Completely Randomized Design and Experimental Grouping (Video Notes)

Flashcards cover experimental design concepts from the video notes: minimizing error variance, heterogeneity of variances, grouping strategies, experimental units in different methods, completely randomized design (CRD), means vs. effects models, confidence intervals, pooled variance for mean differences, SAS box plots, naming conventions, and conclusion writing.

What is the main objective of pre-treatment grouping in the two-method aerobic exercise study?

To minimize the experimental error variance and reduce confounding by age and sex so that treatment effects can be tested more accurately.

What is heterogeneity of variances and why is it a concern in this design?

Heterogeneity of variances means the variability differs across groups; it can violate equal-variance assumptions and bias tests of treatment effects.

In the discussed grouping schemes, why does age balance across methods matter for interpreting method effects?

If age distributions differ by method, age-related differences could be mistaken for method effects, confounding the results.

In the shirts durability experiment, what is the experimental unit for method 1 versus method 2?

Method 1: the entire batch of shirts treated together (one experimental unit per treatment level). Method 2: each individual shirt (each shirt is an experimental unit).

Why is replication of treatments desirable in experimental design?

Replication provides an estimate of experimental error within treatments and improves precision of treatment effect estimates.

What does a completely randomized design (CRD) entail?

Each experimental unit is assigned to one of the treatment levels at random; analyzed with a one-way model Yij = μ + τi + e_ij.

What is the 'means model' for CRD (equal-variance assumption) expressed in notation?

Yij ~ N(μ + τi, σ^2) with μ as the overall mean and τ_i as treatment effects.

What is the 'effects model' (full model) for CRD, and how many parameters does it include?

Yij = μ + τi + eij; there are t + 1 parameters (μ and τ1,…,τ_t).

How is a confidence interval for a treatment mean μ_i formed under the fixed-effects model?

μ̂i ± t(α/2, df) × SE(μ̂_i), using the standard error of the i-th treatment mean.

What is the standard error formula for the difference between two treatment means under pooled variance?

SE(μi − μj) = sqrt(sp^2 (1/ni + 1/nj)), where sp^2 is the pooled variance estimate.

In the SAS box plot described, what do the diamonds, medians, and box width indicate?

Diamonds represent means, horizontal lines represent medians, and the box width is a measure of data variability.

What SAS naming conventions are described for dataset and variable names?

Dataset name must start with a letter (no spaces); variable names must start with a letter; underscores are allowed; spaces are not allowed.

How should conclusions be written in problem submissions according to the notes?

Write a complete sentence in the problem's context that states the conclusion; do not explicitly say 'reject H0' or 'do not reject H0'; include a parenthetical citation of data used.