Exploratory Data Analysis and Descriptive Statistics: Random Variables and Data Types, Study notes of Biostatistics

Download Exploratory Data Analysis and Descriptive Statistics: Random Variables and Data Types and more Study notes Biostatistics in PDF only on Docsity!

Ismor Fischer, 8/11/2008 Stat 541 / 2-

2. Exploratory Data Analysis & Descriptive Statistics

2.1 Examples of Random Variables & Associated Data Types

¾ NUMERICAL ( Quantitative measurements)

X

•

•

•

•

Continuous: X = Length, Area, Volume, Temp, Time elapsed, pH, Mass of tumor (^) X

interval

X

steps Discrete: X = Shoe size, # weeks till death, Time displayed, Rx dose, # tumors

¾ CATEGORICAL ( Qualitative “bins”)

Nominal: X = Color (1 = Red, 2 = Green, 3 = Blue), X 1 2 3

unranked

ID #, Zip Code, Type of tumor

Special Case: Binary

1, “Success” X = 0, “Failure”

| 0

| 1

Ordinal: X = Dosage (1 = Low, 2 = Med, 3 = High), X 1 2 3

ranked

< <

Year (2000, 2001, 2002, …), Stage of tumor (I, II, III, IV)

Random variables are important in experiments because they ensure objective

reproducibility (i.e., verifiability , replicability ) of results.

Example:

1 2 3 4....... 90 91 92 93 94 95 96 97 98 99 100

.....

In any given study, the researcher must first decide what percentage of replicated experiments should, in principle, obtain results that correctly agree (specifically, accept a true hypothesis ), and incorrectly agree (specifically, reject a true hypothesis ), allowing for random variation. Confidence Level: 1 − α = 0.90, 0.95, 0.99 are common choices… Significance Level: α = 0.10, 0.05, 0.01 the corresponding error rates