ANOVA is an inferential statistic used to test if 3 or more population means are equal or to test the affects of interactions.
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The F-test is designed to test if two population variances are equal. It compares the ratio of two variances. If the variances are equal, the ratio of the variances will be 1.The F-test provides the basis for ANOVA which can compare two or more groups.One-way (or one-factor) ANOVA: Tests the hypothesis that means from two or more samples are equal.Two-way (or two-factor) ANOVA: Simultaneously tests the hypothesis that the means of two variables from two or more groups are equal.
Parametric and non-parametric statistics.Another division is descriptive and inferential statistics.Descriptive and Inferential statistics. Descriptive statistics describes a population (e.g. mean, median, variance, standard deviation, percentages). Inferential infers some information about a population (e.g. hypothesis testing, confidence intervals, ANOVA).
Probability is related to statistics in a direct manner. When one is doing a research for statistics, probability has to be used especially in sampling a small region.
Probability is the theoretical basis that underpins statistics.