ANOVA from scratch

This repo contains code that does statistical variance analysis from good ol' first principles.

Usage outline

python3 anova.py [simple|blocked|twoway] [csv_file] [reps]

where

• The first argument is one of the three options specifying what kind of ANOVA to perform. This will essentially determine the number of rows in the final ANOVA table. See below
• [csv_file] is the raw data csv file. No headers for rows or columns. All rows and columns should have the same lengths, respectively. Formatting below.
• [reps] is the number of repetitions the experiment underwent. Place multiple reps directly underneath each other in the same block. So if 1 rep has 3 rows and 3 cols, then 2 reps should have 6 rows and 3 cols. The program will then interpret the csv data correctly.

Usage detail

Simple

Compare any number of samples. The CSV file should have a column for each sample.

Blocked

Compare any number of samples, taking blocks into account. CSV should have a col for each sample, and a row for each blocking level. If 2 reps for instance, then the number of rows should be 2*blocks (2 reps for each blocking factor).

Two-way

Compare any number of samples, taking a second factor and their interaction into account. Just like with blocked, the CSV should have a col for each sample, and a row for each secondary factor level. Scales up with reps just like the blocked design.

Output Example

python3 anova.py twoway emulsion.csv 2

src       DF          SS          MS          F           p
------  ----  ----------  ----------  ---------  ----------
faccol     2  0.631667    0.315833    15.7917    0.00406881
facrow     1  0.00333333  0.00333333   0.166667  0.697261
inter      2  0.0116667   0.00583333   0.291667  0.757035
err        6  0.12        0.02
total     11  0.766667

Dependencies

• tabulate for tabulation
• scipy just for getting the p-val from the F-stat

Why did I bother?

I did a sophomoric statistics course in university where we covered ANOVA. I noticed that it's quite a lot of repetitive work, and it seemed easily programmable. And so I programmed it from first principles (no fancy R or pandas) to prove to myself I could. It also helped a great deal in tests and exams (which were online in 2020 thanks to COVID). Since I wrote it myself from first princips I don't consider it cheating.