12.0_TrtStructure.Rmd

# Treatment Structures and Comparisons {#ch.trtstr}

## Learning Objectives for Chapter
Jen's:
1. Identify the treatment in a factorial experiment
2. State the null and alternative hypotheses of a factorial experiment.
3. Define "main effect" and "interaction"
4.  Given a graph of factorial experiment results, determine if there are main effects and/or interaction effects. 
5. Calculate PLSD confidence intervals for a pairwise comparison of means and determine if two means are significantly different based on the CIs. 


Design factorial treatment combinations to answer a research question.
Create linear combinations of means that address practical real-world questions.
Define statistical interaction and explain it graphically.
Transform real-world question into a null hypothesis about means.
Test hypotheses involving more than one and more than 2 means.
Interpret result of ANOVA with factorial treatments.
Interpret graph of a factorial experiment, including description of L, Q and C trends.
Given a set of treatments, formulate and tests useful contrasts.
Determine if a linear combination of means is a contrast.
Create contrasts to estimate the value and variance of interactions.
Estimate the variance of a linear combination of means.
Make confidence intervals for linear combination of estimated means.
Calculate and use the Least Significant Difference (LSD) to test for differences among treatments.
Apply the Protected LSD and explai how it ameliorates the inflation of alpha?
Create linear combinations of estimated treatment means.
Create contrasts to answer research questions such as effects of treatments, linear and quadratic effects of continuous treatment variables.


## Pairwise Comparisons
## Factorials
## Control vs. Treatments
## Linear, Quadratic and Cubic Trends
## Contrasts
## Linear Combinations

## Exercises and Solutions

## Homework

## Laboratory Exercises

### Plant Sciences

### Animal Sciences