Hypothesis Testing

Hypothesis Testing - Hypothesis Testing Example Problem You...

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Hypothesis Testing
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Example Problem You invent a pill designed to improve intelligence You know that for a standard intelligence test μ = 100 and σ = 15 You select a person at random and give her the smart pill and the intelligence test She scores 110 How can these results be explained? What does the difference between her score and the known population mean indicate? a true effect of the smart pill? or is it a chance occurrence (i.e., a matter of sampling error )?
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Purpose of Hypothesis Testing Statistics Make decisions (inferences) about whether an apparent effect observed in a sample: reflects a true effect that would hold in the larger population or is merely a matter of chance (sampling error)
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Hypotheses Null No true effect in the population The apparent effect is just a matter of sampling error Alternative True effect in the population
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Test the Null Hypothesis Why? It is precise – zero effect Estimate the probability that the null hypothesis is true If this probability is very low (by convention .05 or less), then reject the null hypothesis and decide that the apparent effect is probably a true effect If the probability is greater than .05, then fail to reject the null hypothesis and conclude that any apparent effect may be a matter of sampling error
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General Form of a Hypothesis Testing Statistic Consider the size of an apparent effect relative to how much fluctuation we would expect by chance Although there are many different hypothesis testing statistics, they have the same general form: ( 29 X E X σ - = chance error Sampling effect Apparent Where X is an observed value, E is the expected value of X if there is no true effect, and σ x is the standard deviation (or in most cases the standard error)
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What Does the Hypothesis Testing Statistic Tell Us? The greater the absolute value of a
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Hypothesis Testing - Hypothesis Testing Example Problem You...

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