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As is well known, ANOVA (Analysis of Variance) is the most representative method to evaluate the significance and influence of categorical factors on continuous responses. no see. Types of ANOVA include One-Way ANOVA and Two-Way ANOVA, where one-way or two-way means the number of factors. For example, if you test the difference in yield according to materials A and B, the factor is one material, so it is a one-way ANOVA. On the other hand, if you want to test the difference in yield at materials A and B and heating temperatures of 100 and 110 degrees, the factor is the material and temperature, so this case is called a two-way ANOVA. ANOVA is the most basic form of ANOVA when there are two levels of each factor, such as material A, B, or temperatures of 10 degrees and 110 degrees. Multiple Comparison, where there are three or more levels of a factor Let's take a look at
Generally Analysis of Variance (ANOVA) to test the difference in means, the hypotheses are:
1) Null hypothesis (Ho): All groups have the same mean.
2) Alternative hypothesis (H1): Not all groups have the same mean.
The key lies in rejecting the null hypothesis if at least one group's mean differs from the other group's mean. That is, rejecting the null hypothesis does not mean that all groups have different means. like this Multiple Comparison Let's see if there are any problems that can arise.
For example, assuming that you have an X factor with five groups A, B, C, D, and E and use the ANOVA method to test the difference in mean values between the two groups, all 10 comparisons are possible.At this time, based on the significance level (α, type 1 error) of 0.05, the overall risk of the test is 0.401. Because when the significance level (type I error) is 0.05, the probability of not having a type I error is (1-0.05) = 0.95 , whereas the probability of not having a type I error for 10 comparisons is (0.95) ) 10 = 0.599 .
That is, in 10 comparisons, the probability of a type I error in at least one comparison becomes 1 – 0.599 = 0.401, which increases the likelihood of interpreting a significant difference even though it is not significant. A slightly different method and interpretation is required from the case of
Let's take a look at the Sample Data below in JMP.
(Help / Sample Data Library / big class.jmp)
In order to check whether there is a difference in the mean of height according to age Analyze / Fit Y by X Select age as X and height as Y and click OK. ▼ Oneway ~ / Means / Anova , the result is as follows.
In the above result, you should not judge that there is a difference in height according to age by looking only at P Value (0.0008). This means that there is a difference between at least one of the six age levels (12-17 years old), not all age levels, so be careful.
In the case of multiple comparisons of 3 or more like this, ▼ Oneway ~ / Compare Means You must use one of the five methods below. Let's try all five methods here. (You can run all five methods at once by holding down the alt key and clicking the red triangle next to Oneway.)
The five methods are briefly summarized below.
One. Each Pairs, Student's t
One) LSD Threshold Matrix means that there is a significant difference between Levels expressed as positive values.
2) Connecting Letters Report means that there is no significant difference between Levels containing the same letter.
3) Ordered Difference Report summarizes the test results between the two levels.
4) ▼ Comparisons / Detailed Comparison Report If you click , you can check all the comparison results between the two levels as shown below (here, there are 6 levels to be compared, so there are 15 comparison results in all).
2. All Pairs, Tukey HSD (Honestly Significant Difference)
Compared to Student's t test above, the results are quite conservative. (Statistical significance is interpreted very strictly, so it is often used in practice in situations where such an interpretation is required.)
3. With Best, HSu MCB
This method shows slightly different test results from the above two methods because it compares with the Group with the minimum or maximum Sample Size.
4. With Control, Dunnett's
This method tests against one comparison group (here, 12 years old is selected as the comparison group).
5. Each Pair Stepwise Newman Keuls (SNK) The result is as below.
6. Comprehensive Interpretation
1) In practice Student's T method and Tukey-Kramer (Tukey HSD) method are most used seems to do
2) Among these The Tukey-Kramer method is more conservative and stricter. do.
3) If you click any one of the circles at the top, the level with no significant difference is displayed in the same red color, and the level with a significant difference is displayed in black as shown below. Below is the result when I chose the 13-year-old of the TurkeyKramer method.(The last method, Stepwise Newman Keuls (SNK), does not show these Circles.)
Hello, thank you for the good explanation.
I am using SAS JMP 18.1.0 software and did a Tukey-Kramer HSD post hoc test analysis.
However, there is a problem where characters are not connected in certain groups.
As shown in the picture below, in certain groups, H appears immediately after ABC, while in other groups, it appears as ABCDH.
I think this is a special case.. Is it a software error, or is this statistical method originally supposed to produce such characters?
Since the groups with ABCH and DEFGH are not significantly different from each other (p>.05), it seems that H is not meaningless.
