Download Designing an Experiment

Fundamentals of Statistics
A User’s Guide for Experimental
Design and Data Analysis
Part II: Inferential Statistics
Examples taken from the textbook:
Probability and Statistics For Engineering and Sciences
by Jay L. Devore
Definitions
 Population vs. Sample
 Population – complete set of cases
 Sample – subset of cases drawn from a
population
 Parameter vs. Statistic
 Parameter – numerical characteristic of
population
 Statistic – numerical characteristic of a
sample
Inferential Statistics
 Techniques for analyzing/interpreting data
 Hypothesis Tests
 Mean
 Proportion
 Pairwise Comparisons
Hypothesis Testing
 Note: Only use if your
distribution of data is
NORMAL, or your sample size
is LARGE!
 See me during directed study if you have a
hard time determining whether or not you can
use these techniques
Hypothesis Testing
 Null Hypothesis (H0) – claim initially assumed
to be true (“prior belief”)
 What is Ho in a legal case?
 Alternative Hypothesis (Ha) - the complement
of the null hypothesis
 What is Ha in a legal case?
Hypothesis Testing
Decisions:
Reject the null hypothesis
Or
Fail to reject the null hypothesis
To Reject or Not to Reject?
 Test statistic – function of the sample data on
which the decision is based
 Probability value (P-value) – smallest value at
which we can reject the null hypothesis
 Defines the rejection region
 Reject the null hypothesis if the test statistic is in this region
 Fail to reject the null hypothesis if it does not
Types of Errors
 Type I error – null hypothesis is rejected when it
is true
 Legal system example?
 An innocent person is sent to jail
 Type II error – null hypothesis is not rejected
when actually false
 Legal system example?
 A guilty person is set free
Examples:
 Hypothesis Tests:
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Mean
Proportion
Pairwise Mean Comparison
Pairwise Proportion Comparison
Hypothesis Test I: Mean
Lightbulbs of a certain type are advertised as having an
average lifetime of 750 hours. A random sample of 100
bulbs was selected, the lifetime of each bulb determined.
Can we conduct a hypothesis test?
Answer:
Yes – but why?
Relatively large sample
How do we set up this hypothesis test?
Answer: H0 : µ ≥ 750
Ha : µ < 750
Hypothesis Test II: Proportion
A manufacturer of nickel-hydrogen batteries randomly
selects 100 nickel plates for test cells, cycles them a
specified number of times, and determines that 14 of the
plates have blistered. Does this provide compelling
evidence for concluding that more than 10% of all plates
blister?
Can we conduct a hypothesis test?
Answer:
Yes – relatively large sample
How do we set up this hypothesis test?
Answer: H0 : p ≤ .10
Ha : p > .10
Hypothesis Test III: Pairwise Mean
An article in Agronomy presented the results of an
experiment to compare the yield of Sundance
winter wheat and Manitou spring wheat. Data
from nine test plots is given in the accompanying
table. The claim is that there is no difference,
but the researchers believe that the average
yield for winter wheat is significantly higher than
for spring wheat.
How do we set up this hypothesis test?
Answer: H0 : µ1 - µ2 = 0
Ha : µ1 - µ2 > 0
Hypothesis Test IV: Pairwise Proportion
Ionizing radiation is being given increasing attention
as a method for preserving plants. An article
reports that 119 of 180 untreated bulbs were
marketable (no external sprouting, rotting, or
softening), whereas 153 of 180 irradiated garlic
bulbs were marketable. Does this suggest that
ionizing radiation is beneficial as far as
marketability is concerned?
How do we set up this hypothesis test?
Answer: H0 : p1 – p2 = 0
Ha : p1 – p2 < 0
Questions?