The Language of Statistical Decision Making Lecture 1 Section 1.3 Fri, Jan 20, 2006

Is Chocolate Good for You? A recent study seems to show that chocolate is good for your health. A recent study seems to show that chocolate is good for your health. The news story: The news story: Chocolate Relaxs Heart Chocolate Relaxs Heart Chocolate Relaxs Heart Chocolate Relaxs Heart The study: The study: Acute Consumption of Flavanol-Rich Cocoa and the Reversal of Endothelial Dysfunction in Smokers Acute Consumption of Flavanol-Rich Cocoa and the Reversal of Endothelial Dysfunction in Smokers Acute Consumption of Flavanol-Rich Cocoa and the Reversal of Endothelial Dysfunction in Smokers Acute Consumption of Flavanol-Rich Cocoa and the Reversal of Endothelial Dysfunction in Smokers

Populations and Samples Population – The entire group of objects or individuals of interest in the study. Population – The entire group of objects or individuals of interest in the study. Sample – A part of the population from which the data is actually obtained. Sample – A part of the population from which the data is actually obtained.

Statistical Inferences Statistical inference – A conclusion about the population based on information from a sample of that population. Statistical inference – A conclusion about the population based on information from a sample of that population.

Samples and Inferences Population

Samples and Inferences Population Sample Take Sample

Samples and Inferences Population Sample Data Take Sample Make Observations

Samples and Inferences Population Sample Data Inference Take Sample Make Observations Draw an Inference

Samples and Inferences Population Sample Data Inference Take Sample Make Observations Draw an Inference

Hypotheses Hypothesis – A statement that is proposed, but not known to be true. Hypothesis – A statement that is proposed, but not known to be true. Hypotheses are often proposed explanations of something that is known to be true. Hypotheses are often proposed explanations of something that is known to be true.

Hypotheses The Null Hypothesis – The conventional belief about the population, or the status quo, or the neutral position. The Null Hypothesis – The conventional belief about the population, or the status quo, or the neutral position. It receives the benefit of the doubt. It receives the benefit of the doubt. The Alternative (Research) Hypothesis – An alternative to the null hypothesis. The Alternative (Research) Hypothesis – An alternative to the null hypothesis. It bears the burden of proof. It bears the burden of proof. Typically, the researchers are trying to prove the alternative hypothesis. Typically, the researchers are trying to prove the alternative hypothesis.

Hypothesis Testing Population

Hypothesis Testing Population Null Hypothesis

Hypothesis Testing Population Null Hypothesis Alternative Hypothesis

Hypothesis Testing Population Sample Null Hypothesis Alternative Hypothesis

Hypothesis Testing Population Sample Evidence Null Hypothesis Alternative Hypothesis

Hypothesis Testing Population Sample Evidence Null Hypothesis Alternative Hypothesis Which Hypothesis Is Supported?

Hypothesis Testing Population Sample Evidence Null Hypothesis The evidence may support the Null Hypothesis…

Hypothesis Testing Population Sample Evidence Null Hypothesis …if any discrepancy can be attributed to chance

Hypothesis Testing Population Sample Evidence Alternative Hypothesis The evidence will support the Alternative Hypothesis…

Hypothesis Testing Population Sample Evidence Alternative Hypothesis …if the discrepancy cannot be attributed to chance

Statistical Significance The data are called statistically significant if their deviation from what would be expected under the null hypothesis is too great to be attributed to chance. The data are called statistically significant if their deviation from what would be expected under the null hypothesis is too great to be attributed to chance. Example: The incidence of cancer in one community is 8% and in another community it is 10%. Can the difference be attributed to chance? Example: The incidence of cancer in one community is 8% and in another community it is 10%. Can the difference be attributed to chance?

Let’s Do It! Example 1.3, p. 9 – Is the New Drug Better? Example 1.3, p. 9 – Is the New Drug Better? What are the risks involved in making the wrong decision? What are the risks involved in making the wrong decision? Are the eating habits of beer drinkers and wine drinkers the same? Are the eating habits of beer drinkers and wine drinkers the same? The news story: The news story: Wine Drinkers Eat Healthier Than Beer Drinkers Wine Drinkers Eat Healthier Than Beer Drinkers Wine Drinkers Eat Healthier Than Beer Drinkers Wine Drinkers Eat Healthier Than Beer Drinkers The research: The research: Food buying habits of people who buy wine or beer: cross sectional study Food buying habits of people who buy wine or beer: cross sectional study Food buying habits of people who buy wine or beer: cross sectional study Food buying habits of people who buy wine or beer: cross sectional study