The Wald test is fast and convenient because it uses only the estimate and its standard error. Likelihood ratio tests often perform better when coefficients are large, samples are limited, or the model is numerically unstable.