sobivustihedustesti

A sobivustihedustesti, or goodness-of-fit test in English, is a statistical hypothesis test used to determine whether a sample of data comes from a particular probability distribution. The null hypothesis typically states that the observed data distribution matches the expected distribution. The alternative hypothesis suggests that the observed data does not follow the expected distribution.

Several types of goodness-of-fit tests exist, with the chi-squared goodness-of-fit test being one of the most common. This test is suitable for categorical data. It compares the observed frequencies of data falling into different categories with the expected frequencies that would occur if the data followed the hypothesized distribution. A test statistic is calculated, and its value is compared to a critical value from a chi-squared distribution to determine whether to reject or fail to reject the null hypothesis.

Another widely used test is the Kolmogorov-Smirnov (K-S) test, which is more appropriate for continuous data. The K-S test compares the cumulative distribution function of the observed data with the cumulative distribution function of the hypothesized distribution. It measures the maximum difference between these two functions.

The choice of a specific goodness-of-fit test depends on the nature of the data (categorical or continuous) and the specific distribution being tested against. These tests are crucial in various fields, including statistics, science, and engineering, for validating assumptions about data generation processes.