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21-Nov-2014
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This presentation gives a summary of t-test and its application.

### Transcript of Student's T-Test

• 1. Students t-Test -PIE TUTORS Your Statistical Partner www.pietutors.com committed to deliver 24/7
• 2. Agenda Background Different versions of t-test Main usage of t-test t-test v/s z-test Assumptions of T-test Distribution of t-test and normal distribution Case Studies
• 3. Background Introduced in 1908 by William Sealy Gosset for the quality control of beer. Gosset published his mathematical work under the pseudonym Student. It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known.
• 4. Different Version of T-test Single sample t we have only 1 group; want to test against a hypothetical mean. Independent samples t we have 2 means, 2 groups; no relation between groups, e.g., people randomly assigned to a single group. Dependent t we have two means. Either same people in both groups, or people are related, e.g., husband-wife, left hand-right hand, hospital patient and visitor.
• 5. Main Usage of t-test Among the most frequently used t-tests are: A one-sample location test of whether the mean of a population has a value specified in a null hypothesis. A two-sample location test of the null hypothesis that the means of two populations are equal. All such tests are usually called Student's t-tests, though strictly speaking that name should only be used if the variance of the two populations are also assumed to be equal; the form of the test used when this assumption is dropped is sometimes called Welchs t-test. These tests are often referred to as "unpaired" or "independent samples" t-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping.
• 6. Main Usage of t-test A test of the null hypothesis that the difference between two responses measured on the same statistical unit has a mean value of zero. For example, suppose we measure the size of a cancer patient's tumor before and after a treatment. If the treatment is effective, we expect the tumor size for many of the patients to be smaller following the treatment. This is often referred to as the "paired" or "repeated measures" t-test: see paired difference test. A test of whether the slope of a regression line differs significantly from 0.
• 7. Z-test We can use z-test to test hypotheses about means for large samples (N>100) ( X X )2 N 1 N Consider ( X ) zM est. M Then H 0 : 10; H1 : 10; s X 5; N 200 If est. M est. M sX N sX 5 5 .35 N 200 14.14 (11 10) X 11 z 2.83; 2.83 1.96 p 0.05 0.35
• 8. T-test We use t-test when the sample size is small (N