Data analysis learning records -- complete a simple one-way ANOVA with Excel

Data analysis learning records – use EXCEL Complete a simple one-way ANOVA

One Introduction and concept

Analysis of variance is usually used to test whether there is a difference in the number of three or more samples , More often, we call analysis of variance “F test ”, The two most important concepts are the original hypothesis and the alternative hypothesis ：

The null hypothesis H0: The mean of each group is equal （H1=H2=H3=H4…=Hk）;

The alternative hypothesis H1： The mean of each group is not all equal ;

The judgment method is also very simple , It may be difficult to understand with the concept of Statistics , So I'll put the concept here first , The following will give you a simple example to illustrate .
According to statistics F Value size and correspondence p Value as the criterion of judgment , if p≤0.05, Refuse H0, Accept H1, That is, the population mean of each sample is not all equal ; conversely , received H0, Refuse H1, The population mean of each sample is all equal .

Two example

First of all, here is a set of data for your analysis （ Of samples at different extraction times UV254 The difference in value , Three experiments have been done here ）：

stay excel Before performing one-way ANOVA in, we need to transpose the data .

The next in excel Found in one-way ANOVA , As shown in the figure ：

Click OK excel A prompt box will pop up , The first thing to note is if you are choosing Input area when , Title selected , So down there The flag is on the first line You need to check , Empathy , If your table is horizontally distributed , Then you need to be in How to group Select That's ok , The prompt below will change to The sign is in the first column ; After selecting the input area, we can set whether the generated analysis results are in the current table or in the new table , So here's what I chose New worksheet group , After choosing, let's order determine .

The figure below is the analysis of variance table we generated ：

Let me give a little explanation about the contents in the table , First we know that ：

The original hypothesis and alternative hypothesis are the first point we need to clarify , Then let's focus on obey F The test statistics of the distribution ：

among ,SSA Is the sum of squares between groups ,SSE Is the sum of squares in the group ,k-1 It's the degree of freedom , In the table df It also represents degrees of freedom ,n Is the sample size , here n=18,k=6,SSA/(k-1)=MSA,SSE/(n-k)=MSE;MSE Is the mean square of the Group ,MSA Is the mean square between groups . We can get MSA=0.025533,MSE=0.0321, Of course, these results are all in the table , We can compare it , At this time F The test statistic is equal to MSA/MSE=0.795416.

When the original hypothesis holds, we should obey F Distribution ：F~（5,12）, There are two ways to judge whether the original hypothesis is true （ Whether to reject the original assumption ）. The first one is We can see P value , In this theoretical distribution , Get ratio 0.795416 The more extreme probability is P value ：

P-value=0.573332＞α=0.05
So the original hypothesis holds – namely There was no significant difference .

The second kind The method is also called Critical value method , We can see in the table F crit Value , That is our critical value ：

F0.05（5,12）=3.105875>0.795416
Description is not in the reject field , Original assumption holds – namely There was no significant difference .

3、 ... and summary

1. One way ANOVA is used to test whether the mean values of multiple independent samples are different .
2. When the analysis result of variance reaches the significance level （P≤0.05）, It can only show that the overall mean of multiple groups is not all the same , However, multiple comparisons are needed to know which two groups have differences in mean ; If the result of ANOVA is not significant , You don't need to .
3. Two independent groups can be used to compare the mean of the two groups T test , Of course, one-way ANOVA can also be used , If the number of sample groups exceeds three （ Three or more groups ）, Only one-way ANOVA can be used .

above ！！！（ If there is something wrong Welcome to point out .）