Kolmogorov-Smirnov Test (vs Normal)
Computes the one-sample Kolmogorov-Smirnov test against a normal distribution with specified mean and standard deviation. It measures the largest vertical distance between your data's empirical cumulative distribution and the theoretical normal curve — the D statistic. Unlike tests that look only at skewness or kurtosis, the KS compares the entire distributions, point by point. Enter the sample and the normal parameters (mean and standard deviation) to test.
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Kolmogorov-Smirnov Test (vs Normal)
Computes the one-sample Kolmogorov-Smirnov test against a normal distribution with specified mean and standard deviation. It measures the largest vertical distance between your data's empirical cumulative distribution and the theoretical normal curve — the D statistic. Unlike tests that look only at skewness or kurtosis, the KS compares the entire distributions, point by point. Enter the sample and the normal parameters (mean and standard deviation) to test.
Comparing your data with the entire normal curve
Testing normality can mean different things. Some tests look at a specific aspect, like skewness; the Kolmogorov-Smirnov test looks at the distribution as a whole. It asks how far the cumulative shape of your data strays, at any point, from the shape of a normal distribution with the mean and deviation you specify.
The idea is to build the data's empirical cumulative distribution function, that step curve, and overlay it on the smooth curve of the theoretical normal. The D statistic is simply the largest vertical distance between the two across the whole axis. If the data really come from that normal, the curves track each other and D is small; any systematic shape deviation pulls the curves apart.
Enter the sample and the parameters of the normal you want to test against: the mean and the standard deviation. The tool returns the D statistic and an asymptotic p-value. A technical note: when the mean and deviation are estimated from the data themselves, rather than known beforehand, the test becomes conservative, and variants like Lilliefors' are more appropriate.
Related Tools
Kolmogorov-Smirnov Test (Two-Sample)
Computes the two-sample Kolmogorov-Smirnov test, which checks whether two samples come from the same distribution — without assuming what that distribution is. It compares the empirical cumulative distribution functions of the two samples and takes the largest vertical distance between them, the D statistic. Unlike the t-test, which only compares means, the KS test is sensitive to any difference in shape, spread or location. Enter the two samples of values.
Anderson-Darling Test (Normality)
Computes the Anderson-Darling test, one of the most powerful normality tests available. It measures how far the empirical distribution of your data departs from the normal curve, giving extra weight to the tails — precisely where other tests often miss departures. The tool returns the A² statistic, the adjusted A²* version (corrected for sample size) and an approximate p-value. The smaller the A², the more compatible with normality. Enter at least 8 values.
Grubbs' Test (Outlier)
Computes Grubbs' test, used to identify whether the most extreme value in a sample is a statistical outlier, under the assumption that the data would be normal without it. It compares the deviation of the farthest point from the mean, in standard-deviation units, against a critical value derived from the t distribution. If the G statistic exceeds the critical value, the point is flagged as an outlier. It's the classic test for cleaning data before an analysis. Enter the data and the confidence level.
D'Agostino-Pearson Normality Test (K²)
Computes the D'Agostino-Pearson omnibus normality test, which combines two clues of non-normality into a single verdict: skewness (do the data lean to one side?) and kurtosis (are the tails too heavy or too light?). Each becomes a standardized z score, and the sum of their squares, the K² statistic, follows a chi-square with 2 degrees of freedom. It's more informative than looking at skewness and kurtosis separately. Enter the sample (at least 8 values).
One-Proportion z-Test
Computes the one-proportion z-test statistic, used to check whether the proportion observed in a sample differs from a hypothesized value. For example: out of 100 voters, 45 approve a measure — is that compatible with 50% in the population? The statistic divides the difference between the observed and hypothesized proportions by the standard error computed under the null hypothesis. It applies when the sample size is large enough for the normal approximation. Enter the successes, the total and the hypothesized proportion.
One-Sample Variance Test (Chi-Square)
Computes the chi-square test for the variance of a single sample, which checks whether the population variance equals a reference value. It's the dispersion counterpart of the one-sample t-test for the mean. It shows up often in quality control: is a process's variability within the specified limit, or has it increased? The statistic compares the sample variance with the hypothesized one and follows a chi-square distribution. Enter the sample and the hypothesized variance (σ₀²).
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.