Run a normality test calculator with Jarque-Bera p-value, Shapiro-Wilk-style W, Q-Q fit, skewness, kurtosis, alpha thresholds, and next-step guidance.
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Normality test for pasted data Paste a numeric dataset to screen whether the distribution looks compatible with a normal curve. The calculator reports Jarque-Bera p-value, a Shapiro-Wilk-style ordered statistic for smaller samples, Q-Q fit diagnostics, skewness, kurtosis, and practical next steps.
Example datasets
A compact, roughly bell-shaped sample where the p-value does not reject normality.
Significance level
Common default for normality screening.
Normality assessment
Normality not rejected
The Jarque-Bera p-value of 0.6960 is at or above alpha = 0.05, so this screen does not reject normality. Skewness (0.000), excess kurtosis (-0.834), and the Q-Q fit should still be reviewed before relying on a normal-model assumption.
JB p-value
0.69595
Alpha = 0.05
Q-Q fit
98.209804%
Ordered normal-score R²
Skewness
0
Excess kurtosis
-0.83424
Small sample
Small samples can miss moderate non-normality. Pair the p-value with the Q-Q fit, skewness, kurtosis, and subject-matter context.
The ordered values sit close to expected normal quantiles, so the Q-Q pattern is visually consistent with normality.
No major shape warning from this screen Skewness, kurtosis, and Q-Q residuals do not show a large departure, but normality assumptions should still be checked in the context of the analysis.
Test statistics
Metric
Value
How to read it
Jarque-Bera
0.724955
Combines skewness and excess kurtosis into a normality test statistic.
Shapiro-Wilk-style W
0.982098
Shown for 3-50 values as an ordered-value fit check; values closer to 1 fit normal order statistics better.
Q-Q correlation
0.991009
Correlation between expected normal quantiles and ordered observed z-scores.
Max Q-Q residual
0.217162
Largest ordered z-score gap from its expected normal quantile.
Dataset summary
Count
25
Mean
4
Sample std dev
0.204124
Min to max
3.6 to 4.4
Range
0.8
What to do next
Use with assumptions check
If the analysis depends on normal residuals, confirm the model residuals look normal rather than relying only on raw input values.
Check variance and outliers
A normality screen does not verify equal variances, independence, sampling design, or measurement quality.
Inspect the plot pattern
For smaller samples, p-values can miss departures that are obvious in ordered values or a Q-Q plot.
Interpreting normality tests
The null hypothesis is that the data are compatible with a normal distribution. A p-value below the selected alpha rejects that screen, but a p-value above alpha does not prove the data are perfectly normal. Pair the p-value with the Q-Q fit, sample size, skewness, kurtosis, and the assumptions of the statistical test you plan to run.
Normality test calculator guide: Shapiro-Wilk-style W, Jarque-Bera p-value, skewness
A normality test calculator screens whether a numeric dataset looks compatible with a normal distribution. This page combines a Jarque-Bera p-value, Shapiro-Wilk-style ordered-value statistic for smaller samples, Q-Q fit diagnostics, skewness, excess kurtosis, and practical next-step guidance so you can decide whether a normality assumption is reasonable before using t-tests, ANOVA, regression, control charts, or other normal-model methods.
What a normality test is checking
A normality test starts from a null hypothesis: the data are compatible with a normal distribution. A small p-value means the observed shape would be unusual if that null model were true, so the screen rejects normality at the selected alpha level. A large p-value does not prove the data are perfectly normal; it only means this test did not find strong evidence against normality.
That distinction matters in real work. A dataset can pass a normality test because the sample is small and the test has low power. A large dataset can fail because of a tiny departure that is statistically detectable but not important for the decision. The best normality checks combine p-values with shape diagnostics and context.
Jarque-Bera, skewness, and kurtosis
The Jarque-Bera test focuses on two shape features: skewness and excess kurtosis. Skewness measures whether the distribution is pulled left or right. Excess kurtosis measures whether the tails are heavier or lighter than a normal curve. Normal data has skewness near 0 and excess kurtosis near 0.
Jarque-Bera is especially useful when you want a quick screen for asymmetry and tail heaviness. It is less useful when the main concern is a subtle bend in the middle of a Q-Q plot or a small-sample issue that does not show up clearly through skewness and kurtosis alone.
