Analysis of Variance and Covariance
Analysis of variance (ANOVA) is a procedure for assigning sample variance to
different sources and deciding whether the variation arises within or among
different population groups. Samples are described in terms of variation around
group means and variation of group means around an overall mean. If variations
within groups are small relative to variations between groups, a difference in
group means may be inferred. Hypothesis tests are used to quantify decisions.
Statistics and Machine Learning Toolbox™ offers several ways to perform ANOVA, including an
anova object, command line functions, and an interactive
|Box chart (box plot) for analysis of variance (ANOVA) (Since R2022b)
|Mean response estimates for analysis of variance (ANOVA) (Since R2022b)
|Multiple comparison of means for analysis of variance (ANOVA) (Since R2022b)
|Interactive plot of multiple comparisons of means for analysis of variance (ANOVA) (Since R2022b)
|Analysis of variance (ANOVA) table (Since R2022b)
|Variance component estimates for analysis of variance (ANOVA) (Since R2022b)
Perform ANOVA Without Using Object
Perform Analysis of Covariance (ANCOVA)
- One-Way ANOVA
Use one-way ANOVA to determine whether data from several groups (levels) of a single factor have a common mean.
- Two-Way ANOVA
In two-way ANOVA, the effects of two factors on a response variable are of interest.
- N-Way ANOVA
In N-way ANOVA, the effects of N factors on a response variable are of interest.
- ANOVA with Random Effects
ANOVA with random effects is used where a factor's levels represent a random selection from a larger (infinite) set of possible levels.
- Other ANOVA Models
N-way ANOVA can also be used when factors are nested, or when some factors are to be treated as continuous variables.
- Multiple Comparisons
Multiple comparison procedures can accurately determine the significance of differences between multiple group means.
- Analysis of Covariance
Analysis of covariance is a technique for analyzing grouped data having a response (y, the variable to be predicted) and a predictor (x, the variable used to do the prediction).
- Nonparametric Methods
Statistics and Machine Learning Toolbox functions include nonparametric versions of one-way and two-way analysis of variance.