The Language of The Language of Statistical Decision Statistical Decision

MakingMakingLecture 1Lecture 1

Section 1.3Section 1.3Fri, Jan 20, 2006Fri, Jan 20, 2006

Is Chocolate Good for Is Chocolate Good for You?You?

A recent study seems to show that A recent study seems to show that chocolate is good for your health.chocolate is good for your health.

The news story:The news story: Chocolate Chocolate RelaxsRelaxs Heart Heart

The study:The study: Acute Consumption of Acute Consumption of FlavanolFlavanol

-Rich Cocoa and the Reversal of Endoth-Rich Cocoa and the Reversal of Endothelial Dysfunction in Smokers elial Dysfunction in Smokers

Populations and SamplesPopulations and Samples PopulationPopulation – The entire group of – The entire group of

objects or individuals of interest in objects or individuals of interest in the study.the study.

SampleSample – A part of the population – A part of the population from which the data is actually from which the data is actually obtained.obtained.

Statistical InferencesStatistical Inferences Statistical inferenceStatistical inference – A conclusion – A conclusion

about the population based on about the population based on information from a sample of that information from a sample of that population.population.

Samples and InferencesSamples and Inferences

Population

Samples and InferencesSamples and Inferences

Population

Sample

TakeSample

Samples and InferencesSamples and Inferences

Population

Sample Data

TakeSample

Make Observations

Samples and InferencesSamples and Inferences

Population

Sample Data

Inference

TakeSample

Make Observations

Draw anInference

Samples and InferencesSamples and Inferences

Population

Sample Data

Inference

TakeSample

Make Observations

Draw anInference

HypothesesHypotheses HypothesisHypothesis – A statement that is – A statement that is

proposed, but not known to be true.proposed, but not known to be true. Hypotheses are often proposed Hypotheses are often proposed

explanations of something that is known explanations of something that is known to be true.to be true.

HypothesesHypotheses The The Null HypothesisNull Hypothesis – The conventional – The conventional

belief about the population, or the belief about the population, or the status quo, or the neutral position.status quo, or the neutral position. It receives the It receives the benefit of the doubtbenefit of the doubt..

The The Alternative (Research) HypothesisAlternative (Research) Hypothesis – An alternative to the null hypothesis.– An alternative to the null hypothesis. It bears the It bears the burden of proofburden of proof..

Typically, the researchers are trying to Typically, the researchers are trying to prove the alternative hypothesis.prove the alternative hypothesis.

Hypothesis TestingHypothesis Testing

Population

Hypothesis TestingHypothesis Testing

Population

NullHypothesis

Hypothesis TestingHypothesis Testing

Population

NullHypothesis

AlternativeHypothesis

Hypothesis TestingHypothesis Testing

Population

Sample

NullHypothesis

AlternativeHypothesis

Hypothesis TestingHypothesis Testing

Population

Sample Evidence

NullHypothesis

AlternativeHypothesis

Hypothesis TestingHypothesis Testing

Population

Sample Evidence

NullHypothesis

AlternativeHypothesis

WhichHypothesis

IsSupported?

Hypothesis TestingHypothesis Testing

Population

Sample Evidence

NullHypothesis

The evidence may

supportthe Null

Hypothesis…

Hypothesis TestingHypothesis Testing

Population

Sample Evidence

NullHypothesis

…if anydiscrepancy

can beattributedto chance

Hypothesis TestingHypothesis Testing

Population

Sample Evidence

AlternativeHypothesis

Theevidence willsupport theAlternative

Hypothesis…

Hypothesis TestingHypothesis Testing

Population

Sample Evidence

AlternativeHypothesis

…if thediscrepancycannot beattributedto chance

Statistical SignificanceStatistical Significance The data are called The data are called statistically statistically

significantsignificant if their deviation from if their deviation from what would be expected under the what would be expected under the null hypothesis is too great to be null hypothesis is too great to be attributed to chance.attributed to chance.

Example: The incidence of cancer in Example: The incidence of cancer in one community is 8% and in another one community is 8% and in another community it is 10%. Can the community it is 10%. Can the difference be attributed to chance?difference be attributed to chance?

Let’s Do It!Let’s Do It! Example 1.3, p. 9 – Is the New Drug Example 1.3, p. 9 – Is the New Drug

Better?Better? What are the risks involved in making What are the risks involved in making

the wrong decision?the wrong decision? Are the eating habits of beer drinkers Are the eating habits of beer drinkers

and wine drinkers the same?and wine drinkers the same? The news story:The news story:

Wine Drinkers Eat Healthier Than Beer DrinWine Drinkers Eat Healthier Than Beer Drinkers kers

The research:The research: Food buying habits of people who buy wine oFood buying habits of people who buy wine o

r beer: cross sectional studyr beer: cross sectional study