SMHS UbiquitousVariation

== Scientific Methods for Health Sciences - Ubiquitous Nature of Process Variability ==

IV. HS 850: Fundamentals

Ubiquitous variation

1) Overview: In real world, variation exists in almost all the data set. The truth is no matter how controlled the environment is in the protocol or the design, virtually any repeated measurement, observation, experiment, trial, or study is bounded to generate data that varies because of intrinsic (internal to the system) or extrinsic (ambient environment) effects. And the extent to which they are unalike, or vary can be noted as variation. Variation is an important concept in statistics and measuring variability is of special importance in statistic inference. And measure of variation, which is namely measures that provided information on the variation, illustrates the extent to which data are dispersed or spread out. We will introduce several basic measures of variation commonly used in statistics: range, variation, standard deviation, sum of squares, Chebyshev’s theorem and empirical rules.

2) Motivation: Variation is of significant importance in statistics and it is ubiquitous in data. Consider the example in UCLA’s study of Alzheimer’s disease which analyzed the data of 31 Mild Cognitive Impairment (MCI) and 34 probable Alzheimer’s disease (AD) patients. The investigators made every attempt to control as many variables as possible. Yet, demographic information they collected from the outcomes of the subjects contained unavoidable variation. The same study found variation in the MMSE cognitive scores even in the same subject. The table below shows the demographic characteristics for the subjects and patients included in this study, where the following notation is used M (male), F (female), W (white), AA (African American), A (Asian).

	Variable	Alzhelmer's disease	MCI	Test Statistics	Test Score	P-value
Age (years)	76.2 (8.3) range 52-89	73.7 (7.3) range 57-84	Student’s T	to=1.284	p=0.21
Gender (M:F)	15:19	15:16	Proportion	z,sub.o,sub.=-0.345	p=0.733
Education (years)	20.43	4.21	17.2	5.78	31.68	25.9	115
Race (W:AA:A)	18.67	4.21	18.67	5.31	27.66	22.35	157
MMSE	20.43	4.21	17.2	5.78	31.68	25.9	115

Race (W:AA:A) 29:01:04 26:02:03 0.55 MMSE 20.9 (6.3) range 4-29 28.2 (1.6) range 23-30 Wilcoxon rank sum p<0.001

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