# Software for median polishing

Is there any easy-to-use software for Tukey median-polishing rows and columns with lots of missing values?

• Can you define "easy-to-use" ;-)? Are you willing to do some programming (like in Python or R), or do you only want something w/ a point & click interface? Dec 19, 2012 at 20:30

Well R has medpolish built in, and it can deal with some level of missingness:

 > a  # some data
[,1]     [,2]     [,3]     [,4]
[1,] 32.45884 29.50403 38.54330 30.06207
[2,] 27.92059 25.00838       NA 13.93309
[3,] 37.91911 23.98091 36.00139 27.73731
[4,] 29.20283 29.68059 18.41809 29.92471
[5,]       NA 30.98312 23.55309 22.63105
[6,] 24.96472 33.52443 24.85243 37.43364


The medpolish command is simple:

 > medpolish(a,na.rm=TRUE)    # Pretty easy to use
1 : 86.06071
Final: 85.59585

Median Polish Results (Dataset: "a")

Overall: 29.01548

Row Effects:
[1]  2.2356134 -4.0668144  3.4436953 -0.1729532 -5.2644925  0.1729532

Column Effects:
[1]  1.2077470  0.4488938 -0.1978902 -1.1544723

Residuals:
[,1]     [,2]     [,3]      [,4]
[1,]  0.00000 -2.19595   7.4901 -0.034543
[2,]  1.76418 -0.38917       NA -9.861103
[3,]  4.25219 -8.92715   3.7401 -3.567392
[4,] -0.84743  0.38917 -10.2265  2.236662
[5,]       NA  6.78324   0.0000  0.034543
[6,] -5.43146  3.88711  -4.1381  9.399689


This is not particularly hard to do in a spreadsheet by the way (but note that you would normally iterate it; nevertheless it's quite doable).

However if you have really large amount of missingness, you may not be able to estimate effects for all rows and columns (if one is all-missing for example)

Edit: as whuber notes below, a lot of missingness may result in problems of bias or nonconvergence

• upvoted because I didn't know anything about median polishing and your example is clear enough to get at least a superficial idea of it! Dec 19, 2012 at 21:02
• @Elvis Thanks. I tend to think of it as a bit like a two-way main-effects ANOVA model... but for medians rather than means. There's good coverage of it in "Understanding Robust and Exploratory Data Analysis", Hoaglin, Mosteller and Tukey (eds); it's also in Mosteller and Tukey's "Data Analysis and Regression". Also description and an example here (starts on page 7). Dec 19, 2012 at 21:39
• (+1) Median polish is used extensively throughout Tukey's EDA text. It is easily implemented even in a spreadsheet. With any appreciable amount of missingness it becomes problematic, being potentially biased and often not converging at all.
– whuber
Dec 20, 2012 at 2:25