Description: The normality test is a fundamental statistical tool that allows determining whether a dataset follows a normal distribution, that is, if it fits the characteristic bell shape of the normal curve. This test is crucial in statistical analysis, as many statistical techniques and models, such as linear regression and t-tests, assume that the data are normally distributed. The normality test evaluates the null hypothesis that the data come from a population with a normal distribution. There are different methods to perform this test, including the Shapiro-Wilk test, the Kolmogorov-Smirnov test, and the Anderson-Darling test, each with its own characteristics and sensitivity levels. The choice of method may depend on the sample size and the nature of the data. The interpretation of the results of the normality test is based on the obtained p-value; a low p-value indicates that the null hypothesis is rejected, suggesting that the data are not normally distributed. On the other hand, a high p-value suggests that there is not enough evidence to reject normality. In summary, the normality test is an essential component in applied statistics, as it provides a basis for selecting appropriate statistical methods and interpreting results.
History: The normality test has evolved over time, with its roots in the development of probability theory and statistics in the 19th century. One of the earliest tests was the Kolmogorov-Smirnov test, proposed in 1933, which focused on comparing the empirical distribution of data with the normal distribution. Later, in 1965, the Shapiro-Wilk test was introduced, which has become one of the most widely used due to its high power in small samples. Over the years, multiple normality tests have been developed and refined, adapting to different contexts and statistical needs.
Uses: Normality tests are used in various research and data analysis fields, including social sciences, biology, economics, and psychology. They are essential for validating normality assumptions before applying statistical techniques that depend on this condition. For example, in clinical studies, they are used to analyze the effectiveness of a treatment, ensuring that the obtained data fit a normal distribution before applying variance analysis. They are also useful in developing predictive models, where the normality of errors is a key assumption.
Examples: A practical example of a normality test is in a study on the height of a population. If height data is collected and regression analysis is to be applied, a normality test would first be conducted to verify if the height data follows a normal distribution. If the result indicates that the data are not normal, data transformations or non-parametric statistical methods could be considered. Another example is in the evaluation of exam results, where a normality test can be used to determine if scores follow a normal distribution before applying statistical analyses to compare groups of students.