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

http://search.dilbert.com/search?p=R&srid=S3-USCDR02&lbc=dilbert&w=made%20up%20numbers&url=http://dilbert.com/strips/comic/2008-05-08/&rk=3&uid=86701825&sid=2&ts=custom&rsc=lU4p-oJebWa-gaHh&method=and&isort=date&view=list&filter=type:comic

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

http://search.dilbert.com/search?p=R&srid=S3-USESD01&lbc=dilbert&w=DATA&url=http://dilbert.com/strips/comic/2004-10-14/&rk=33&uid=64262503&sid=2&ts=custom&rsc=6RF90OZjJYFk8zQY&method=and&isort=date&view=list&filter=type:comic

http://search.dilbert.com/search?p=R&srid=S3-USESD01&lbc=dilbert&w=DATA&url=http://dilbert.com/strips/comic/2008-05-07/&rk=18&uid=64262503&sid=2&ts=custom&rsc=56293hRPrpCOas8N&method=and&isort=date&view=list&filter=type:comic

http://search.dilbert.com/search?p=R&srid=S3-USESD01&lbc=dilbert&w=DATA&url=http://dilbert.com/strips/comic/2006-11-11/&rk=24&uid=64262503&sid=2&ts=custom&rsc=INYF1gLT:WwDlzXl&method=and&isort=date&view=list&filter=type:comic