Richard Baldy College of Agriculture One-Click Anovas – Analysis of Variance with Microsoft Excel

Overview of Presentation Demonstration of “One-Click ANOVA” with an experiment set out in a Latin-square design. Goal of project: develop data analysis software agriculture undergraduates would use in college in their post college careers Why the goal? Software creation

Demonstration of “One-click Anova” Latin square randomization Latin-square design with 1 experimental factor

Background for Developing Data Analysis Software Agriculture Undergraduates Would Use in College and After Graduation Snapshot of California’s agriculture Industry input into curriculum development Our students

Features of the Industry Sophisticated producers of 350 different crops and commodities in the nation’s most populous state

Features of the industry continued Public demands fewer chemical inputs Yet, public expects industry to do the research –Industry economically powerful. Has the money –Public cannot support research of 350 commodities –Research needs local ecosystem focus to advance goal of ecologically sound agricultural production Much on-farm research yields results once/yr  Easy to forget involved data analysis procedures

Most will not attend graduate school Characteristics of our students

They will enter industry. Some will teach high school agriculture

Industry Input Continue to give hands-on experience Integrate curriculum around ecosystem concepts Teach problem solving: –Working in emotionally “charged” settings –Leadership –Experimentation including data analysis –

Experimentation, Data Analysis Course Expectations: Undergraduates experiment and analyze data They report research via scientific papers, posters, web pages and seminars And continue as farmer-researchers, consultant- researchers, high school teacher-researchers “Dick, you are a plant physiologist, develop and teach this course.”

Faculty Wish List Completely randomized design Randomized complete block design Latin-square design Split-plot design Ancova Simple and multiple regression Analysis of count data

Why Excel? Students familiar with Excel. Therefore, teach data analysis, not a program –saves time Students’ computers come with Excel – saves $ Graduates use Excel for other purposes, not just data analysis Specific experimental design templates friendlier than general purpose programs e.g., SYSTAT OK for regression

Why Not SYSTAT? Expensive. Cheaper student version lacks required capability such as split-plot My experience. Used daily use for weeks. Left it for 3 months. Had to relearn –Number codes for treatments are confusing –For split-plot have to recalculate Anova –Remember ag research data analyzed once/yr

Excel’s Limits As an Anova Platform “Out of the box” Anova procedures handle few designs; Do not handle missing data No mean separation tests No orthogonal contrasts No automatic charting of treatment means

Overcoming Excel’s Limitations Such formulas are not for a world where experimental cows die – become missing data. No residuals for testing normality, equal variance Text book formulas

Instead Use Method That Gives Residuals For missing data, use iteration to find values that gives residual total = zero

The Right Model Example: randomized block design, single experimental factor. Need to solve for three sums of squares: Treatment Block Error

Model for Error Term Treatment Mean + Block Mean – Grand Mean Subtract the above estimate from datum to obtain residual Square residuals Sum of squared residuals = Error SS

Model for Block Term Datum - treatment mean = residual Square and sum residuals = confounded error and block SS Error SS confounded with block SS Treatment SS From this sum of squares subtract the error term’s sum of squares. Treatment SS Block SS Error SS

Datum – block means = residual Square and sum residuals = confounded error and treatment SS Model for Treatment Term Error confounded with treatment SS Block SS From this sum of squares subtract the error term’s sum of squares. Block SS Treatment SS Error SS

Finding Correct Substitute Data Pivot table gives means to be used in estimates. Set substitute datum to some value, e.g., 0 Substitute datum – estimate = residual New substitute datum = former substitute datum – residual Refresh pivot table, obtain new means for estimates Circular argument – need careful control of calculation order to avoid crashes

Let’s see how a pivot table summarizes these data

These are just data in this pivot table and are not used in computing estimates. If this were a Factor A x Factor B summary, these numbers would also be means and used in estimates

calculate Looked up in pivot table Residual = Response-Estimate. Thus, 0.0 – 44 = -44 Response = Response-Residual. Thus, New response = 0- (-44) = 44

refresh

calculate

How to handle different sized data sets Have pivot table summarize 65,000+ rows. –Simple to program –Takes 5-10 minutes for analysis. Rodney’s autofill code + ASSUME page tip on Offset function  cut run times 70 – 90%

Neville’s time trimming suggestion Refreshing pivot tables for each iteration = 1-2 minutes/analysis  Use DAVERAGE function

DAVERAGE(DataRange, ResponseColumn, Criteria for selecting responses to average)INDIRECT(HC1))

Further Topics Experiment planning –Formulate additional, orthogonal hypotheses –Estimate number of replicates Additional work

Experiment planning: Formulate additional hypotheses. Test with single degree of freedom orthogonal contrasts

An Example of Estimating Number of Replicates. Example Will Be for Randomized Complete Block Design. # reps RBD 1 experimental factor

Additional Work Simplify mean separation tests for factorial designs Example using split-plot design Split-plot design with blocks

Additional Work (Continued) Replace trial and error method to develop models Open development to others Share programs