Session__6_notes - OVERVIEW OF HYPOTHESIS TESTING There are...

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OVERVIEW OF HYPOTHESIS TESTING
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There are three ways that we make inferences from a sample to a population: 1. Point estimation 2. Interval estimation (confidence intervals) 1. Hypothesis testing Hypothesis testing and interval estimation use different languages, but usually produce similar results.
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What is a hypothesis? A scientific hypothesis is a prediction of an outcome, based on theoretical considerations, often resulting from an informed guess or creative insight. Example: A specific reading intervention will improve students’ reading abilities. A statistical hypothesis is a statement about the numerical value of an unknown parameter. Example: H : μ = 0 Scientific hypotheses can be tested statistically using statistical hypotheses.
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There are several types of hypotheses that we might test (see page 257): 1. A statement about a single parameter H : μ = 0 The population mean is 0.
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Hypothesis testing is a procedure, based on sample evidence and probability theory, used to determine whether the hypothesis is a reasonable statement and should not be rejected, or is unreasonable and should be rejected. 5 What is hypothesis testing?
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The Steps of Hypothesis Testing In hypothesis testing, we work with two competing hypotheses: the null and the alternate hypothesis.
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The null hypothesis is the statement that you are testing. The null hypothesis always states that the treatment has no effect, no change, nothing happened. Example: The average GPA at Penn State equals 3.5. H : μ = 3.5
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The alternative hypothesis is the opposite of the null hypothesis. The alternative hypothesis states that the treatment has an effect, something changed, and something happened. Example: The average GPA at Penn State does not equal 3.5 H : μ ≠ 35 Alternative hypothesis is generally the one that is believed to be true by the researcher.
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Example: Data from a large national study shows that average weight for 2-year old children is μ = 26 pounds (σ=4). Researchers want to know of a special diet impacts weight. In our sample, the mean was 31. Is the special diet changing the average weight? What is our null hypothesis? H : μ = 26 Even with the special diet, the mean weight
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μ=50 Sampling Distribution It is unlikely that we would get a sample mean of this value . .. ... if in fact this were the population mean. ... Therefore, we reject the null hypothesis that μ = 50. 20 When would you reject the null hypothesis? (Example, H 0 : μ = 50)
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Important points about hypothesis testing: Neither decision entails proving the null hypothesis or the alternative hypothesis. We merely state there is enough evidence to behave one way or the other. Use the following language when interpreting a test: Reject the null hypothesis Fail to reject the null hypothesis or Retain the null hypothesis No matter what decision we make, there is always a chance we made an error.
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This note was uploaded on 01/27/2011 for the course EDPSY 400 at Pennsylvania State University, University Park.

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Session__6_notes - OVERVIEW OF HYPOTHESIS TESTING There are...

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