# [R] measure smoothness

Tue Nov 27 18:21:51 CET 2007

```Assuming that the data are sampled at equal intervals, you can do the
following:

# the following plots show that the 3rd set of data (in green) is smoothest
plot(A[1:11,1], A[1:11,2], type="o")
lines(A[12:22,1], A[12:22,2], type="o", col=2)
lines(A[23:33,1], A[23:33,2], type="o", col=3)

# Here are some numerical tests
# Roughly, average first-derivative
sqrt(mean(diff(A[1:11,2])^2))
sqrt(mean(diff(A[12:22,2])^2))
sqrt(mean(diff(A[23:33,2])^2))

# Roughly, average second-derivative
sqrt(mean(diff(A[1:11,2], diff=2)^2))
sqrt(mean(diff(A[12:22,2], diff=2)^2))
sqrt(mean(diff(A[23:33,2], diff=2)^2))

It is clear that the "new smoothed" data is the smoothest.

Ravi.

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Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Al Lelopath
Sent: Tuesday, November 27, 2007 11:20 AM
To: r-help at r-project.org
Subject: [R] measure smoothness

I have 3 sets of Cartesian data, one is 'original' data and the other
2 are "smoothed"data. The smoothed data is the result of applying a
smoothing algorithm to the original.One set of smoothed data is the
'old' algorithm and the other set is the 'new' algorithm.

Does R have the capability of telling me which data is "smoother"?

Example data (subsets of entire data set):

original:
61	1.419584402
62	1.487019923
63	1.436887012
64	1.39522855
65	1.455934713
66	1.51774951
67	1.603945531
68	1.67847891
69	1.559326003
70	1.57563213
71	1.591873853

old smoothed:
61	1.337874627
62	1.391745721
63	1.387506435
64	1.382959722
65	1.413494505
66	1.445366725
67	1.474782643
68	1.474782643
69	1.474782643
70	1.474782643
71	1.500106199

new smoothed:
61	1.399345513
62	1.416106263
63	1.451252527
64	1.486278253
65	1.505360173
66	1.522991093
67	1.535206073
68	1.546861126
69	1.589831189
70	1.608288145
71	1.620107467

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