Lecture Notes

Pairwise Comparisons: Witchweed and Fertilizer

• Using amines to produce interaction plots.
• Subtle differences can still be significant.
• Plots guide recommendations for fertilizer or weed control.
• Tukey's tests can be used.
• Focus on the two-way interaction.
• P-values are adjusted for family-wise error rate.
• Large effect sizes can still indicate differences.

Factorial Designs

• Address multiple research questions at once (reduces type one errors).
• Gain a better understanding of potential mechanisms.
• Look at how things might interact.
• Understand what a main effect is and what an interaction is.
• Learn how to read ANOVA tables (start from the bottom up).
• Focus on significant interactions when interpreting the ANOVA table.

Model Assumptions for ANOVA

• Check model assumptions throughout the process.
• Use residuals from the models and graphical approaches.
• Two main approaches: residuals vs. fitted and QQ plots.
• Using raw data to test assumptions is incorrect.
• Residuals are more powerful and informative.

Confidence Intervals in E-means Plots

• Confidence intervals make plots more messy but show where the differences are.
• Overlapping confidence intervals may indicate non-significance.

Assumptions of Maize Example

• Testing equal variance with fitted versus residual plots.
• QQ plots test for normality.
• Real-world data can be messy.
• Transformations (e.g., log transformation) may worsen assumptions.
• ANOVA is robust, especially with balanced designs.
• Normality assumption is less critical than equal variance.
• Cite papers (e.g., Tony Underwood) to support robustness against normality departures.
• Acknowledge assumption failures and interpret results with caution to reduce type one errors.

Data Transformations

• Perform transformations with purpose.
• Log transformation is best for count data.
• Square root transformation is harsher.
• Arcsine transformation is for proportion data.
• Avoid excessive transformations, as they can make data unrecognizable.
• Consider the foundations of the test if transformations fail.
• Cite a paper to support deviations from normality.

Post Hoc Tests and Alternatives

• Post hoc tests are used.
• Kruskal-Wallis test is for simple one-way ANOVA designs.

Project 2 Introduction

• Project one helped start thinking about data and its implications.
• Project two uses real data (subset of data from a paper).
• Download data from Canvas (pre-processed).
• Choose one of the four provided data sheets or derive your own.
• Develop a scientific question or questions to answer using the data set.
• Full scientific paper and analysis pipeline.
• Start early due to the complexity of the task.

Tips for Project 2

• Read the paper and find out who cited it for inspiration.
• Questions can be agricultural, ecological, or a combination.
• Determine experimental design, treatment design, and model equation.
• Use ANOVAs and multiple regressions (taught in the unit) to answer questions.
• No t-tests.
• Use residuals.

Guide to Writing a Scientific Paper

• Follow the set formula for scientific papers.
• Key points to cover:
  • Introduction.
  • Methods.
  • Results.
  • Discussion.
• Use references and citations.
• Consult first-year notes on scientific writing.

Metadata

• Metadata sheet in the Excel file explains columns and variables.
• Metadata is data about data.
• Helps communicate how variables were measured.
• Standard practice for open science and data sharing.
• Important skill for using data sets collected by others.

Report Template

• Quattro template (R Markdown template available for those with rendering issues).
• Ensure embed resources is set to true in Quattro YAML heading.
• Use code folding.
• Use the template as a basis and adapt it.