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.

One example of a non-orthogonal design is a nested design, in which one variable is nested within another. For example, imagine an experiment studying the effects of different types of exercise on weight loss. In this study, there are two variables: type of exercise (cardio, strength training, or both) and duration of exercise (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.

Another example of a non-orthogonal design is a factorial design, in which multiple independent variables are manipulated simultaneously. For example, imagine an experiment studying the effects of different types of learning on test performance. In this study, there are two variables: type of learning (lecture, hands-on, or both) and type of test (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.

Non-orthogonal designs have several advantages and disadvantages compared to orthogonal designs. One advantage is that non-orthogonal designs can allow for more efficient use of resources, as fewer experimental units are needed to compare multiple variables. Additionally, non-orthogonal designs can provide more information about the interaction effects between variables, which can be difficult to detect in orthogonal designs.

However, non-orthogonal designs also have some disadvantages. One disadvantage is that they are more complex to analyze statistically, as the variables are not independent and may have multiple correlations. Additionally, non-orthogonal designs may be more prone to Type I errors, where a significant effect is detected when there is actually no true effect. This can be particularly problematic if the design is not properly planned and controlled for.

Overall, non-orthogonal designs can be useful tools in experiments when used appropriately, but it is important to carefully consider the potential advantages and disadvantages and plan the design accordingly.