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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.