Ismor Fischer, 8/11/2008 Stat 541 / 2-1
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
int
e
rv
a
l
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
