My expeirment consists of three groups: A, B and C. The sample size for each group is only 2 (n = 2). Can I use One-way ANOVA analysis followed by LSD post hoc test to tell if the difference is significant or not? If no, Why?
Someone told me that for One-way ANOVA analysis, the sample size must be 3 or larger (n ≥ 3). But when I try to do it in SPSS (n = 2), it works except that the result of Levene test is missing.
My questions are：
1. Is there a requirement for sample size when doing One-way ANOVA, although larger is better.
2. If yes, is it n ≥ 3? Why? If no, why I can not get the Levene test result in SPSS.
3.
Thanks in advance.
Actually, your total sample size must be one more than the number of coefficients in your model. In your case (one-way ANOVA with 3 groups) your model estimates three coefficients, so your total sample size must be 4. Technically, the ANOVA should work even with nA=1, nB=1 and nC=2 (since N = nA+nB+nC=4 > 3).
Small samples come with other problems: low power (no estimate becomes significant, also when the population effects was actually relevant), and distributional assumptions really matter (so you must give good arguments that the distributional assumptions are really reasonable in your case).
Testing distributional assumptions (you mentioned the Levene test) is nonsense. There are many good discussions in RG about this topic you may read. Often, researchers cannot give convincing arguments why the distributional assumptions would be reasonable. In this case it's simply unclear how the results should be interpreted. With large samples you could demonstrate that the observed data do not relevantly disagree with the distributional assumptions - but this option does not exist for small samples (there is simply no or not enough information in the data!). The more important is the good understanding of the data-generating process - something that is often just a black box for the researcher. There can be good arguments to use an ANOVA with small samples (even with n=2 per groups), but blindly relying on the hope that it should be ok is too risky and should not be accepted. It's more honest then to admit that the data are not sufficiently conclusive to make any inference (and -in this case- it's kind of stupid to perform such experiments in the fist place - but that's a different topic).
Hello Yu Ting Zhang I am just writing a short answer about why Levene test is not calculated and the software gives an error. (with n =2)
Levene's test uses the F distribution and therefore has two types of degrees of freedom. (df1 & df2)
The issue is not on df1, but on df2.
df2 = number of cases minus the number of groups.
I think the ANOVA will work with 2 samples from each group. The total is n=6 for the experiment. That said, just because you can push numbers through a model does not mean that you should. With such a small sample size there are issues with power, and repeatability. It is also a terrible risk designing experiments in that way. If one sample is lost due to an accident or act of God, then the experiment is ruined. There are cases where one could reasonably use such small sample sizes, but there is no indication that any of them apply in this case.
Essentially at n=3 your are making a number of unprovable assumptions about your data to make up for the lack of data. This sort of research is done, and published. However, publication does not make it good science.
I would hesitate to run a one-way ANOVA with such small group sizes. The experiment may in the end not be very meaningful. I would rethink the entire experiment to see if it is possible to have more meaningful sample sizes or not. Not all experiments are meant to be published, and not all publications make it a good science, as Timothy Ebert has said above.
find the answer in this paper
Article Development of New LSD Formula when Numbers of Observations ...
- Badges
- Science topic
- Similar topics
- Filing