A food scientist is studying factors that affect food spoilage. The scientist uses a 2-level factorial experiment to assess several factors that could impact the rate of food spoiling.
The scientist analyzes a 2-level factorial design to determine how preservative type, vacuum packaging pressure, contamination level, and cooling temperature affect the spoilage of fruit. The response is binary—whether spoilage is detected or not—in a sample of 500 containers of fruit.
Choose Stat > DOE > Factorial > Analyze Binary Response.
In Event
name, enter Event.
In Number of
events, enter Spoilage.
In Number of
trials, enter Containers.
Click Terms.
Under Include terms in the model up through
order, choose 2.
Click OK in each dialog box.
Interpret the results
In the Deviance table, the p-values for three of the main effect terms—Preservative, VacuumPress, and ContaminationLevel—are significant. Because the p-values are less than the significance level of 0.05, the scientist concludes that these factors are statistically significant. None of the two-way interactions are significant. The scientist can consider reducing the model.
The Deviance R2 value shows that the model explains 97.95% of the total deviance in the response, which indicates that the model fits the data well.
Most of the VIFs are small, which indicates that the terms in the model are not correlated.
The Pareto plot of the effects allow you to visually identify the important effects and compare the relative magnitude of the various effects. In these results, three main effects are statistically significant (α = 0.05) - preservative type (A), vacuum seal pressure (B), and contamination level (C). In addition, you can see that the largest effect is preservative type (A) because it extends the farthest. The effect for the preservative by cooling temperature interaction (AD) is the smallest because it extends the least.
Factorial Binary Logistic Regression: Spoilage versus Preservative, VacuumPress, ...
Method
Link function Logit
Rows used 16
Response Information
Event
Variable Value Count Name
Spoilage Event 506 Event
Non-event 7482
Containers Total 7988
Odds Ratios for Continuous Predictors
Unit of Odds 95%
Change Ratio CI
VacuumPress 10.0 * (*, *)
ContaminationLevel 22.5 * (*, *)
CoolTemp 5.0 * (*, *)
Odds ratios are not calculated for predictors that are included in interaction
terms because these ratios depend on values of the other predictors in the
interaction terms.
Odds Ratios for Categorical Predictors
Odds 95%
Level A Level B Ratio CI
Preservative
Any level Any level * (*, *)
Odds ratio for level A relative to level B
Odds ratios are not calculated for predictors that are included in interaction
terms because these ratios depend on values of the other predictors in the
interaction terms.
