Calculator Input
Example Data Table
You can load this sample directly into the calculator using the example button above.
| Observation | Value | Observation | Value | Observation | Value |
|---|---|---|---|---|---|
| 1 | 14.8 | 2 | 15.1 | 3 | 15.4 |
| 4 | 15.6 | 5 | 15.9 | 6 | 16.1 |
| 7 | 16.3 | 8 | 16.4 | 9 | 16.8 |
| 10 | 17.0 | 11 | 17.3 | 12 | 17.5 |
| 13 | 17.9 | 14 | 18.1 | 15 | 18.4 |
Formula Used
1. Order the sample values:
x(1) ≤ x(2) ≤ ... ≤ x(n)
2. Compute plotting positions:
Blom: p(i) = (i - 0.375) / (n + 0.25)
Hazen: p(i) = (i - 0.5) / n
Weibull: p(i) = i / (n + 1)
3. Convert each plotting position to a theoretical normal quantile:
z(i) = Φ⁻¹(p(i))
4. Fit the normal probability line by regression:
x(i) = a + b · z(i)
5. Estimate residual error:
s = √[ Σ(x(i) - x̂(i))² / (n - 2) ]
6. Compute approximate pointwise confidence intervals:
SE[x̂(i)] = s · √[ 1/n + (z(i) - z̄)² / Sxx ]
CI = x̂(i) ± t(α/2, n-2) · SE[x̂(i)]
This calculator plots ordered data against theoretical normal quantiles, fits a straight reference line, and adds approximate confidence bounds around that fitted relationship.
How to Use This Calculator
- Paste your sample values into the data box.
- Select a confidence level for the interval bands.
- Choose the plotting position method you prefer.
- Set the displayed decimal precision if needed.
- Click Generate Plot to calculate results.
- Review the chart, fitted line, confidence bounds, and detailed table.
- Use the CSV and PDF buttons to export your report.
FAQs
1. What does this plot test?
It compares ordered sample values with expected normal quantiles. Points near the fitted line suggest the data follow a roughly normal pattern. Systematic curvature, clustering, or strong tail departures suggest skewness, heavy tails, or outliers.
2. What do the confidence intervals represent?
They are approximate pointwise confidence bands around the fitted probability line. They show expected uncertainty in the fitted relationship at each theoretical quantile. They do not guarantee that every observation must fall inside the bands.
3. How many data points should I enter?
Use at least three values, but larger samples give more stable lines and bands. Ten or more observations usually make the shape easier to interpret, especially when you want to inspect tail behavior.
4. Which plotting position method should I choose?
Blom works well for many practical datasets. Hazen is also common, while Weibull is simple and intuitive. Keep the same method when comparing samples so the plotted quantiles remain consistent.
5. Why is the slope important?
The slope estimates sample spread on the plot scale. For normally distributed data, it is closely related to the standard deviation. Larger slopes indicate wider dispersion across ordered observations.
6. Can I use this for non-normal data?
Yes. The chart is useful precisely because it reveals non-normal structure. Strong bends, gaps, or extreme tail points can indicate skewness, mixtures, outliers, truncation, or other departures from normality.
7. What does the intercept mean?
The intercept estimates the plot value when the theoretical quantile equals zero. In practice, it approximates the sample center and is closely related to the mean when the data are nearly normal.
8. Do exports include the computed table?
Yes. CSV export saves the calculated rows for further analysis. PDF export captures the visible report area, including summary metrics, the plot, and the detailed results table on the page.