Normaalisuustestiä

Normaalisuustestiä refers to statistical tests used to determine if a dataset follows a normal distribution. A normal distribution, also known as a Gaussian distribution or bell curve, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. Many statistical methods, such as t-tests and ANOVA, assume that the data being analyzed are normally distributed. Therefore, performing a normality test is often a crucial preliminary step before applying these parametric statistical techniques.

Commonly used normality tests include the Shapiro-Wilk test, the Kolmogorov-Smirnov test (often with Lilliefors correction), and the Anderson-Darling test. The Shapiro-Wilk test is generally considered to be powerful for a wide range of sample sizes. The Kolmogorov-Smirnov test compares the empirical cumulative distribution function of the data with the cumulative distribution function of a normal distribution. The Anderson-Darling test is similar to the Kolmogorov-Smirnov test but gives more weight to the tails of the distribution.

The null hypothesis for most normality tests is that the data are normally distributed. If the p-value from the test is below a chosen significance level (commonly 0.05), the null hypothesis is rejected, suggesting that the data are not normally distributed. If the p-value is above the significance level, the null hypothesis is not rejected, meaning there is not enough evidence to conclude that the data deviate from a normal distribution. Visual methods, such as histograms and Q-Q plots, are also frequently used in conjunction with formal tests to assess normality.