1. Simple understanding of orthogonal experimental design
It should not be difficult to simply understand the orthogonal experiment. In fact, you only need to look at the ppt of the second link below to have a good understanding of the orthogonal experiment, and then for the actual spss, you only need to look at the fifth link. The papers can be well mastered. You can simply take a look at the other links after reading the second and fifth links, so that you can basically understand the orthogonal experiment, and then use spss to easily do the analysis of variance based on the orthogonal experiment. However, after reading it myself, I had doubts about the blank column settings. After thinking and querying, I finally got some understanding. You can read the second part of this blog post.
Simple contact with orthogonal experiment design
gives a good introduction to orthogonal experiment design
how to understand blank column
spss to do orthogonal experiment variance analysis
A well-written introduction article
2. Understanding of blank columns
Orthogonal experiment is a bit difficult to understand is the setting of the blank column. We all know that if you want to use the results of the orthogonal experiment for variance analysis, you must either leave a blank column or do repeated measurements. Repeated measurements are easy to understand, because repeated measurements The intra-group variation can be obtained. With the intra-group variation, that is, after obtaining the random error, we can determine whether the difference between the two levels of a certain factor is caused by the different levels of this factor or the random error.
So first of all, we can naturally think that the purpose of leaving blank columns is of course to get random errors, that is, within-group variation, so why leave blank columns to do this? Let's take the example from link one in the first part of this blog post .
For the orthogonal experiment in the above figure, when performing the analysis of variance, for example, if we need to add water to whether the content has a significant effect, then we actually control the decoction time and the number of decoctions to analyze whether the content is different when the amount of water is added There are significant differences; similarly, when studying whether the decoction time has a significant effect on the content, it is actually controlling the amount of water and the number of decoctions to analyze whether the content is significantly different at different decoction times. The same is true for the analysis of the influence of the number of decoctions on the content. So when there is an empty column, similar to the above analysis, when we study whether the empty column has a significant effect on the content , we control the amount of water added, the decoction time, and the number of times of decoction, and then analyze whether the content of the empty column is at different levels. Significant difference, and notice that it is an empty column at this time, so in fact, the analysis at this time can get a random error (because the amount of water, the decoction time, and the number of decoctions are controlled, the effect of the empty column on the content That is random error). In fact, it can also be understood from the perspective of regression, that is, after subtracting the influence of the first three independent variables from the content (dependent variable), what remains is the residual, which is the within-group variation. In this way, with an empty column, you can actually estimate the random error, that is, the variation within the group, and then you can perform the analysis of variance. Therefore, in the actual experiment or subsequent data analysis, you don’t need to worry about the empty columns, you don’t need to do experiments, and you don’t need to put the empty columns in the analysis of variance model. When writing the report, fill in 1 according to the orthogonal table. 2, 3 is fine, just like the picture above. Of course this is a popular explanation. I personally think that the key to the inner mathematical principle lies in the degree of freedom When the orthogonal table is completely filled, the degree of freedom is not enough, and the random error cannot be calculated. When there are empty columns, it is actually reduced by one factor, then the random error can be estimated. Of course This is just my feeling. It has not been deduced by theory. If there are any problems or errors or supplements, please let me know. Thank you very much!