A researcher tests the yields of six varieties of alfalfa on four randomly selected fields. The yield for each variety was recorded for each field.
The researcher wants to know whether the variety of alfalfa affects the mean yield. The researcher has 4 fields where they can collect data. However, the researcher wants to be able to model how the alfalfas will grow in fields that are not in the experiment. Thus, the researcher makes the field where the alfalfa grows a random factor. The researcher fits the mixed effect model and uses it to calculate a range of likely values for future observations at specified settings.
Minitab uses the conditional equation and the marginal equation obtained from the stored model to calculate the two types of fits. The conditional fit of 3.885 represents the mean yield of planting variety 1 of alfalfa in field 1. The marginal fit of 3.480 is the mean yield of planting variety 1 of alfalfa in a randomly selected field in the future.
The confidence intervals indicate that you can be 95% confident that the mean yield for variety 1 of alfalfa in field 1 is between 3.666 and 4.104, and the mean yield for variety 1 of alfalfa in a randomly selected field is between 3.058 and 3.902. The prediction intervals indicate that you can be 95% confident that a single new yield for variety 1 of alfalfa from field 1 will be between 3.462 and 4.309, and a single new yield for variety 1 of alfalfa from a randomly selected field will be between 2.536 and 4.424.