1. Case introduction
Want to extract plant phenols from a certain herbal medicine, use professional knowledge to find that there may be three conditions that may affect the extraction of plant phenols, each condition has three levels, want to find the best extraction conditions for plant phenols through experiments, which extract plant The reference standard for phenols is the content of plant phenols (the case data is fictitious and has no practical reference significance, and no need to consider the interaction term). Data are as follows:
2. Problem analysis
The purpose of this case analysis is to find the best extraction conditions for plant phenols, and there are three factors and three levels. If one experiment is analyzed and the final comparison is made, a total of 3*3*3=27 experiments are required. Obviously, it takes a long time and the efficiency is not high. In order to solve this problem, an orthogonal experiment can be used to complete it, which can not only save a lot of time, but also obtain experimental results with high efficiency. As for those who want to find plant phenols Optimal extraction conditions can be investigated using ANOVA .
3. Software operation and result interpretation
(1) Orthogonal table design
1. Software operation
The first step of the analysis requires the design of the orthogonal table. Use SPSSAU to quickly obtain the orthogonal table. Enter the SPSSAU page, click on the orthogonal experiment in the medical experiment/research, select the number of factors and the number of levels of each factor. Due to the data The number of factors is three and the number of each level is three, so the operation is as follows, and finally click to start the analysis, as follows:
2. Design results
The generated orthogonal table is as follows:
There are 9 experiments in total, and the obtained orthogonal table satisfies the characteristics (the number of occurrences of different numbers in each column is equal, and the number of occurrences of each number pair in any two horizontal columns of number pairs is equal). The obtained orthogonal table can be uploaded to the SPSSAU system for further analysis.
(2) Data import
1. Data format
Upload and analyze the obtained orthogonal table and experimental data. The first step is to sort out the correct data format and upload data with labels. For example, the number 1 in factor 1 means that the amount of water added is 6, and 2 means that the amount of water added is 8. , and so on. Organized as follows:
2. Import data
Import the sorted data into the SPSSAU system, click the "Upload Data" button in the upper right corner of the page, click Upload File, and upload the data, as follows:
Analysis of variance was performed after uploading the data. The result is as follows:
(3) Analysis of variance
- Software operation
ANOVA can be subdivided again. When the number of X is one, we call it one-factor variance; when X is two, it is two-factor variance; when X is three, it is called three-factor variance, and so on. When X is more than 1, it is collectively called multi-factor variance. Since the dependent variable is "content" and the independent variables are "amount of water added", "time" and "number of times", a three-factor variance analysis is used. Click the three-factor ANOVA in the advanced method → drag and drop the analysis item → click to start the analysis.
- Interpretation of results
The result is as follows:
From the results of the three-factor analysis of variance, it can be obtained that the amount of water added is significant ( F= 32.738 , p= 0.030<0.1), indicating that the main effect exists, and the number of times ( F =56.721, p =0.017<0.1) indicates the existence of the main effect, Although time would like the p-value to be 0.079 if the significance level is 0.1, it also shows significance. And the specific comparison found that the primary and secondary relationship of the three factors is: "number of times > water addition > time"
What should I do if I want to know which level of influencing factors is the best? It can be viewed intuitively by drawing a graph or analyzed by multiple comparisons after the event. Since drawing a graph is more intuitive and easy to analyze, this example uses a graph for analysis. The results are as follows:
The abscissa is the number of factor levels. It can be seen from the figure that the optimum water addition is 8L, the optimum decoction time is 1.5h, and the optimum decoction times is 2. The optimal combination is "add water 8l, time is 1.5 hours is the best, the water content is 30%, and the number of decoctions is 2 times."
4. Conclusion
An orthogonal table with three factors and three levels was obtained through an orthogonal experiment, and then the correct data was sorted out and uploaded to the system, and a three-factor analysis of variance was performed to obtain the primary and secondary relationship of the three factors: "number of times > water addition > time" And the optimal combination obtained through the graphics is "the amount of water added is 8l, the time is 1.5h is the best, the water content is 30%, and the number of times of decoction is 2 times".
5. Knowledge Tips
(1) Why can't the data be used for multi-factor analysis of variance?
Orthogonal table and multi-factor ANOVA are completely independent, so sometimes the orthogonal table comes out but multi-factor ANOVA cannot be performed because the number of experiments is too small and the degree of freedom is insufficient to perform multi-factor ANOVA. For example, the orthogonal table L9.3.4 is an orthogonal table with 4 factors and 3 levels. If multi-factor analysis of variance is required, at least the required number of degrees of freedom needs to be greater than: 4*(3-1)+1=9, then at least 10 experiments are required to perform multi-factor analysis of variance with an orthogonal table of 4 factors and 3 levels . There are two solutions, one is to choose an orthogonal table with a higher number of experiments; the other is to do at least one more experiment by yourself (and the experimental combination cannot be the same as the existing combination in the orthogonal table).
(2) Is the orthogonal table different from the literature results?
There are many orthogonal tables, and the generated orthogonal tables may be different for the same number of factors and levels.
(3) Explanation of type selection for post hoc multiple comparisons?
It is generally recommended to use the Bonferroni correction method is better. If the samples of each group are different, Scheffe can be used, and if the samples of each group are identical, the Tukey method can be used.