方差分析如何计算（懿说学区20）
方差分析如何计算（懿说学区20）方差分析的前提假定是：ANOVA also known as "ANOVA" or "F test" was first proposed by R.A. Fisher a British statistician when he made statistical analysis of agricultural experiments around 1920. Because it can effectively obtain a large amount of information from a small number of experiments it is widely used in industry commerce biology medicine and many other fields.上一期，我们学习了相关样本的非参
Yishuo School District (20) | SPSS Statistical Analysis (30) ANOVA Theory
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上一期，我们学习了相关样本的非参数检验，自此，我们非参数检验的内容就暂告一段落，接下来，我们将进入到“方差分析”一节的学习生活中。
In the last issue we learned about the nonparametric test of related samples. Since then the content of our nonparametric test has come to an end. Next we will enter the learning life of the "Analysis of Variance" section.
方差分析，又称为“变异数分析”或者叫“F检验”，最早是由英国统计学家R.A.Fisher于1920年前后对农业试验作统计分析时提出的。由于它可以由少量的试验有效地获得大量的信息，所以广泛应用于工业、商业、生物、医学等众多领域。
ANOVA also known as "ANOVA" or "F test" was first proposed by R.A. Fisher a British statistician when he made statistical analysis of agricultural experiments around 1920. Because it can effectively obtain a large amount of information from a small number of experiments it is widely used in industry commerce biology medicine and many other fields.
方差分析的前提假定是：
- 各处理样本之间是随机且相互独立的。
- 各样本来源的总体应该服从正态分布，否则应该使用非参数检验来处理。
- 各样本的样本方差应该相同。
The premise assumptions of ANOVA are: 1. The processing samples are random and independent of each other. 2. The population of each sample source should obey the normal distribution otherwise it should be processed by using the nonparametric test. 3. The sample variance of each sample should be the same.
由于各种因素的影响，研究得到的数据呈现波动性。造成波动的原因可能是一些不可控的随机因素或者是研究中施加的对结果产生影响的可控因素。方差分析是从观测变量的方差入手，观测控制变量的不同水平是否对观测变量有显著影响。方差分析认为，如果控制变量的不同水平对观测变量有显著影响，那么，它和随机变量共同作用必然使得观测变量值有显著变动。
Due to the influence of various factors the data obtained from the study shows volatility. The reason for the fluctuation may be some uncontrollable random factors or controllable factors imposed in the study that affect the results. The analysis of variance starts with the variance of the observed variables and whether the different levels of the observed control variables have a significant impact on the observed variables. Analysis of variance believes that if the different levels of the control variable have a significant impact on the observed variable then it and the random variable must work together to make the value of the observed variable change significantly.
根据控制变量的个数可以将方差分析分成单因素方差分析、多因素方差分析以及协方差分析。根据观测变量的个数可以分为一元方差分析和多元方差分析。
According to the number of control variables ANOVA can be divided into single factor ANOVA multi factor ANOVA and covariance analysis. According to the number of observation variables it can be divided into one-way ANOVA and multivariate ANOVA.
方差分析通常按照如下步骤进行：
The analysis of variance is usually carried out as follows:
壹
方差分析条件检测
即检测方差分析的三个前提假定，然后还需要控制变量的类别有限（即控制变量是取值有限的名义尺度或顺序尺度）。
That is to test the three premises of ANOVA and then to limit the categories of control variables (that is the control variables are nominal scales or sequential scales with limited values).
贰
提出原假设
控制变量在不同水平下观测变量各总体均值无显著性差异，对应协方差分析，则是扣除协变量影响后，控制变量不同水平下观测变量各总体均值无显著性差异。
There is no significant difference in the overall mean value of the observed variables at different levels of the control variable. The corresponding covariance analysis means that there is no significant difference in the overall mean value of the observed variables at different levels of the control variable after deducting the influence of covariates.
叁
构造检验的统计量
针对不同分析方法的数学模型，计算平方和、均方，并计算检验统计量（F）。
For the mathematical models of different analysis methods calculate the sum of squares mean square and test statistics (F).
肆
统计决策
如果F值对应的显著性概率P值小于预先设定好的显著性水平α，则拒绝原假设，认为控制变量不同水平下各总体均值有显著性差异；反之，认为控制变量不同水平各总体均值没有显著性差异。
If the significance probability P value corresponding to F value is less than the preset significance level α， Then the original hypothesis is rejected and it is considered that there is a significant difference in the average value of each population under different levels of control variables; On the contrary it is considered that there is no significant difference between the overall mean values of different levels of control variables.
下期预告：本期，我们学习了
方差分析的理论知识。
下一期，我们将会学习
单因素方差分析的理论和实例。
Preview of the next issue: In this issue we learned the theoretical knowledge of ANOVA. In the next issue we will learn the theory and examples of one-way ANOVA.
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参考资料：百度百科，《SPSS 23 统计分析实用教程》
翻译：百度翻译
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