Wald Test Calculator

Advanced Statistical Tests

This calculator performs a Wald test to determine the statistical significance of a parameter estimate.

Practical Examples

See how the Wald Test is applied in different scenarios. Load an example to see how the calculation works.

Basic Significance Test

General

A standard test to see if a coefficient is significantly different from zero.

β̂: 2.5, β₀: 0

SE: 1.1, α: 0.05

Impact of Education on Wages

Economics

Testing if an additional year of education (coefficient = 0.08) has a non-zero effect on wages, with a standard error of 0.02.

β̂: 0.08, β₀: 0

SE: 0.02, α: 0.05

Drug Efficacy Trial

Medical

A study finds a new drug has an effect size of -0.5 with a standard error of 0.2. Is this effect significantly different from zero?

β̂: -0.5, β₀: 0

SE: 0.2, α: 0.01

Testing Against a Specific Value

Advanced

Testing if a parameter estimate of 1.2 (SE = 0.15) is significantly different from a theoretical value of 1.0.

β̂: 1.2, β₀: 1.0

SE: 0.15, α: 0.05

Other Titles
Understanding the Wald Test: A Comprehensive Guide
An essential tool for hypothesis testing in statistical analysis, the Wald test helps determine the significance of parameters in a model.

What is the Wald Test?

  • Core Principle
  • The Wald Statistic
  • Relationship to Other Tests
The Wald test is a parametric statistical test used to assess the significance of individual parameters in a statistical model. It determines whether an independent variable has a statistically significant relationship with the dependent variable. The core idea is to test whether the estimated coefficient of the parameter is significantly different from a specific value, which is usually zero (the null hypothesis).
Core Principle
The test works by comparing the maximum likelihood estimate of the parameter (β̂) to its hypothesized value (β₀). The difference is then standardized by dividing by the standard error of the estimate. A large Wald statistic suggests that the estimated parameter is far from the hypothesized value, leading to the rejection of the null hypothesis.
The Wald Statistic
The formula for the Wald statistic (W) is:
W = ( (β̂ - β₀)² ) / ( SE(β̂)² )
Under the null hypothesis, this statistic follows a chi-squared (χ²) distribution with one degree of freedom. We compare the calculated W value to a critical value from the χ² distribution (or, more commonly, calculate a p-value) to make a decision.

Step-by-Step Guide to Using the Calculator

  • Inputting Your Data
  • Choosing a Significance Level
  • Interpreting the Results
Using the calculator is straightforward. Follow these steps for an accurate analysis.
1. Enter the Parameter Estimate (β̂)
This is the coefficient you want to test. You can find this value in the output of your regression analysis (e.g., from R, Python, Stata, SPSS).
2. Enter the Hypothesized Value (β₀)
This is the value you are testing against. To check if the parameter is statistically significant, you typically use 0. However, you can use any value to test other hypotheses.
3. Enter the Standard Error (SE)
The standard error of the estimate is also available in your model's output, usually right next to the coefficient itself.
4. Select the Significance Level (α)
This determines the threshold for statistical significance. A value of 0.05 is the most common, meaning you accept a 5% chance of incorrectly rejecting the null hypothesis.
Interpreting the Results
The calculator provides the Wald statistic, the p-value, and a clear conclusion. If the p-value is less than your chosen significance level (α), you reject the null hypothesis and conclude that your parameter is statistically significant.

Real-World Applications of the Wald Test

  • Economics and Finance
  • Biostatistics and Medicine
  • Social Sciences
The Wald test is widely used across various disciplines to validate statistical models.
Economics and Finance
Economists use the Wald test to determine if variables like interest rates, inflation, or government policy have a significant effect on economic outcomes like GDP growth or unemployment.
Biostatistics and Medicine
In clinical trials, researchers use it to test whether a new drug has a statistically significant effect on a health outcome compared to a placebo. It helps validate if the observed effect is real or due to chance.
Social Sciences
Sociologists and political scientists might use the Wald test to see if factors like education level, income, or location significantly predict behaviors like voting patterns or survey responses.