The practical use of Least Square Means?

[#1]

My query is regarding the use of Least Square Means – and my first “posting” in JMP – apologies if I don’t follow correct protocol!

Our business produces animal feeds. Incoming ingredients are sampled, tested and the analytical results pulled into JMP whereby analytical trends are monitored using Graph Builder (I prefer this to Control Chart). The aim is to ascribe single nutrient values for our ingredients (say protein in soyabean meal) which is then inputted into our Formulation system to optimise animal feeds to the correct nutrient specification.

As well as this graphical output, I’m also using Analyse/Fit Model to look at statistical differences in our data (e.g. are two suppliers of our soya providing the same protein content?). I generally use the “LSMeans Tukey HSD”. The output produces the table including a simple arithmetic mean and a Least Square Mean (LSM). I confess to not knowing what the LSM really is, except to guess it’s been “modelled”!

Normally I would use the arithmetic mean (having first removed extreme outliers), but when I look at the LSM it looks (I may be wrong!) more robust and with naturally variable ingredients might, I’m thinking, give me a better numeric value for using in our formulation system. I’ve seen that in some instances the mean and LSM are identical, and in other cases these numbers are quite different.

So, if this can de distilled into one question … then, “is it valid to use LSM’s in the above application?” Thank you. John S.

[#2 · Accepted solution]

It is always valid to use the LS Means. These statistics are based on the model. The arithmetic means are based on the sample. Except for the case of a balanced design when the two means are the same, the arithimetic mean will be biased. The LS Means won't.

[#3]

Thanks for your reply.

To help me understand this in a little more detail, can you point me to any articles or commentary on how LSM's work and how they are superior to arithmetic means please? A pathway to a simple literature reference would be ideal. Thank you.  

[#4]

You could start with JMP and select Help > Books > Fitting Linear Models. Use the search feature of your PDF viewer to find "LSMeans." It should take you first to a section that describes the Effect Details report in Fit Least Squares. The location of this information can vary across JMP versions. For example, it starts on page 98 in JMP 14.