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In statistics, one-way analysis of variance (or one-way ANOVA) is a technique to compare whether two or more samples' means are significantly different (using the F distribution). This analysis of variance technique requires a numeric response variable "Y" and a single explanatory variable "X", hence "one-way".
ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In ...
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 ...
The formula for the one-way ANOVA F-test statistic is =, or =. The "explained variance", or "between-group variability" is = (¯ ¯) / where ¯ denotes the sample mean in the i-th group, is the number of observations in the i-th group, ¯ denotes the overall mean of the data, and denotes the number of groups.
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 ...
The F statistic is a ratio of a numerator to a denominator. Consider randomly selected subjects that are subsequently randomly assigned to groups A, B, and C. Under the truth of the null hypothesis, the variability (or sum of squares) of scores on some dependent variable will be the same within each group.
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3 ANOVA. 4 Regression. 5 Time series analysis. 6 Charts and diagrams. 7 ... "A Short Preview of Free Statistical Software Packages for Teaching Statistics to ...