Kolmogorov Smirnov Normal Reference Calculator
Compare an empirical sample CDF with a fully specified normal CDF using the two-sided KS distance.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sort the observations and compare both sides of each empirical CDF jump to the entered continuous normal reference.
D=maxᵢ(i/n−F(xᵢ),F(xᵢ)−(i−1)/n); asymptotic p=Kolmogorov survival at √n D
Worked example
For a single reference probability F(0)=0.5, a sample consisting only of zeros has KS distance 0.5 regardless of sample count; such ties need the stated inference caution.
Assumptions and input details
Mean and SD must be prespecified independently, not estimated from this sample: this is not Lilliefors. The p-value is the limiting large-sample approximation, unreliable for small samples and tied/discrete observations. No exact finite-n inference.
References: NIST: KS goodness-of-fit test
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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