In the previous article "A magical JMP function table to realize the comparison of all groups of data", we introduced the commonly used methods between groups and the basic features of JMP operations. At the beginning of this article, we will analyze several common The inter-group comparison method and its operation process are introduced one by one. Today’s article will start with group comparisons of continuous variables.
For inter-group comparisons of continuous variables, if you want to choose a reasonable analysis method, there are several prerequisites that must be considered first, namely normality and homogeneity of variance.
What are normality and variation homogeneity?
Common data distribution forms include normal distribution, Poisson distribution, exponential distribution, etc. Normality test refers to the test to determine whether the overall distribution conforms to the normal distribution. The homogeneity test of variation number is a test to determine whether the number of variations between each group of samples is the same.
In the practical application of comparisons between continuous variables, many people often make the mistake of not considering whether the data conforms to normality or variation, but directly use the t test or analysis of variation (ANOVA) to perform statistical analysis on the data, and the correct The best analysis process is to take a look at what your data distribution looks like before choosing a method.
The content of this article is to introduce two important conditions that need to be considered before choosing a statistical method: how to judge whether the data satisfies the normal distribution, and how to judge whether the number of variations between groups is equal. Only when these two conditions are determined can a reasonable analysis method be selected.
在JMPNormality test
Next, let's take a look at how to use the "Distribution" platform in JMP to implement normality testing. Taking the data in (Figure 1) as an example, to explore whether there are differences in the BMI values of smoking and non-smoking people, we first need to normalize the BMI values. test, and then determine whether the t test or the rank sum test should be used based on the distribution of the data.
Figure 1 - Data used in this article
It should be noted that when comparing between groups, normality testing needs to be performed in groups, that is, the distribution of BMI in the two groups of smokers and non-smokers is tested separately, rather than the distribution of BMI values in all people. Next, I will explain how to perform the specific operation. First, select "Analysis" → "Distribution" (Figure 2).
Figure 2 - Schematic diagram of normality calibration operation step 1
Because we want to explore the BMI distribution of two groups of people, smoking and non-smoking, BMI is the outcome and smoking is the group. So in the dialog box, put BMI into "Y, column"; put smoking into "Based" (Figure 3). The output results are shown in Figure 4.
Figure 3 - Schematic diagram of normality calibration operation step 2
Figure 4 - Output results
You often see "basis" in JMP, which means "separately" or "stratified". For example, dragging smoking into the basis means performing operations on smokers and non-smokers separately. This is different from the meaning of "grouping", which means comparison between groups, such as comparing the differences between smokers and non-smokers. In subsequent articles, we will also explain this concept.
If you are not used to this kind of vertical bar chart and want to turn the bar chart horizontally, you can click the triangle button in the upper left corner of the results interface and select "Stack" in the drop-down menu (Figure 5).
Figure 5 - Schematic diagram of stacking operation
The output results are shown in Figure 6. Here are various statistics of BMI for the two groups of smokers and non-smokers respectively, including the mean, standard deviation, median, first & third quartiles, etc.
Figure 6 - Output results
Click the red triangle button to the left of "BMI", and click "Continuous Fitting" → "Fitting Normality" in the drop-down menu (Figure 7).
Figure 7 - Schematic diagram of normality calibration operation step 3
The results of normal fitting are shown in Figure 8.
Figure 8 Output results
Click the red triangle button on the left and click "Goodness of Fit" in the drop-down menu (Figure 9), and the normality test results will be displayed.
Figure 9 - Schematic diagram of normality calibration operation step 4
The normality test result is shown in (Figure 10). The p value is equal to 0.9128, which is greater than 0.05. It cannot be considered that the normal distribution is not satisfied, that is, the conclusion that "the data does not obey the normal distribution" cannot be drawn. Therefore, the data can be treated as a normal distribution. analyze.
Figure 10 - Normality test results
The normality test operation method for the BMI of non-smoking people is the same as above. The results are shown in (Figure 11), which is a non-normal distribution.
Figure 11 - Normality test results
According to the above normality test results, we should use the rank sum test for comparison between groups, because as long as any one group of data in the two sets of data has a non-normal distribution, the "rank sum test" must be used for comparison between groups.
在JMPImplementation of homogeneity test of variation numbers in
If when comparing between groups, it is found that both sets of data are normally distributed, it does not mean that the t test can be performed directly. A homogeneity test of the variation number is also required to determine whether the t test or the corrected t test should be used next. Test (t' test).
What is variation homogeneity test?
The homogeneity of variation test is a test to determine whether the variances between groups are the same. Why do we need to test the homogeneity of variations? Because when comparing groups, if the variances between groups are too different, the differences in means will be covered up, leading to erroneous conclusions.
Commonly used methods for testing homogeneity of variation numbers include:
F Bilateral test, Brown-Forsythe test, Levene's test, Bartlett's checksum, and O'Brien's test. Among them, the F bilateral test is used to test the homogeneity of variation numbers in two sets of data; the others are used to test the homogeneity of variation numbers in multiple sets of data. In practice, Levene's method and Bartlett's method are more commonly used, but Bartlett's method can only be used for normality. For data, the Levene method can also be used for non-normal data, with a wider range of applications.
Taking the data in (Figure 1) as an example, if you analyze whether there are differences in the physical health scores of people with different degrees of dyspnea, you will first conduct a normality test. If the test results find that both sets of data are normally distributed, then you will conduct a homogeneous variation test. Sex test.
Variation homogeneity test is an important step in comparison between groups, and its operation is implemented in the JMP menu "Fit Y with X" module. In the previous article, we have briefly introduced the operation of comparison between groups.
Choose Analyze→Fit Y by X. In this example, the physical health score is the result, and the degree of dyspnea is the group. Therefore, in the dialog box, put the physical health score into "Y, response" and the degree of dyspnea into "X, factor". See the operation (Figure 12).
Figure 12 - Discrepancy verification operation
Click the red triangle button next to the "Dyspnea-Physical Health Score" single factor analysis and select "Unequal Variances" in the drop-down menu (Figure 13).
Figure 13 Variation homogeneity test operation
The output results are shown in Figure 14. If the p-value of the homogeneity test of the variants is greater than 0.05, the variants can be considered to be homogeneous.
Figure 14 - Variation homogeneity test results
This case is a test for the homogeneity of variation numbers in two groups. You can choose any test result (because the two groups are special cases of multiple groups). If each test result shows P<0.05, the corrected t test (t' test).
Note: If it is a variation homogeneity test for multiple sets of data, the results of the F bilateral test will not appear in the results.
The above are some methods and precautions for the JMP-based normality check sum variation homogeneity test shared today. In the next article, we will introduce how to perform t-test in JMP. Stay tuned! Download JMP and start your data analysis journey.
Original article: How to implement normality test and variance homogeneity test in JMP?
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