The Language of Statistical Decision Making Lecture 1 Section 1.3 Fri, Sep 2, 2005

Populations and Samples Population – The entire group of objects or individuals under study. 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.

Samples and Inferences Population

Samples and Inferences Population Take Sample Sample

Samples and Inferences Population Take Sample Make Observations Sample Data

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

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

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

Hypothesis Testing Population

Hypothesis Testing Null Hypothesis Population

Hypothesis Testing Null Hypothesis Population Alternative Hypothesis

Hypothesis Testing Null Hypothesis Population Alternative Hypothesis Sample

Hypothesis Testing Null Hypothesis Population Alternative Hypothesis Sample Evidence

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

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

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

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

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

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. 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! Let’s do it! 1.1, p. 6 – Fair Die? Let’s do it! 1.2, p. 7 – Stress Can Cause Sneezes. Example 1.3, p. 9 – Is the New Drug Better? What are the risks involved in making the wrong decision? See Making Intelligent Errors, by Walter Williams.