Means table for Analyze Definitive Screening Design

Fitted Mean (factors)

Fitted means use the coefficients from the fitted model to compute the mean response for each level combination of a factor or interaction. Data means use the raw response variable means for each factor level combination. The two types of means are identical for balanced designs but can be different for unbalanced designs.

Interpretation

The fitted means estimate the average response at different levels of one factor while averaging over the levels of the other factors.

Use the Means table to understand the statistically significant differences between the factor levels in your data. The mean of each group provides an estimate of each population mean. Look for differences between group means for terms that are statistically significant.

For main effects, the table displays the groups within each factor and their means. For interaction effects, the table displays all possible combinations of the groups. If an interaction term is statistically significant, do not interpret the main effects without considering the interaction effects.

In these results, the Means table shows how the mean thickness varies by time, machine setting, and each combination of time and machine setting. Setting is statistically significant and the means differ between the machine settings. However, because the Time*Setting interaction term is also statistically significant, do not interpret the main effects without considering the interaction effects. For example, the table for the interaction term shows that with a setting of 44, time 2 is associated with a thicker coating. However, with a setting of 52, time 1 is associated with a thicker coating.

General Linear Model: Thickness versus Time, Operator, Setting

Means Term Fitted Mean Time 1 67.7222 2 68.7222 Setting 35 40.5833 44 73.0833 52 91.0000 Time*Setting 1 35 40.6667 1 44 70.1667 1 52 92.3333 2 35 40.5000 2 44 76.0000 2 52 89.6667

SE Mean

The standard error of the mean (SE Mean) estimates the variability between fitted means that you would obtain if you took samples from the same population again and again.

For example, you have a mean delivery time of 3.80 days, with a standard deviation of 1.43 days, from a random sample of 312 delivery times. These numbers yield a standard error of the mean of 0.08 days (1.43 divided by the square root of 312). If you took multiple random samples of the same size, from the same population, the standard deviation of those different sample means would be around 0.08 days.

Interpretation

Use the standard error of the mean to determine how precisely the fitted mean estimates the population mean.

A smaller value of the standard error of the mean indicates a more precise estimate of the population mean. Usually, a larger standard deviation results in a larger standard error of the mean and a less precise estimate of the population mean. A larger sample size results in a smaller standard error of the mean and a more precise estimate of the population mean.

Data Mean (covariate)

The mean of the covariate is the average of the covariate values, which is the sum of all the observations divided by the number of observations. The mean summarizes the sample values with a single value that represents the center of the covariate values.

Interpretation

This value is the mean of the covariate. Minitab holds the covariate at the mean value when calculating the fitted means for the factors.

Standard Deviation (StDev)

The standard deviation is the most common measure of dispersion, or how spread out the individual covariate values are around the mean.

Interpretation

Use the standard deviation to determine how much the covariate varies around the mean. Minitab holds the covariate at the mean value when calculating the fitted means for the factors.

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