chikvadratfordeling

The chi-squared distribution, often referred to as the *chikvadratfordeling* in Dutch, is a probability distribution that arises in the context of statistical hypothesis testing. It is particularly useful for assessing how well observed frequencies in a categorical variable match expected frequencies under a given model. The distribution is defined by a single parameter, known as the degrees of freedom (often denoted as *k*), which determines its shape.

The chi-squared distribution is derived from the sum of the squares of *k* independent standard normal random variables. It is right-skewed and approaches a normal distribution as the degrees of freedom increase. The distribution is widely used in statistical tests such as the chi-squared goodness-of-fit test and the chi-squared test of independence, which evaluate whether observed data fits a specified distribution or whether two categorical variables are independent.

In hypothesis testing, the chi-squared statistic is calculated by comparing observed and expected frequencies across categories. A high chi-squared value suggests a significant discrepancy between observed and expected results, leading to the rejection of the null hypothesis. The critical values for the chi-squared distribution are tabulated for different significance levels and degrees of freedom, allowing researchers to determine statistical significance.

The chi-squared distribution is also foundational in Bayesian inference, particularly in the context of conjugate priors for inverse-gamma distributions. Additionally, it plays a role in the analysis of variance (ANOVA) and other statistical models where variance estimation is required. Its flexibility and broad applicability make it a cornerstone of modern statistical analysis.