8.3 Split-split plot designs
3 min read•august 7, 2024
Split-split plot designs are a powerful tool for studying three factors simultaneously in experimental research. They allow researchers to investigate and interactions between factors at different levels of experimental units.
This design is particularly useful when some factors are harder to change than others. It provides a structured approach to analyzing complex experiments, helping researchers uncover intricate relationships between variables.
Experimental Design
Three-Factor Experiments
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Maxwell B. Joseph: Split violin plots View original
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Top images from around the web for Three-Factor Experiments
Maxwell B. Joseph: Split violin plots View original
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Maxwell B. Joseph: Split violin plots View original
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Maxwell B. Joseph: Split violin plots View original
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Maxwell B. Joseph: Split violin plots View original
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Maxwell B. Joseph: Split violin plots View original
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- Three-factor experiments involve studying the effects of three independent variables (factors) on a response variable
- Each factor has two or more levels, and the experiment is designed to investigate the main effects of each factor and their interactions
- The three factors are typically referred to as the factor, split-plot factor, and split-split plot factor
- The experimental units are divided into whole plots, split plots, and split-split plots to accommodate the three factors
Factors and Plots
- The whole plot factor is the first factor applied to the experimental units
- Whole plots are the largest experimental units to which the levels of the whole plot factor are randomly assigned
- The split-plot factor is the second factor applied to the experimental units
- Each whole plot is divided into smaller units called split plots, and the levels of the split-plot factor are randomly assigned to these split plots
- The split-split plot factor is the third factor applied to the experimental units
- Each split plot is further divided into even smaller units called split-split plots, and the levels of the split-split plot factor are randomly assigned to these split-split plots
Data Structure
Nested Structure
- Split-split plot designs have a nested structure, where the split-split plots are nested within the split plots, which are nested within the whole plots
- This nested structure reflects the hierarchical nature of the experimental design
- The nesting of the experimental units leads to different sources of variation and error terms in the analysis
Interactions and Analysis
- In split-split plot designs, the primary interest is often in the triple interaction among the three factors
- The triple interaction represents the combined effect of all three factors on the response variable
- The analysis of variance () for split-split plot designs includes main effects for each factor, two-way interactions between pairs of factors, and the triple interaction
- The ANOVA table for a is more complex than for simpler designs due to the nested structure and multiple error terms
Results
Error Terms
- Split-split plot designs have three different error terms, corresponding to the three levels of the design
- The whole plot error is used to test the significance of the whole plot factor and its interactions with other factors
- The split plot error is used to test the significance of the split-plot factor and its interactions with other factors
- The split-split plot error is used to test the significance of the split-split plot factor and its interactions with other factors
- The correct error term must be used for each hypothesis test to ensure valid inferences
Interpretation of Results
- Interpreting the results of a split-split plot analysis involves examining the significance of the main effects, two-way interactions, and the triple interaction
- Significant main effects indicate that the levels of a factor have different effects on the response variable, averaged over the levels of the other factors
- For example, if the main effect of the whole plot factor is significant, it means that the response variable differs across the levels of the whole plot factor, regardless of the levels of the split-plot and split-split plot factors
- Significant two-way interactions indicate that the effect of one factor depends on the level of another factor
- For instance, a significant interaction between the whole plot and split-plot factors suggests that the effect of the split-plot factor varies across the levels of the whole plot factor
- A significant triple interaction indicates that the combined effect of all three factors on the response variable is not additive
- In other words, the effect of one factor depends on the levels of the other two factors simultaneously
- Interpreting a significant triple interaction can be complex and may require further investigation, such as examining interaction plots or conducting post-hoc tests
Key Terms to Review (19)
ANOVA: ANOVA, or Analysis of Variance, is a statistical method used to test differences between two or more group means. This technique helps determine if at least one of the group means is significantly different from the others, making it a powerful tool in experimental design for comparing multiple treatments or conditions.
Blocking: Blocking is a technique used in experimental design to reduce the impact of variability among experimental units by grouping similar units together. This method allows researchers to control for specific variables, ensuring that comparisons between treatment groups are more accurate and reliable. By minimizing extraneous variability, blocking can enhance the precision of the experiment and improve the validity of conclusions drawn from the data.
Control Group: A control group is a baseline group in an experiment that does not receive the experimental treatment or intervention, allowing researchers to compare it with the experimental group that does receive the treatment. This comparison helps to isolate the effects of the treatment and determine its effectiveness while accounting for other variables.
Dependent Variable: The dependent variable is the outcome or response that researchers measure in an experiment, which is affected by the independent variable. It plays a crucial role in determining the effects of various treatments or conditions, making it essential for drawing conclusions from experimental data.
