Means table for Analyze Binary Response for Definitive Screening Design

Fitted Mean Probability

Fitted means use the coefficients from the fitted model to compute the mean response for each level combination of a factor or interaction.

Interpretation

The fitted mean probabilities are useful because the data mean probabilities might not be good indicators of main effects and interaction effects. Differences between the data mean probabilities can represent unbalanced experimental conditions instead of differences due to changes in the factor levels. Fitted mean probabilities solve this problem by estimating the results of a balanced design.

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

For main effects, the table displays the groups within each factor and their probabilities. 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 probability of food spoilage varies by preservative type, vacuum pressure, contamination level, and cooling temperature. The factors of Preservative, Vacuum Pressure, and Contamination Level are statistically significant at the 0.05 level. None of the interactions are statistically significant at the 0.05 level.

For example, with the preservative type of Formula 1, the fitted mean probability is 0.04918. This is smaller than the fitted mean probability of 0.07501 when the preservative is Formula 2.

Factorial Binary Logistic Regression: Spoilage versus Preservative, VacuumPress

Means Fitted Mean Term Probability SE Mean Preservative Formula1 0.04918 0.00345 Formula2 0.07501 0.00422 VacuumPress 5 0.05387 0.00364 25 0.06860 0.00406 ContaminationLevel 5 0.05291 0.00360 50 0.06983 0.00410 CoolTemp 10 0.06406 0.00393 20 0.05774 0.00379 ContaminationLevel*CoolTemp 5 10 0.06005 0.00535 50 10 0.06833 0.00570 5 20 0.04659 0.00475 50 20 0.07135 0.00582

SE Mean

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

For example, the probability that a patient qualifies for inclusion in a study for a new treatment is 0.63, with a standard error of 0.02. If you took multiple random samples of the same size from the same population, the standard deviation of those different sample proportions would be around 0.02.

Interpretation

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

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

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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