ANOVA Analysis of Variance STATISTICA #05 | STATISTICS STATISTICA
ANOVA (Analysis of Variance) in STATISTICA. How to perform ANOVA (Analysis of Variance) in STATISTICA?
Initial data requirements for ANOVA (Analysis of Variance), graphical representation, example, interpretation, and algorithm for ANOVA (Analysis of Variance).
Analysis of variance is a method in mathematical statistics aimed at finding relationships in experimental data by examining the significance of differences in mean values. Unlike the t-test, it allows for comparison of mean values across three or more groups. It was developed by R. Fisher for analyzing the results of experimental studies. The term ANOVA (from the English "ANalysis of VAriance") is also used in the literature.
The essence of ANOVA (Analysis of Variance) is to study the influence of one or more independent variables, usually referred to as factors, on a dependent variable. Dependent variables are represented by absolute scale values (ratio scales). Independent variables are nominal (scale of names), meaning they reflect group membership and can have two or more gradations (or levels).
Depending on the type and number of variables, a distinction is made between:
univariate and multivariate ANOVA (one or more independent variables);
univariate and multivariate ANOVA (one or more dependent variables);
analysis of variance with repeated measures (for dependent samples);
analysis of variance with fixed factors, random factors, and mixed models with factors of both types.
The starting points of ANOVA are the normal distribution of the dependent variable;
equality of variances in the compared populations; and the random and independent nature of the sample.
The simplest case of ANOVA is univariate one-factor analysis for two or more independent groups, when all groups are combined according to a single characteristic. The analysis tests the null hypothesis of equality of means. When analyzing two groups, ANOVA is equivalent to a two-sample Student's t-test for independent samples, and the F-statistic is equal to the square of the corresponding t-statistic.
To confirm the hypothesis of equal variances, Levene's test is typically used. If the hypothesis of equal variances is rejected, the main analysis is inapplicable. If the variances are equal, Fisher's F-test is used to assess the ratio of between- and within-group variability.
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