Illeszkedésvizsgálatok

Illeszkedésvizsgálatok, a statistical term, refers to methods used to determine how well a given theoretical probability distribution or model fits a set of observed data. This is a crucial step in data analysis, hypothesis testing, and model building. The core idea is to quantify the discrepancy between the empirical distribution of the data and the expected distribution under a particular hypothesis.

Commonly used goodness-of-fit tests include the chi-squared (χ²) test, the Kolmogorov-Smirnov (K-S) test, and the Anderson-Darling test. The chi-squared test is often applied to categorical data or binned continuous data, comparing observed frequencies to expected frequencies. The K-S test is used for continuous data and compares the cumulative distribution functions of the observed data and the theoretical distribution. The Anderson-Darling test is another test for continuous data that places more weight on the tails of the distribution than the K-S test.

The outcome of an illeszkedésvizsgálat is typically a p-value. A small p-value suggests that the observed data is unlikely to have come from the hypothesized distribution, leading to the rejection of the null hypothesis (that the data fits the distribution). Conversely, a large p-value indicates that the data is consistent with the hypothesized distribution, and the null hypothesis is not rejected. The choice of test depends on the type of data, the specific hypothesis being tested, and the sensitivity required.