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Session__9_notes - From last class you should be able to 1...

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From last class, you should be able to: 1. Know when to use one-sample Z vs. one-sample t tests 2. Describe the shape of the t-distribution 3. Determine the number of degrees of freedom given an example 4. Identify the critical value associated with a given number of degrees of freedom using Table C 5. Calculate the t-statistic for a one-sample t-test 6. Be able to go through all steps of hypothesis testing using one-sample t-tests 7. Define a p-value 8. Read SPSS output for a one-sample t-test
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HYPOTHESIS TESTING: Overview of tests for mean differences
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Unknown μ = ? Population A: Taught by Method A Unknown μ = ? Population B: Taught by Method B Sample A Sample B Do achievement scores for children taught by method A differ from the scores for children taught by method B?
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T-tests are used to examine the differences between two means on a dependent variable. An independent variable is the grouping variable. It is measured on a nominal or ordinal scale with two levels. Example: Method A vs. Method B The dependent variable is the variable for which means are computed. It is measured on an interval or ratio scale. Example: Achievement Test Score
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There are two types of t-tests for comparing two means: 1. The independent-measures t-test examines differences in means for two groups. Independent variable could be gender, method of instruction, type of profession Example: What is the difference between males and females on motivation? Examines variability between participants 1. The repeated measures (or paired) t-test examines differences in mean for the same group at different points in time. Independent variable could be pre- vs. post-test, fall vs. spring semester, morning vs. evening Example: Do students improve from the pre-test to the post-test score following instruction? Examines variability within participants
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Table C: Percentile points of t- Distribution (p.621) Directional Non-directional Example: 95% confidence, two-tailed test, n=14 Critical value is 2.160
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HYPOTHESIS TESTING: INDEPENDENT-MEASURES T- TEST
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The independent t-test is used to see if the means are different for between participants factors with two levels. The null hypothesis for a two-tailed test is: H 0 : There is no difference between the means. H 0 : µ1 = µ2 or H 0 : µ1-µ2=0 The alternative hypothesis is: H 1 : There is a difference between the means. H 1 : µ1 ≠ µ2 or H 1 : µ1-µ2 ≠ 0
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Research Questions Hypothesis No Difference Any Difference Pop 1 Pop 2 Pop 1 < Pop 2 Pop 1 Pop 2 Pop 1 > Pop 2 H 0 μ 1 - μ 2 = 0 μ 1 - μ 2 0 μ 1 - μ 2 0 H a μ 1 - μ 2 0 μ 1 - μ 2 < 0 μ 1 - μ 2 > 0 Just as with the one-sample tests, we can have one-tailed or two tailed tests. You believe that μ 2 has the higher mean. You believe that μ 1 has the higher mean.
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The independent t-test has certain assumptions: 1. Data are normally distributed within their respective populations 2. Variances of the two populations are equal ( homogeneity of variance ) This can pose a problem when the sample sizes are unequal 1. Individual observations are independent (i.e., not paired, dependent, or associated)
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