TEACHING TESTING, P-VALUES, AND CIs WITH THE BINOMIAL
AND MINITAB AND W/OUT THE NORMAL DISTRIBUTION
DSI BALTIMORE
NOVEMBER 18 2013
JOSEPH G VAN MATRESCHOOL OF BUSINESS
UAB
PROBLEM SETTING
• ONE-SEMESTER REQUIRED STAT COURSE FOR
MBAs
• TRADITIONAL COURSE WITH PROBABLITY
DISTRIBUTIONS AND SAMPLING
DISTRIBUTIONS BEFORE INFERENCE
• LITTLE TIME LEFT FOR REGRESSION ANALYSIS
AT END OF COURSE
• MINITAB IS THE STAT PACKAGE
• CONCERN THAT WILL BE FACED WITH SAME
PROBLEM IN UNDERGRADUATE COURSE
(CURRENTLY TWO REQUIRED COURSE)
SOLUTION
• INTRODUCE PROBABILITY DISTRIBUTIONS WITH
EXPECTED VALUE AND VARIANCE (NO CHANGE)
• INTRODUCE ONLY ONE “NAMED” PROBABILITY
DISTRIBUTION, THE BINOMIAL: FUNCTION,
PARAMETERS, W/ CALCULATOR AND MINITAB
PROBLEMS
• NO SAMPLING DISTRIBUTIONS
• INTRODUCE INFERENCE: HYPOTHESIS TESTS, P-
VALUES AND CIs
• INTRODUCE THE PROPORTIONS TEST AND THE
MEDIAN TEST: OBTAIN ANSWERS W/ BINO
ONLY AND THEN W/ MTB BUILT-IN TESTS
4
CS RESEARCH2/16/12
E(X)=22.27/1/12:BMY-31
BIOTECH INVESTMENT: FIRM HAS TESTED DRUG ON FOUR PTS. AND CURED ALL; CURRENT STANDARD OF CARE CURES 50%IS DRUG CURE RATE NO BETTER THAN STD CARE?
Ho: P<=.50Ha: P>.50P-VALUE=P(SAMPLE RESULT AS OR MORE EXTREMETHAN THAT OBSERVED, GIVEN Ho TRUE=P(X<=0|n=4, P=.5)=.0625 W/ CALCULATOR
LEARN TO WRITE P-VAL AS A CUMULATIVEDOWNWARD PROB B/C OF MINITAB
Cumulative Distribution Function
Binomial with n = 4 and p = 0.5
x P( X <= x )0 0.0625
CONFIDENCE INTERVAL:
A (1-ALPHA) CI CONSISTS OF
ALL HYPOTHETICAL VALUES
THAT WOULD NOT BE
REJECTED IN A TEST AT THE
ALPHA LEVEL OF SIGNIFICANCE
SWITCHED BACK TO NUMBER CURED; NOTE CI IS INCLUDED BY MTB
RELATED PROBLEMS:
1. CURRENT STANDARD OF CARE=.30
n=4, ALL 4 CURED
Ho: P<=.30
P-VAL=.0081
MORALE: SMALL SAMPLES CAN PROVIDE SIGNIFICANT
RESULTS
2. CURRENT STANDARD OF CARE=.50
n=10, 9 ARE CURED
Ho: P<=.50
P-VAL=.0107
MORALE: CAN HAVE SOME FAILURES IF n IS LARGER