Multifaktoranalys

Multifaktoranalys is a statistical approach for studying the effect of two or more independent factors on one or more dependent variables. It encompasses experimental designs and statistical models that decompose variation into components attributable to the main effects of each factor and their interactions.

In experimental settings, designs such as full factorial (all combinations of factor levels) or fractional factorials are used. The analysis is typically conducted with analysis of variance (ANOVA) or with regression-based approaches, including general linear models. When there are multiple dependent variables, MANOVA can be applied. If the dependent variable is binary or count data, generalized linear models or generalized estimating equations may be used.

Key outputs include estimated factor effects, interaction effects, and associated test statistics (F-statistics, t-values) along with confidence intervals and p-values. Assumptions include independence of observations, homogeneity of variances, and normality of residuals in ANOVA, or appropriate distributional assumptions in regression. Interpreting main effects requires caution if significant interactions are present, and researchers distinguish between fixed and random factors, or use mixed-effects models as needed.

Applications span fields such as engineering, psychology, medicine, agriculture, and market research, wherever multiple factors are suspected to influence outcomes. The method is foundational in experimental design, enabling efficient testing of factor effects and optimization of processes.

Historically, multifaktoranalys builds on factorial experimental methods developed by Ronald Fisher, extending to modern regression and multivariate techniques. In Swedish statistical usage, the term may be used broadly for analyses that partition variance across several factors.