External Validity: External validity refers to the extent to which research findings can be generalized to, or have relevance for, settings, people, times, and measures beyond the specific conditions of the study. This concept connects research results to real-world applications, making it essential in evaluating how applicable findings are to broader populations and situations.
Factorial Design: Factorial design is a type of experimental design that involves the simultaneous examination of two or more factors to understand their individual and combined effects on a response variable. This approach allows researchers to study interactions between factors, making it a powerful method for understanding complex systems and relationships in experimentation.
Independent Variable: An independent variable is a factor or condition that is manipulated or controlled by the researcher in an experiment to observe its effect on a dependent variable. It serves as the primary element in establishing cause-and-effect relationships within research, influencing the outcomes of various experimental designs and analyses.
Interaction Effects: Interaction effects occur when the effect of one independent variable on a dependent variable changes depending on the level of another independent variable. This concept is crucial for understanding how different factors work together to influence outcomes in experimental designs.
Internal Validity: Internal validity refers to the degree to which an experiment accurately establishes a causal relationship between the independent and dependent variables, free from the influence of confounding factors. High internal validity ensures that the observed effects in an experiment are genuinely due to the manipulation of the independent variable rather than other extraneous variables. This concept is crucial in designing experiments that can reliably test hypotheses and draw valid conclusions.
Main Effects: Main effects refer to the individual impact of each independent variable on the dependent variable in an experimental design. Understanding main effects is crucial for interpreting the results of experiments, as they indicate how changes in a factor influence the outcome, independent of other factors in a study.
Mixed models: Mixed models are statistical models that incorporate both fixed effects and random effects, allowing researchers to analyze data that has multiple sources of variation. This makes them particularly useful in experimental designs where data may be collected from different groups or over time, accommodating the hierarchical structure of the data. They provide a flexible framework for understanding complex relationships and dependencies among variables.
Placebo: A placebo is a substance or treatment with no therapeutic effect, often used in clinical trials to compare the effects of an actual drug or intervention against a control group. It plays a crucial role in experimental design by helping to isolate the psychological and physiological effects of an active treatment from any perceived benefits that might arise simply from believing one is receiving treatment. Placebos help researchers understand the true efficacy of new treatments while controlling for variables like expectations and psychological responses.
Random Assignment: Random assignment is a technique used in experimental research to ensure that participants are allocated to different groups or conditions in a way that is not influenced by any biases or pre-existing differences. This process helps to create equivalent groups, enhancing the credibility of the experiment's conclusions by minimizing confounding variables.
Replication: Replication refers to the process of repeating an experiment or study to verify results and enhance reliability. It ensures that findings are not due to chance or specific conditions in a single study, thus contributing to the robustness of research conclusions and generalizability across different contexts.
Split-split plot design: A split-split plot design is an advanced experimental design used in research that allows for the study of multiple factors at different levels of experimental units. This design incorporates three levels of experimental units: whole plots, subplots, and sub-subplots, which makes it useful for examining interactions among factors that are difficult to manage in traditional designs. The flexibility of this design is particularly beneficial when dealing with large and complex agricultural or industrial experiments.
Sub-subplot: A sub-subplot is a component of a split-split plot design, which adds another layer of treatment to both the subplot and sub-subplot levels. This term is important for understanding how experiments can efficiently manage multiple factors at different levels, allowing for a more detailed analysis of interactions and variations in experimental results. It helps researchers evaluate not just main effects but also interactions among various treatments across different experimental units.
Subplot: A subplot refers to a smaller, secondary experimental unit within a larger experimental framework, particularly in the context of split-split plot designs. It allows researchers to study multiple levels of variation by assigning treatments at different levels, enabling a more nuanced understanding of interactions between variables. Subplots are essential for dissecting complex experimental designs that involve hierarchical structuring of treatments.
Treatment: In experimental design, a treatment refers to the specific condition or intervention applied to subjects in an experiment. This concept is essential as it helps researchers assess the effects of varying factors on outcomes, ensuring that the differences observed can be attributed to the treatments rather than other variables. Treatments can be manipulated in several ways, including through the use of different doses, types, or levels of an independent variable, allowing for rigorous testing and comparison of results across multiple experimental conditions.
Whole plot: In the context of experimental design, a whole plot refers to the primary unit of observation in a split-plot design, where treatments are applied to larger experimental units that are then divided into smaller units for further treatment application. This structure allows for the examination of two or more treatment factors at different levels of experimental hierarchy, which is especially useful when one factor is harder or more expensive to manipulate.