Lecture Notes

Pairwise Comparisons & Interaction Plots

• Revisiting the interaction with witchweed and fertilizer.
• Use emmeans to produce interaction plots.
• Differences can be subtle but significant; observe changes in slopes.
• Plots guide recommendations for fertilizer or weed control.

Tukey's Tests

• Focus on the two-way interaction.
• P-values are adjusted (family-wise error rate).
• Error rates add up quickly with multiple combinations.
• Effect sizes can still be substantial.

Factorial Designs: Power & Efficiency

• Address multiple research questions at once.
• Reduces Type I errors.
• Better understanding of mechanisms via interaction analysis.
• More representative of real-world scenarios.

Key Concepts

• Main effect vs. interaction.
• Reading ANOVA tables (start from the bottom).
• If interaction is significant, focus on it.
• Avoid simply dumping significant results from the ANOVA table.

Model Assumptions for ANOVA

• Easier to check with residuals, especially in complex models.
• Graphical approaches: residuals vs. fitted, QQ plots.
• Use residuals from ANOVA model for plots.
• Testing assumptions with raw data is penalized; use residuals.

Workflow & Confidence Intervals

• Extra notes include confidence intervals on emmeans plots.
• Confidence intervals can reveal where differences lie.
• Example: Levels of nitrogen, varieties of rice.
• Overlapping confidence intervals indicate non-significance.

Assumptions of Maize Example

• Fitted vs. residual plots test equal variance.
• QQ plots assess normality.
• Real-world data can be messy; normality may be questionable.
• Transformations (e.g., log) might worsen other assumptions.

ANOVA Robustness

• ANOVA robust against departures from normality, especially with balanced designs (equal replication).
• Less robust against unequal variances.
• If transformation fails, cite literature (e.g., Tony Underwood) to justify proceeding with caution.
• Acknowledge increased risk of Type I errors and interpret results cautiously.

Transformations

• Transform with purpose.
• Log transformation for count data.
• Square root for harsher transformation.
• Arc-sine for proportion data (percentages).
• Avoid excessive transformations that make data unrecognizable.
• If transformations fail, acknowledge and proceed with caution.

Alternative Tests

• Kruskal-Wallis test for simple one-way ANOVA designs only.

Project introduction

Project 2 Details

• Focus: Real-world data analysis from a provided dataset related to a published paper.
• Data Pre-processing: Some pre-processing done, dataset on Canvas (not from the paper directly).
• Task: Choose a dataset (or derive your own from the provided sheets). Formulate scientific questions answerable with the data.
• Deliverable: A full scientific paper, including analysis pipeline.
• Timeline: Start early; this is a significant task.

Data and Question Generation

• Read the original paper thoroughly.
• Identify papers that cite the original paper for inspiration.
• Questions: Can be agricultural, ecological, or a combination. Follow your interests.
• Analysis Design: Determine experimental design, treatment design, and model equation.
• Analysis Techniques: Primarily ANOVAs and multiple regressions.
• No t-tests (focus on techniques learned in the unit).
• Always analyze residuals, not raw data.
• Scientific Paper Guide
• Provided on canvas.
• Use notes from first year biology.

Writing a Scientific Paper

• Structure: Follow a set formula.
• Key Components:
  • Abstract: (\approx 250 words, overview of the whole paper).
  • Introduction: Context, background, and justification. What's the question?
  • Methods: Experimental design, treatments, and analysis.
  • Results: Present data, not interpret it.
  • Discussion: Interpret your results and relate them back to the question and other studies.
  • References: Cite appropriately.

Data Set & Template

• Metadata Sheet: Included in the Excel file, explains the columns (a 'read me' for the data).
• Data papers - publish the data set for other to use.
• Templates: Provided in Quattro or R Markdown (use R Markdown if Quattro rendering issues persist). Word document is also an option.
• Embed resources: Important to set as TRUE to see renders when using Quattro.

AI Use

• AI tools can be used in coding and plots (improving). AVOID using it to do interpretations, do reports for you or doing analysis for you.
• Acknowledge if used. Include in referencing section.
• State prompts and how verified.

References & Appendices

• References: Follow journal style guide; be consistent.
  Primary literature (journal articles, textbooks, reputable web pages.
• Appendix: Supplementary information (optional).
  Example: Plots about testing the ANOVA model assumptions.