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  2. Expected mean squares - Wikipedia

    en.wikipedia.org/wiki/Expected_mean_squares

    In statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance (ANOVA). They can be used for ascertaining which statistic should appear in the denominator in an F-test for testing a null hypothesis that a particular effect is absent.

  3. Analysis of variance - Wikipedia

    en.wikipedia.org/wiki/Analysis_of_variance

    The definitional equation of sample variance is = (¯), where the divisor is called the degrees of freedom (DF), the summation is called the sum of squares (SS), the result is called the mean square (MS) and the squared terms are deviations from the sample mean. ANOVA estimates 3 sample variances: a total variance based on all the observation ...

  4. Mixed-design analysis of variance - Wikipedia

    en.wikipedia.org/wiki/Mixed-design_analysis_of...

    Andy Field (2009) [1] provided an example of a mixed-design ANOVA in which he wants to investigate whether personality or attractiveness is the most important quality for individuals seeking a partner. In his example, there is a speed dating event set up in which there are two sets of what he terms "stooge dates": a set of males and a set of ...

  5. Multivariate analysis of variance - Wikipedia

    en.wikipedia.org/wiki/Multivariate_analysis_of...

    The image above depicts a visual comparison between multivariate analysis of variance (MANOVA) and univariate analysis of variance (ANOVA). In MANOVA, researchers are examining the group differences of a singular independent variable across multiple outcome variables, whereas in an ANOVA, researchers are examining the group differences of sometimes multiple independent variables on a singular ...

  6. Mean square - Wikipedia

    en.wikipedia.org/wiki/Mean_square

    In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. [ 1 ] It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the data), [ 2 ...

  7. Mean squared error - Wikipedia

    en.wikipedia.org/wiki/Mean_squared_error

    If a vector of predictions is generated from a sample of data points on all variables, and is the vector of observed values of the variable being predicted, with ^ being the predicted values (e.g. as from a least-squares fit), then the within-sample MSE of the predictor is computed as

  8. One-way analysis of variance - Wikipedia

    en.wikipedia.org/wiki/One-way_analysis_of_variance

    The ANOVA produces an F-statistic, the ratio of the variance calculated among the means to the variance within the samples. If the group means are drawn from populations with the same mean values, the variance between the group means should be lower than the variance of the samples, following the central limit theorem. A higher ratio therefore ...

  9. Analysis of covariance - Wikipedia

    en.wikipedia.org/wiki/Analysis_of_covariance

    While the inclusion of a covariate into an ANOVA generally increases statistical power by accounting for some of the variance in the dependent variable and thus increasing the ratio of variance explained by the independent variables, adding a covariate into ANOVA also reduces the degrees of freedom. Accordingly, adding a covariate which ...