JB = (n / 6) x (S^2 + K^2 / 4)
Jarque-Bera statistic, where n is sample size, S is skewness, and K is excess kurtosis.
p-value = exp(-JB / 2)
For the two-degree-of-freedom chi-square approximation used by the Jarque-Bera normality test.
Shapiro-Wilk-style W and Q-Q fit
Many competitor tools emphasize the Shapiro-Wilk test because it is widely used for small and moderate samples. This calculator reports a Shapiro-Wilk-style ordered-value statistic for 3 to 50 observations by comparing sorted data with expected normal order statistics. Values closer to 1 indicate that the ordered values line up better with a normal curve.
The Q-Q fit diagnostics are included because they make the result more practical. Q-Q correlation and the largest ordered z-score residual help you see whether the p-value is being driven by skew, tail behavior, or a point that sits far away from its expected normal quantile. This does not replace a formal Q-Q plot, but it gives the calculator a useful numeric version of the same idea.
Choosing the alpha level
Alpha is the cutoff used to decide whether the p-value is small enough to reject normality. The common default is 0.05. A stricter 0.01 threshold rejects normality only with stronger evidence. A more sensitive 0.10 threshold flags possible non-normality earlier.
The right alpha depends on the consequence of the assumption. If a downstream method is highly sensitive to non-normality, a more conservative screen can be justified. If the method is robust, the sample is large, or the departure is practically small, the decision should not rely on alpha alone.
What to do if the data fails the normality test
First, inspect the data. Check whether extreme values are real observations, data-entry mistakes, mixed populations, measurement-limit artifacts, or values from a different process. Normality tests are not a substitute for understanding how the data was generated.
If the departure is real, consider a transformation, robust method, or non-parametric alternative. Right-skewed positive data may respond to a log or square-root transform. Rank-based tests, bootstrap confidence intervals, robust regression, or median-and-quantile summaries may be better when a normal-model assumption is not defensible.
Limits of a normality calculator
This calculator tests the numeric values you enter. For regression, ANOVA, and many designed experiments, the normality assumption often applies to residuals rather than raw measurements. If you paste the wrong series, the normality result may answer the wrong question.
The calculator does not prove independence, equal variances, random sampling, measurement reliability, or absence of outliers. It also uses an educational Shapiro-Wilk-style ordered statistic rather than a full statistical package implementation with exact small-sample p-values. Treat the output as a high-quality screen, not a replacement for a full statistical review.
It screens whether a numeric dataset looks compatible with a normal distribution. People usually run a normality test before methods such as t-tests, ANOVA, regression diagnostics, capability analysis, or control-chart work where a normal-model assumption may matter.
Which normality test should I use?
Shapiro-Wilk is commonly preferred for small and moderate samples, while Jarque-Bera is useful when skewness and kurtosis are the main shape concerns. This calculator reports Jarque-Bera, a Shapiro-Wilk-style ordered statistic, and Q-Q fit diagnostics so you can compare several signals instead of relying on one number.
How many data points do I need for a reliable normality test?
With fewer than about 8 observations, normality tests have low power. Samples under 30 should be interpreted with caution and visual or ordered-value diagnostics. Larger samples make tests more sensitive, but they can also reject tiny departures that may not matter practically.
What does a normality test p-value mean?
The p-value estimates how unusual the observed shape would be if the data were compatible with a normal distribution under the test's assumptions. If the p-value is below the chosen alpha, the calculator rejects normality. If it is above alpha, it does not prove normality; it only means the screen did not find enough evidence to reject it.
What should I do if my data fails the normality test?
Check for data-entry errors, outliers, mixed groups, and measurement artifacts first. If the non-normality is real, consider transforming the data, using robust statistical methods, using non-parametric tests, or reporting medians and quantiles instead of relying on means and standard deviations alone.
Should I test raw data or model residuals?
It depends on the method. For regression and ANOVA, the normality assumption usually applies to residuals, not the raw response variable. For one-sample checks, process data, or measurement distributions, raw values may be appropriate. Paste the series that matches the assumption you need to evaluate.
Why can a large dataset fail normality even when the histogram looks fine?
Large samples give normality tests more power, so small deviations can become statistically significant. In that situation, look at Q-Q fit, skewness, kurtosis, outliers, and the robustness of the downstream method before treating the result as a practical blocker.
Can normality tests prove that data is normally distributed?
No. They can reject normality when evidence is strong enough, but they cannot prove that a dataset is exactly normal. The safest wording is that normality was not rejected at the selected alpha level.
