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One way ANOVA of SPSS
2022-04-23 12:15:00 【Vegetable effort code】
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
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