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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.