Description: The Jarque-Bera test is a statistical test used to determine whether a sample of data follows a normal distribution. This test evaluates two fundamental characteristics of the distribution: skewness and kurtosis. Skewness measures the symmetry of the distribution, while kurtosis assesses the “height” and “tail thickness” of the distribution compared to a normal one. In simple terms, the Jarque-Bera test compares the shape of the data distribution with that of a normal distribution, where skewness is expected to be zero and kurtosis to be three. If the test results indicate that the data do not meet these conditions, it can be concluded that the sample does not come from a normal distribution. This test is particularly useful in data analysis across various disciplines, such as economics, biology, and engineering, where the normality of data is a key assumption for many statistical techniques. The Jarque-Bera test is based on the calculation of a statistic that follows a chi-squared distribution, allowing for effective evaluation of the null hypothesis of normality.
History: The Jarque-Bera test was developed by Carlos Jarque and Anil K. Bera in 1980. Its aim was to provide a statistical tool that would allow researchers to assess the normality of data more effectively, especially in contexts where traditional tests were not suitable. Since its introduction, the test has been widely adopted in various research and data analysis fields, becoming a standard in normality assessment.
Uses: The Jarque-Bera test is primarily used in statistical analysis to verify the normality of data before applying techniques that assume this condition, such as linear regression and t-tests. It is also applied in the evaluation of econometric models and in the validation of assumptions in research studies. Its ability to detect deviations from normality makes it a valuable tool in scientific research and professional practice.
Examples: A practical example of the Jarque-Bera test could be in a financial study analyzing the returns of a stock. Before applying a regression model to predict future returns, analysts might use the test to ensure that the return data is normally distributed. If the test indicates that the data is not normal, analysts might choose data transformations or use statistical methods that do not require normality.
