This is an unbalanced design, as the number of replicates is not the same across the Judge & Product category combinations. Unbalanced multi-way designs: Observed Means & LS Means differĬonsider now the original dataset where each judge rates two products several times such as:Ī typical way to analyze such a design is to use a 2-way ANOVA with an interaction term between the two factors (Judge x Product). Means & LS means differ when dealing with a bit more complex models such as unbalanced multi-way ANOVAs that include interactions. Judge 1 has a mean grade of 6.2 and judge 2 has a mean grade of 7.3. In this case, the mean grade of each judge computed by hand will be exactly the same as LS Means arising from a 1-way ANOVA. We want to compare the mean grade per judge. Each judge rates the product several times. Imagine a situation where two judges are rating the same product. One-way ANOVA: Observed Means & LS means are always the same The data are unbalanced as the number of ratings for each product differs according to the judge. The data correspond to several ratings given by two judges for two products A & B. Least Squares Means ( LS Means): Means that are computed based on a linear model such as ANOVA.ĭataset to illustrate the difference between Observed Means & LS Means Observed Means: Regular arithmetic means that can be computed by hand directly on your data without reference to any statistical model. In this article, we will frequently refer to two types of means defined as follows: Some definitions: Observed Means and Least Squares Means It also develops an illustration using Excel and XLSTAT. This article highlights the difference between Least Squares Means computed from linear models such as ANOVA and traditional observed means.
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