One way ANOVA of SPSS

variance analysis

variance analysis also called F test , In practical application, it is often necessary to The mean value of multiple whole Compare , And analyze whether there is differences , Is the difference significant , At this time, we need to use analysis of variance .

variance analysis To study The independent variables and The dependent variable An analytical method of whether there is a relationship between them and its strength . Its essence is to compare all measured values

Three concepts of analysis of variance

1. factors

Only the observed variables are affected 、 The conditions for observing and measuring changes

2. level

Different levels of factor quantity 、 Different categories

3. Observation variables

It's our sample data

Before analyzing variance , Three assumptions must be met first

1. The data should obey the normal distribution

2. The variance of each population should be equal , That is, homogeneity

3. The observations of each group are independent , Don't influence each other

The basic steps of ANOVA are

1. Put forward hypothesis test first , There are assumptions n A level , The mean value of each level is expressed in u1、u2、u3... Equal representation , To test n Whether the mean value between the two levels is equal , Now we propose a zero Hypothesis , Suppose the mean values between them are equal .

2. Construct a statistic , such as F statistic

3. Specify the significance level alpha （ That letter ）, It's usually 0.05 or 0.01

4. Finally, through statistics F You can calculate the probability P value , Passing probability P Value compared to our specified significance level . if P value < Significance level , Just reject the original hypothesis , It is considered that there are significant differences between the average values of each population ;P value > Significance level , It cannot be considered that there is a significant difference between the average of each population .

------------------------------------------------------ Now let's get to the point ---------------------------------------------------

example ：

 

 

First step ： Defining variables

The second step ： Input data

The third step ： Analyze

hold Group Put in factor In the box , hold Increased number of red blood cells In the List of dependent variables .

 

  Then click on the right “ contrast ”

Check “ polynomial ”, The default grade is “ linear ” 

  Click on continue

  Then click on “ After the fact comparison ”, The following dialog box will pop up .

  Check “LSD” , Click to continue

Click on “ Options ”, Check “ describe ”、“ Homogeneity test of variance ”、“ Average value diagram ”. Then click continue

  Finally, click OK , You get the output

Step four ： The results of the analysis

We see “ Homogeneity test of variance ” In the table , The significance is greater than 0.05, Therefore, we believe that the overall variance is equal , That is, it satisfies the prerequisite of homogeneity of variance . So we can analyze the following table

  We can see “ANOVA” In this watch ,F The corresponding significance is less than 0.05, Therefore, the original hypothesis is rejected , It is considered that among the four groups of data , There is a significant difference between at least one group of data and several other groups of data .

Let's move on , We can find out which group of data is significantly different from other groups of data

  Let's see this “ Multiple comparisons ” surface , Look at the column I circled , As long as there are stars, there is a significant difference , So we found the data in our example , There were significant differences between each group and the other groups .

Similarly, we can see from the mean graph