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- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/10%3A_ANCOVA_Part_IIExtending ANCOVA to model quantitative predictors with higher-order polynomials, using orthogonal polynomial coding. Fitting a polynomial to express the impact of the quantitative predictor on the res...Extending ANCOVA to model quantitative predictors with higher-order polynomials, using orthogonal polynomial coding. Fitting a polynomial to express the impact of the quantitative predictor on the response is also called trend analysis and helps to evaluate the separate contributions of linear and nonlinear components of the polynomial.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/10%3A_ANCOVA_Part_II/10.01%3A_ANCOVA_with_Quantitative_Factor_LevelsOverview of ANCOVA with quantitative factor levels.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/03%3A_ANOVA_Models_Part_I/3.06%3A_One-Way_ANOVA_Greenhouse_Example_in_MinitabRunning one-way ANOVA on the greenhouse example using Minitab.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/01%3A_Overview_of_ANOVAOverview of analysis of variance (ANOVA) and experimental design concepts. The 7-step process for statistical hypothesis testing.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/07%3A_Randomization_Design_Part_I/7.06%3A_Chapter_7_SummaryAn RCBD is employed to account for a blocking factor, or a nuisance variable, which is not of interest but may have an impact on the response. In an RCBD, with no replicates, the interaction between t...An RCBD is employed to account for a blocking factor, or a nuisance variable, which is not of interest but may have an impact on the response. In an RCBD, with no replicates, the interaction between the treatment and the blocking variable is assumed to be negligible and the Mean Square(MS) value of this interaction serves as the estimate of the error variance which turns out to be the denominator of the \(F\)-statistic for testing treatment significance.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/05%3A_Multi-Factor_ANOVA/5.02%3A_Nested_Treatment_Design/5.2.02%3A_Nested_Model_in_MinitabEnter the factors 'Region' and 'City' in the Factors box, then click on Random/Nest...Here is where we specify the nested effect of City in Region. Then specify "Region" and "City(Region)" for the com...Enter the factors 'Region' and 'City' in the Factors box, then click on Random/Nest...Here is where we specify the nested effect of City in Region. Then specify "Region" and "City(Region)" for the comparisons by checking the boxes. Figure \(\PageIndex{5}\): Tukey simultaneous 95% CIs differences of means graph for Ex_hours, by Region. Figure \(\PageIndex{6}\): Tukey simultaneous 95% CIs differences of means graph for Ex_hours, by City(Region).
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/06%3A_Random_Effects_and_Introduction_to_Mixed_Models/6.02%3A_Battery_Life_ExampleComparing the effects of battery brand as a fixed vs. a random effect, depending on the study design. Includes a worked example for using R to model a single random effect for the battery data.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/06%3A_Random_Effects_and_Introduction_to_Mixed_Models/6.07%3A_Mixed_Model_Example/6.7.03%3A_Using_Rlibrary(emmeans) pairwise_conf_intervals<-emmeans(mixed_schools,list(pairwise~region:school_type),adjust="Tukey") CI<-confint(pairwise_conf_intervals) $`emmeans of region, school_type` # region school...library(emmeans) pairwise_conf_intervals<-emmeans(mixed_schools,list(pairwise~region:school_type),adjust="Tukey") CI<-confint(pairwise_conf_intervals) $`emmeans of region, school_type` # region school_type emmean SE df lower.CL upper.CL # EastUS Private 85.8 2.42 4 79.0 92.5 # WestUS Private 89.5 2.42 4 82.8 96.2 # EastUS Public 73.2 2.42 4 66.5 80.0 # WestUS Public 93.2 2.42 4 86.5 100.0 #Degrees-of-freedom method: kenward-roger #Confidence level used: 0.95 $`pairwise differences of region, sc…
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californ...The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/05%3A_Multi-Factor_ANOVA/5.04%3A_Try_ItPractice exercises for identifying the model type, number of factors, residual effect, and degrees of freedom of a scenario.
- https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Analysis_of_Variance_and_Design_of_Experiments/09%3A_ANCOVA_Part_IIntroduction to analysis of covariance (ANCOVA), using the classic case in which the ANOVA model is extended to include the linear effect of a continuous covariate.
