BIOS14: ONE-WAY ANOVA(单因素方差分析) using R_one-way anova with post hoc dunnett鈥檚 test-优快云博客

本文链接：https://blog.youkuaiyun.com/qq_43063824/article/details/103485770

这篇博客介绍了如何使用R进行单因素方差分析(ANOVA)及其后续检验，包括Kruskal-Wallis检验。内容涵盖了ANOVA的基本原理、假设，以及数据导入、模型构建、假设检验、结果解释等步骤，并通过具体实例演示了如何进行posthoc测试和计划对比。此外，还讨论了当ANOVA假设不成立时，如何使用Kruskal-Wallis非参数检验作为替代方法。

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NOTES

1 Intruduction of ANOVA

1.1 terminology

If we have 4 groupps of samples, with mean $\mu_1, \mu_2, \mu_3, \mu_4$ , respectively. If we use t-test to test whether the means of 4 population are equle, we have to repeat 6 times t-test.
If all tests are made at some specified significance level (the possibility of error I $\alpha$ ), the overall level of 6 tests together will be $1-(1-\alpha)^6 = 0.625 >> 0.05$ .

Generally speaking, with the increase of the times of carrying on the significant test, the significant level will decrease.

ANOVA (analysis of variance) is used to test equality of multiple overall mean value.

Suppose we want to compare the quality of different industries according to the number of complaints received.

Here, the object be tested (diferent industries) is defined as factor, and the proformence of the factor(the number of complaints received) is defined as treatment. One-way anova means there are only one factor.

1.2 Principles and basic ideas

describe with plot
Using scatter plot to explore the data, and check the diference.
error separation
SST: Reflecting the error of all datas.
SSE: Reflecting the with-in group error.
SSA: Reflecting the group error.
error analysis
Analyse where the error comes from, with-in group or between group.

1.3 Assumption

The populations are normal distributions.
The populations have the same variance.
observation is independent.

Typically:
$H_0: \mu_1=\mu_2=...=\mu_k \\ H_1: \mu_i \ne \mu_j\quad for\ some\ pair(i, j)$

Exrcise

Start by installing (if needed) and loading:

car
lmtest
multcomp

One-way anova analysis is used when we want to see if the mean of a continuous variable differs between groups (i.e. between levels of a single categorical variable, a.k.a. factor). It is a generalisation of the t-test, and can be applied to more than two groups. The significance of the categorical variable depends on the relationship between the wit