分析因子设计的二元响应示例

一位食物科学家正在研究影响食物腐败的因子。该科学家使用 2 水平因子试验,以评估可能会影响食物腐败率的多个因子。

该科学家分析 2 水平因子设计,以确定防腐剂类型、真空包装压力、污染程度和冷却温度如何影响水果的腐败。在由 500 个水果容器组成的样本中,响应是二元的:是否检测到腐败。

  1. 打开样本数据食物腐败.MTW.
  2. 选择统计 > DOE > 因子 > 分析二值响应
  3. 事件名称中,输入事件
  4. 事件数中,输入腐败
  5. 试验数中,输入容器
  6. 单击
  7. 模型中包含项的阶数下,选择 2
  8. 单击每个对话框中的确定

解释结果

在“偏差”表中,其中三个主效应项(即防腐剂、真空压力和污染程度)的 p 值显著。因为 p 值小于显著性水平 0.05,所以科学家得出这些因子在统计意义上显著的结论。所有双因子交互作用都不显著。科学家可以考虑简化模型。

偏差 R2 值显示模型可以解释响应中总偏差的 97.95%,这表明该模型与数据的拟合良好。

大部分 VIF 很小,这表明模型中的项不相关。

通过效应的 Pareto 图,您可以直观地识别出重要效应,并比较各种效应的相对量值。在这些结果中,三个主效应在统计意义上显著 (α = 0.05) - 防腐剂类型 (A)、真空密封压力 (B) 和污染程度 (C)。此外,还可以发现最大的效应是防腐剂类型 (A),因为它延伸得最远。防腐剂乘以冷却温度这一交互作用 (AD) 的效应最小,因为它延伸得最近。

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
Coded Coefficients Term Effect Coef SE Coef VIF Constant -2.7370 0.0479 Preservative 0.4497 0.2249 0.0477 1.03 VacuumPress 0.2574 0.1287 0.0477 1.06 ContaminationLevel 0.2954 0.1477 0.0478 1.06 CoolTemp -0.1107 -0.0554 0.0478 1.07 Preservative*VacuumPress -0.0233 -0.0117 0.0473 1.05 Preservative*ContaminationLevel 0.0722 0.0361 0.0474 1.06 Preservative*CoolTemp 0.0067 0.0034 0.0472 1.05 VacuumPress*ContaminationLevel -0.0430 -0.0215 0.0469 1.04 VacuumPress*CoolTemp -0.0115 -0.0058 0.0465 1.02 ContaminationLevel*CoolTemp 0.1573 0.0786 0.0467 1.02
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.
Model Summary Deviance Deviance R-Sq R-Sq(adj) AIC AICc BIC 97.95% 76.75% 105.98 171.98 114.48
Goodness-of-Fit Tests Test DF Chi-Square P-Value Deviance 5 0.97 0.965 Pearson 5 0.97 0.965 Hosmer-Lemeshow 6 0.10 1.000
Deviance Table Source DF Adj Dev Adj Mean Chi-Square P-Value Model 10 46.2130 4.6213 46.21 0.000 Preservative 1 22.6835 22.6835 22.68 0.000 VacuumPress 1 7.3313 7.3313 7.33 0.007 ContaminationLevel 1 9.6209 9.6209 9.62 0.002 CoolTemp 1 1.3441 1.3441 1.34 0.246 Preservative*VacuumPress 1 0.0608 0.0608 0.06 0.805 Preservative*ContaminationLevel 1 0.5780 0.5780 0.58 0.447 Preservative*CoolTemp 1 0.0051 0.0051 0.01 0.943 VacuumPress*ContaminationLevel 1 0.2106 0.2106 0.21 0.646 VacuumPress*CoolTemp 1 0.0153 0.0153 0.02 0.902 ContaminationLevel*CoolTemp 1 2.8475 2.8475 2.85 0.092 Error 5 0.9674 0.1935 Total 15 47.1804
Regression Equation in Uncoded Units P(Event) = exp(Y')/(1 + exp(Y'))

Y' = -2.721 + 0.188 Preservative + 0.0172 VacuumPress - 0.00249 ContaminationLevel - 0.0286 CoolTemp - 0.00117 Preservative*VacuumPress + 0.00160 Preservative*ContaminationLevel + 0.00067 Preservative*CoolTemp - 0.000096 VacuumPress*ContaminationLevel - 0.000115 VacuumPress*CoolTemp + 0.000699 ContaminationLevel*CoolTemp

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