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Introduction to the t statistic

Introduction to the t statistic. Steps to calculate the denominator for the t-test. 1. Calculate variance or SD s 2 = SS/n-1 2. Calculate the standard error. T-test Procedure. Set the hypotheses (null and alternative)

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Introduction to the t statistic

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  1. Introduction to the t statistic

  2. Steps to calculate the denominator for the t-test 1. Calculate variance or SD s2= SS/n-1 2. Calculate the standard error

  3. T-test Procedure Set the hypotheses (null and alternative) Set the decision criteria (by selecting the alpha level, directionality, and critical values). Compute the test-statistic (t) Compare obtained t-statistic to critical value(s) Make a statistical decision Concluding statement

  4. Conducting a t-test It’s not a normal distribution, and you don’t use the unit normal table Using the t-distribution (William Sealy Gosset, 1908) instead

  5. T-distribution Bell-shaped and symmetrical A ‘family’ of distributions - depends on the degrees of freedom The mean of the t-distribution is zero

  6. T-distribution table • When the df is NOT listed in the table provided in Appendix B, you should look up the critical t for both of the surrounding df values listed and use the LARGER value for t

  7. Measuring Effect Size with the t Statistic (cont.) • Estimated Cohen’s d

  8. Measuring Effect Size with the t Statistic (cont.) • percentage of variance accounted for = r2 (aka 2)

  9. Assumptions for a One-sample t-Test 1. Independent observations 2. The sample data come from a normal population distribution

  10. Example 1 • The legal highway limit near populated areas in many parts of the US is 55 mph. To determine whether people exceed the 55mph, suppose a state monitored the speeds of 25 cars at selected highway locations. Can we conclude that the average speed is higher than the 55 mph limit?

  11. Example 1 - Data 55 60 60 55 57 60 55 58 63 54 65 56 61 58 55 57 59 53 59 65 56 61 55 54 59 Find the following: • Mean • SS • s2 • s

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