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hypothesis testing

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University of Toronto St. George
Damian Dupuy

Statistics Lecture November 16, 2011 • Non-parametric data: don’t have mean or standard deviation but you are dealing with how many things are in a category • Non-directional: there is a significant different between the sample and the population miu is not equal to xbar • Directional: xbar is significantly less than or greater than the population; xbar= > or < miu • Most important hypothesis testing error’s is a type one error Hypothesis testing- Test Selection • Test used is a function of the research question and research assumptions • Tests will vary according to the number of samples drawn, sampling design and scale of information • Ex. ttc might be testing how many people would ride the ttc before a fare increase and post increase to see how their riding patterns differ • One of the most common is the One-Sample Means test or One Sample Difference of Means Test • Is there a significant difference between the sample mean and the population mean • Should always have significant difference in the hypothesis and also state it in the conclusion • You will either be using the z test or the t test [less than 30 sample size] Z= xbar-miu s/sqroot of n t= xbar-miu s/sqroot of n-1 • Placing a probability statement on the likelihood of sampling error occurring • We usually select a fairly low significance level in order to avoid type 1 error [usually 0.05 or 0.01] • Conclusion of the test is expressed in terms of the level of significance of the result • In classic hypothesis testing, rejective the null hypothesis at .05 is the same as saying the statistical test is significant at the .05 level Hypothesis testing- Rejection regions • Selecting a significance level allows the regions of rejection and non-rejection of the null hypothesis • Entire set of values that a test statistic could assume • Regions of rejection can be directional or non-d
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