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One-Way Analysis of Variance (ANOVA)

1925

Ronald A. Fisher

One-way ANOVA is used to determine whether there are any statistically significant differences between the means of three or more independent groups. It analyzes the effect of a single categorical independent variable, known as a factor, on a continuous dependent variable. The null hypothesis states that all group means are equal, [latex]H_0: \mu_1 = \mu_2 = \dots = \mu_k[/latex].

One-way ANOVA is the simplest form of this statistical technique. It extends the two-sample t-test to situations with more than two groups, avoiding the problem of inflated Type I error that arises from performing multiple pairwise t-tests. The ‘one-way’ or ‘one-factor’ designation indicates that the groups are defined by a single categorical variable. For example, in a study comparing the effectiveness of three different diets, ‘diet type’ is the single factor. The underlying statistical model for an observation [latex]y_{ij}[/latex] (the i-th observation in the j-th group) is [latex]y_{ij} = \mu + \tau_j + \epsilon_{ij}[/latex], where [latex]\mu[/latex] is the overall grand mean, [latex]\tau_j[/latex] is the effect of being in group j, and [latex]\epsilon_{ij}[/latex] is the random error term. The analysis proceeds by calculating the F-statistic. If the F-test yields a significant result (i.e., the p-value is below a chosen significance level), it indicates that at least one group mean is different from the others. However, ANOVA does not specify which groups are different. To identify the specific differences, post-hoc tests like Tukey’s HSD or Bonferroni correction are required.

农业, 方差分析, 统计分析, 统计测试

UNESCO Nomenclature: 1209

- 统计资料

类型

抽象系统

中断

实质性

使用方法

广泛使用

前体

Student’s t-test for two independent samples
Concept of experimental control and randomization
方法 of least squares

应用

agriculture: comparing the yield of a crop under several different fertilizer treatments
medicine: evaluating the impact of various drug dosages on patient recovery time
education: comparing the effectiveness of different teaching methods on student test scores
营销: testing if different packaging designs lead to different sales figures
制造业: assessing if different production lines result in products with the same average quality metric

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Related to: one-way 方差分析, single factor, group means, hypothesis testing, F-test, treatment effect, independent groups, experimental design, statistical significance, post-hoc tests.