Calculator Inputs
Example Data Table
| Scenario | Estimate | Standard Error | Null Value | Alpha | Test Type |
|---|---|---|---|---|---|
| Logistic coefficient test | 0.8500 | 0.2100 | 0.0000 | 0.05 | Two-sided |
| Mean difference coefficient | 1.4200 | 0.4800 | 0.0000 | 0.01 | Right-tailed |
| Elasticity constraint test | -0.6300 | 0.1900 | -1.0000 | 0.05 | Left-tailed |
These rows are illustrative and help demonstrate how coefficient estimates and standard errors feed the Wald procedure.
Formula Used
Two-sided p-value: 2 × [1 − Φ(|Z|)]
Left-tailed p-value: Φ(Z)
Right-tailed p-value: 1 − Φ(Z)
Confidence interval: Estimate ± Zcritical × Standard Error
This method is common for regression coefficients, proportions, and large-sample parameter inference where asymptotic normality is reasonable.
How to Use This Calculator
- Enter the parameter label so your output remains easy to read.
- Provide the estimated coefficient or parameter value.
- Enter the standard error from your model or summary table.
- Set the null value, often zero for significance testing.
- Choose alpha and confidence level based on your analysis requirement.
- Select the correct alternative type: two-sided, left-tailed, or right-tailed.
- Optionally add sample size, variance, scale, and analysis notes.
- Click the compute button to view the result summary, interval, p-value, and chart above the form.
Frequently Asked Questions
1. What does the Wald test measure?
It checks whether an estimated parameter differs significantly from a specified null value using the estimate, its standard error, and the normal approximation.
2. When is the Wald test appropriate?
It is appropriate in large-sample settings where the estimator is approximately normally distributed, such as many regression and generalized linear model outputs.
3. What is the null value in this calculator?
The null value is the hypothesized benchmark for the parameter. In many coefficient tests, that benchmark is zero.
4. How is the p-value calculated?
The p-value comes from the standard normal distribution after converting the estimate and standard error into a Wald z statistic.
5. Why does standard error matter so much?
Standard error controls the scale of uncertainty. Smaller standard errors produce larger Wald statistics for the same estimate difference.
6. What does rejecting H₀ mean here?
Rejecting H₀ means the observed estimate is statistically inconsistent with the null value at the chosen significance level.
7. Can this calculator handle one-sided tests?
Yes. You can choose left-tailed or right-tailed testing, and the calculator adjusts the p-value and critical threshold accordingly.
8. Is the Wald test always the best option?
No. In small samples or unstable models, likelihood ratio or score tests can perform better than a Wald-based approximation.