Factorial Design allows the investigation of sets of categorical predictors, and the interaction between them. Today we will go over some basics of One Fixed Factor and One Random Factor Design.

**Keywords:**

**Factor:** categorical predictors

**Fixed Factors: **Estimate the **difference in means** between groups defined by specified categorical predictors.

*e.x. ANOVA model, one measurement per subject.*

**Random Factors: **Estimate the **variance components** of categorical predictors in larger populations rather than the specific difference in means.

*e.x. MIXED model, multiple measurements per subject.*

#### 1. One Fixed Factor Design and Analysis

Balanced(equal sample size in each group) one-factor experiment.

ex. Measure a specific brain structure for each subject, 10 subjects per group, one time each for three different treatments.

we can view one-factor design as ANOVA (continuous outcome with one categorical preditor)

- The difference in the group Mean Value

Further investigation for pairwise comparison(coefficient of Linear Reg, Bonferroni, Tukey)

#### 2. One Random Factor Design and Analysis

ex. Repetitively measure a specific brain structure 3 times for each subject at different time points under 3 different treatments.

Goal: understand the variability due to treatment and person to person variability

Key point: we are not interested in the subject level, therefore we treat them as random factors.

Happy Studying!

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