Comparison of Designs in Experimental Research
Explore the differences between fixed vs. random effects, as well as cross vs. nested designs in experimental research. Understand when to use each design type and their implications for data analysis and inference.
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Presentation Transcript
Lecture Five Fixed v.s. Random Designs Cross v.s. Nested Designs
Fixed v.s. Random effects Fixed Effects Random Effects All treatments of interest were used in the experiment, and the researcher intends to make inference about only this fixed set of treatments. Each effect is estimated with its variation and compared with other effects. Only some of all treatments were used in the experiment, and the researcher intends to make inference about a larger set of treatments. The once from which the experimental set was randomly selected.
Effects Fixed Model Random Model Fixed (constant) Fixed (constant) such that: . Fixed (constant) Random variable ~ iidN(0, 2) and independent of ( ). Random variable ~ iidN(0, e2) for each treatment population. i Random variable ~ iidN(0, e2) for each treatment population. ij Fixed Effects Random Effects To test (Means) (or H0: i=0) v.s. To Test (Variances) = = = 0: H = 2 : 0 H 1 2 k 0 v.s. : 0 H at least one 2 : 0 H 1 i 1
Cross vs. Nested Designs Cross Classification: Treatments occur when every level of factor (A) occurs with every level of factor (B). Nested Classification: Treatments occur when each level of factor (B) occurs with only one level of factor (A). Factors can be fixed or random, but factor (B) in the nested model is almost always random.
