Non Orthogonal Designs
- Factors/contrasts are partially correlated and can overlap; levels are not independent.
- Common in nested and factorial arrangements; can use fewer experimental units and reveal interactions.
- Harder to analyze than orthogonal designs and may increase risk of Type I errors without careful planning.
Definition
Section titled “Definition”Non-orthogonal designs, also known as non-orthogonal contrasts, are a type of statistical design used in experiments to compare the effects of multiple variables on a dependent variable. Unlike orthogonal designs, which have independent variables that are completely uncorrelated and do not overlap, non-orthogonal designs have variables that are partially correlated and may overlap in some way.
Explanation
Section titled “Explanation”Non-orthogonal designs arise when factor levels or contrasts are not independent, so information about one factor overlaps with information about another. This overlap differentiates them from orthogonal designs, where factors are uncorrelated and effects can be estimated independently. Because of the partial correlations, analysis of non-orthogonal designs requires methods that account for the dependencies among variables.
The source gives two specific forms that illustrate non-orthogonality:
- Nested designs, where one variable is described in relation to levels of another variable.
- Factorial designs arranged such that levels of one variable are not independent of levels of another.
Advantages noted in the source include more efficient use of resources (fewer experimental units) and greater potential to provide information about interaction effects. Disadvantages include increased statistical complexity, the presence of multiple correlations among variables, and a greater susceptibility to Type I errors if the design is not properly planned and controlled.
Examples
Section titled “Examples”Nested design
Section titled “Nested design”An example described is a nested design with two variables: type of exercise and duration of exercise. Type of exercise has levels cardio, strength training, or both; duration of exercise has levels short, medium, or long. The type of exercise variable is nested within the duration of exercise variable, meaning that each level of duration of exercise has all three levels of type of exercise. This creates a non-orthogonal design because the levels of type of exercise are not independent of the levels of duration of exercise.
Factorial design
Section titled “Factorial design”Another example described is a factorial design with two variables: type of learning and type of test. Type of learning has levels lecture, hands-on, or both; type of test has levels multiple choice, essay, or both. This creates a non-orthogonal design because the levels of type of learning are not independent of the levels of type of test.
Use cases
Section titled “Use cases”- When experiments must compare multiple variables while using fewer experimental units.
- When detecting or estimating interaction effects between variables is a priority.
Notes or pitfalls
Section titled “Notes or pitfalls”- Analysis is more complex because variables are not independent and may have multiple correlations.
- Non-orthogonal designs may be more prone to Type I errors (detecting a significant effect when none exists) if not properly planned and controlled.
Related terms
Section titled “Related terms”- Orthogonal designs
- Non-orthogonal contrasts
- Nested design
- Factorial design