You can identify similar cases, for example where we obtain several measurements from a single EU, or even several measurements from a given MU. The difficulty comes when we take measurements ( e.g., plant height) from each of the plants, and therefore the EU differs from the MU. Treatment levels should always be applied randomly to different EU, as in the above example where a treatment level ( e.g., fertilizer) was applied to a plot, and thus all four plants within the plot have the same treatment level. However, the most important aspect is to clearly distinguish between experimental units (EU) and the measurement units (MU). Pseudo-replication is not always easy to recognize, particularly for experiments that contain multiple layers or strata. We will discuss both aspects with emphasis on the use of linear models (LM) and linear mixed models (LMM).
#ASREML R BOUND HOW TO#
How to correctly deal with this pseudo-replication within a statistical analysis.How to identify pseudo-replication in a study, and.In this topic, there are two important elements to consider: You can imagine, that pseudo-replication has important implications for statistical inference and scientific research, however, it is common to find this mistake in research papers. In this case our critical t-value at a 5% significance level will change from 2.447 to 2.042, making our p-value and confidence interval incorrect. For example, in the experiment above, a t-test comparing the two treatment means should have a total of 6 df, but under pseudo-replication we will incorrectly consider that we have 30 df. This inflation of the df leads to p-values that are lower than what they should be, and therefore, with pseudo-replication we are more likely to reject our null hypothesis. In statistical terms if pseudo-replication is not properly accounted for the degrees of freedom ( df) are incorrect, and generally inflated. Even though we might have a total of 16 observations per treatment, these have a structure, and the treatment was randomized to the plots not to the plants. The experimental units (EU) are the plots, while the individual plants, or measurement units (MU), are the pseudo-replicates. What is the replication of a given treatment in this experiment? The replication per treatment is four, but in total 16 plants are treated. In this experiment one treatment ( e.g., control) is applied to four plots at random, and the other treatment ( e.g., fertilizer) to the remaining four plots. To illustrate this, we will consider an experiment that compares two treatments applied to eight plots, each containing four plants (see figure below). Almost always this incorrect identification will make the statistical analyses invalid. This can occur at the planning or execution stage of a study, or during the statistical analyses. Pseudo-replication is associated with the incorrect identification of the number of samples or replicates in a study.
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