Normality Calculator

What normality testing is for

Before you lean on t-tests or control charts, check whether your data plausibly come from a normal distribution. A normality test compares your sample against the normal curve that its fitted mean and standard deviation imply, flagging departures in skewness, tail weight, or both. Students checking textbook assumptions and analysts validating metric distributions reach for it constantly.

Tests in the Shapiro-Wilk and Jarque-Bera style return a statistic and a p-value: small p-values mean data shaped like yours would be rare under normality.

How the statistic and p-value work

Jarque-Bera style statistics build on shape measures: JB = n/6 * (S^2 + (K - 3)^2 / 4), where S is skewness and K is kurtosis, which equals 3 for a normal curve. With n = 60, S = 0.2, and K = 3.3, JB = 10 * (0.04 + 0.0225) = 0.625, giving p about 0.73, so normality stands.

Departures bite quickly. At the same n, skewness of 1.0 with normal kurtosis gives JB = 10 and p about 0.007, an emphatic rejection, while a p-value above alpha leaves the normal assumption defensible.

Testing your data step by step

Paste your observations into the Data to test field, separated by commas, spaces, or line breaks. Then set Alpha, usually 0.05, to define how much departure you will tolerate. Larger samples only sharpen the verdict.

Press Calculate and read the statistic with its p-value. If p lands below alpha, switch to a rank-based alternative such as the Mann-Whitney U, or transform the data, for example with logarithms, rather than forcing an invalid parametric test.