Is anova the same as regression

Analysis of variance

Your contact point for statistics basics and more!

The analysis of variance can be used to examine whether groups of feature carriers differ significantly in one or more features. You can use it to measure the effect of one or more nominally scaled variables (so-called independent variables - UV) to one or more metrically / quasi-metrically scaled dependent variables (so-called dependent variables - AV) measure. In general, one could intuitively try this with several paired mean difference tests. In this case, however, it would lead to type I error inflation. With an α of 0.05, the probability that no type I error occurs in a mean difference test would be (1 - α) = 0.95. In the case of one test with four objects of investigation, however, the pairwise comparison would require six mean value difference tests and the probability that not a single type I error is made in these six tests is reduced to only (1 - α)6 = 0.74. With the analysis of variance, all mean values ​​can now be compared with one another simultaneously.

Depending on how many independent or dependent variables are considered, a distinction is made between several types of analysis of variance.

An independent variable and a dependent variable are referred to as the simple analysis of variance (ANOVA). If there are several independent variables and one dependent variable, however, one speaks of one n-factorial analysis of variance (also n-fold analysis of variance), where the n stands for the number of independent variables. In the case of one independent variable and several dependent variables, however, one speaks of one multiple analysis of variance (MANOVA). If there are several dependent variables and several independent variables, then one speaks of an n-factorial multiple variance analysis (n-factorial MANOVA), where the n stands for the number of independent variables.

In addition to the ANOVA / MANOVA, there is also the ANCOVA / MANCOA. These terms include single / multiple analyzes of covariance. In comparison to the analysis of variance, in the analysis of covariance potential confounding variables are included in the analysis as so-called covariates. With this step, the influence of metrically scaled variables on the variance of the dependent variable (s) can be calculated out.

One-way analysis of variance

With the simple analysis of variance, or one-way analysis of variance, it is possible to draw conclusions about differences in mean values ​​by comparing variances. It compares the variance within the group with the variance between the groups. Significance then arises, the lower the variance within the group and the greater the variance between the groups.

Interaction effects

No interaction

Lines in the interaction diagram run parallel. The factors do not influence each other in terms of their effect on the dependent variable. Accordingly, the main effects can be interpreted directly.

Ordinal interaction

Lines in the interaction diagram show the same trend, but there is no overlap (there are clear main effects). The ranking of the effects remains unchanged.

Disordinate interaction

Lines in the interaction diagram cross, the main effects are not clear or cannot be interpreted.

Difference between analysis of variance and analysis of regression

Both analysis of variance and analysis of regression can be viewed as a sub-form of the general linear model and analysis of variance as a special case of linear regression. A demarcation is therefore not so easy. In practice, analysis of variance is usually used for several independent variables with a nominal scale level, but if the independent variables are metrically scaled variables, regression analysis is the right choice.

swell

  • Marketing management - strategies - instruments - implementation - corporate management, Christian Homburg, 4th edition
"I don't trust any statistics that I haven't faked myself."