There are issues with all multiple range tests and these are associated with the power of the test. That is the ability to detect true differences when they exist. For all multiple range tests the maximum number of means that should be tested is 6-7. Once you move above this number you are increasing your chance of false positives. That is you are no longer testing at the 5% level for signfiicance.For example , if you test 15 means with LSD it is more likely that you will find a difference than not- but you have lost the power of the test and your conclusion is wrong. This is a common mistake in many experiments and can be addressed by orthogonal contrasts. For more on this issue search about type 1 and type 2 errors. This is covered well in most statistics books. Different multiple range tests have a different level of conservatism in their calculation of differences and therefore control type 1 and type 2 errors at different rates - e.g. Tukey's Honestly significant test is mroe conservative than lsd or Duncan's - which test you use is up to you - when it is appropratie to use one - but most journals wil lwant the SEM reported so researchers can choose to do their own multiple range test based on your resutls.

For your specific issue - lsd is no longer important if you have an interaction with a factorial experiment. The whole point of a factorial experment is to look at several responses at different levels. As soon as you have an interaction you should graph the data and look to explain the interaction- the individual mean values are meaningless. You are then expected to point out where the interaction has occurred - again this is most obvious when the data are graphed for a two or three way interaction in a factorial experiment. In some cases people actually ignore the three way interaction, because its interpretation is frequently biologically meaningless, and collapse those degrees of freedom into the error term to focus on the more important two way interactions or main effects.

If you do set up a factorial experiment, using 4 levels of one least (e.g. a nutrient level, light level, temperature etc) factor is advised so that you can see the response variable over a range or treatments. Plotting this and showing the SEM as an error bar is the most useful way of presenting results from factorial experiments. If you have an interaction the lines on the graph will overlap - or follow a different pattern with the treatments - this is showing that the response to e.g. light, water, nutrient was different between e.g. two species - the individual mean results are less important here- hence the lsd is not important - the shape of the response of the second factor treatments are.

what need to be interpreted. And remember the statistics are only a tool- the key factor is the mechnistic interpretation of that result - what does it mean- biologically- here is where plant and crop physiology become important -explaining mechanistically why you got the resutls you did.

The problem with LSD test, whatever the case (interaction or main effects) is that it really do not correct the comparisons. So, it is almost like comparing groups using a series of t-tests, without ANOVA.

Usually, it is used by researchers that do not know about statistics and perform ANOVA using SPSS. They select all post-hoc tests and selcted the result which best fits they hypothesis. As LSD perform almost no corrections, usually it is the result with more "signifficant differences"...

Dear Sandro,

can you cite any paper dealing with this?

With regards to your opinion, I almost exclusively work with balanced and very controlled experiments and when I tried to apply different tests to separate means, I got the same results. The matter is: which test is correct to separate interaction? and above all why?

I can see that you suggest ad hoc comparisons by means of a t-test, but this imply that the overall variation of the data set is not take into account. A question arises from it: it that important to take into account of the total uncontrolled variation (i.e. the residual error MS) or not?

Again, can you cite any paper dealing with latter?

Sincerely.

S.

Sergio,

You can conclude that by simple examination of the LSD's formula and some simple simulations. But can see it at this paper too:

https://www.dropbox.com/s/j9h8lu21l333xv4/The%20Maximum%20Familywise%20Error%20Rate%20of%20Fisher%27s%20Least%20Significant%20Difference%20Test.pdf

I do not recomended the use of t-tests! I just stated that using LSD test is the same of using t-tests without correction, which is a mistake.

Another interesting (and old) paper about this matter is:

https://www.dropbox.com/s/ie2klyzn1tvxzsp/Pairwise%20Multiple%20Comparison%20Procedures.pdf

Regards

There are issues with all multiple range tests and these are associated with the power of the test. That is the ability to detect true differences when they exist. For all multiple range tests the maximum number of means that should be tested is 6-7. Once you move above this number you are increasing your chance of false positives. That is you are no longer testing at the 5% level for signfiicance.For example , if you test 15 means with LSD it is more likely that you will find a difference than not- but you have lost the power of the test and your conclusion is wrong. This is a common mistake in many experiments and can be addressed by orthogonal contrasts. For more on this issue search about type 1 and type 2 errors. This is covered well in most statistics books. Different multiple range tests have a different level of conservatism in their calculation of differences and therefore control type 1 and type 2 errors at different rates - e.g. Tukey's Honestly significant test is mroe conservative than lsd or Duncan's - which test you use is up to you - when it is appropratie to use one - but most journals wil lwant the SEM reported so researchers can choose to do their own multiple range test based on your resutls.

For your specific issue - lsd is no longer important if you have an interaction with a factorial experiment. The whole point of a factorial experment is to look at several responses at different levels. As soon as you have an interaction you should graph the data and look to explain the interaction- the individual mean values are meaningless. You are then expected to point out where the interaction has occurred - again this is most obvious when the data are graphed for a two or three way interaction in a factorial experiment. In some cases people actually ignore the three way interaction, because its interpretation is frequently biologically meaningless, and collapse those degrees of freedom into the error term to focus on the more important two way interactions or main effects.

If you do set up a factorial experiment, using 4 levels of one least (e.g. a nutrient level, light level, temperature etc) factor is advised so that you can see the response variable over a range or treatments. Plotting this and showing the SEM as an error bar is the most useful way of presenting results from factorial experiments. If you have an interaction the lines on the graph will overlap - or follow a different pattern with the treatments - this is showing that the response to e.g. light, water, nutrient was different between e.g. two species - the individual mean results are less important here- hence the lsd is not important - the shape of the response of the second factor treatments are.

what need to be interpreted. And remember the statistics are only a tool- the key factor is the mechnistic interpretation of that result - what does it mean- biologically- here is where plant and crop physiology become important -explaining mechanistically why you got the resutls you did.

Dear, I guess the Bonferroni correction is used to counteract the problem of non-orthogonality. If you have significance interactions in factorial designs what can be not useful is to test the main factors (that interact).

Thanks to Sandro for the papers about LSD, very interesting and usefull!!! Now I must find time of quality to read it.

As far as I know, the very moment you find out that the effect of interaction is significant, you should try to determine what cuased this interaction. The type of procedure you adopt afterwards depends on the nature of the treatments. For example, let's say, there were two factors in your experiment: three genotypes and five levels of a particular ingredient. In this case, you might consider finding the trend (regression) for each genotype individually. Actually, you will find out how every genotype responds to addition of that ingredient. I would not use PLSD for this type of data. For other types, there are other ways. But as far as I know PLSD is not a good choice for significant interaction. You may use PLSD for significant interaction provided that you first slice your data (I mean categorize them into three groups(genotypes)), then compare means of the level of the other factor for each genotype seperately using PLSD. But if there were numeric level for the other factor like the one I mentioned above, finding trend would be better.

As a rule of thumb, if you have more than 6 treatments or treatmemt combination, do not use LSD as a means of mean comparison. And lsd is recommended when you want to carry out a pre planned comparison (eg. Control against the rest of treatmens which are not> 6). Otherwise use unplanned comparison methods like DMRT, TUKEY.... you may get some explanation about when to use these comparison methods from gomez and gomez 1984

is it necessary to mention LSD or HSD values when exhibiting data in tables or graphs?

am in the similar problem.....