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Hypothesis testing in the REAL world t tests: single sample repeated measures independent samples

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Need for the t test Hypothesis testing using z requires knowledge of population parameters (mean, SD) Typical psychological experiments ▫No knowledge of parameters ▫Often don’t really care e.g. compare effects of IV manipulation in experimental and control group ▫Underlying population not critical ▫Interested in change produced by IV ▫Typically use ESTIMATES

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Estimation Best predictor of population mean? ▫Sample mean Best predictor of population SD? ▫Sample SD BUT sample SD will systematically underestimate true population variability biased estimate bias to reject null hypothesis

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How do we fix it? Adjust the formula for SD ▫Now we’ll call it s n-1 degrees of freedom ▫Number of scores in a sample that are free to vary Adjust our comparison distribution

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The t distribution Shape-shifter

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Using the t table df p cutoff (critical) value Things to note: ▫As df increases, critical value decreases Related to sample size ▫With an infinite sized sample, what are the CVs? ▫n=30

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A sample problem: pg 232 Conceptual and computational formuli SPSS Steps in hypothesis testing: hopefulness following a flood 1. Null hypothesis M(flood) = M(neutral) Alternative M(flood) not= M(neutral) Neutral = score of 4

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2. Comparison distribution use estimates from sample estimated mean sample mean estimated SD (s) s of the sampling distribution 3. Cutoff/critical value use t table with appropriate df 4. Compute t 5. Decide 6. Tell grandma

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A saner approach…. Computational formula SPSS

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Types of t tests t test for single sample ▫Compares sample mean to known or predicted population mean (e.g. “neutral” hopefulness; no ESP baseline probability) t test for dependent means ▫Compares samples (from the same people) collected before and after a given manipulation aka – within subjects, repeated measures, paired samples t test for independent means ▫Compares samples from two unique sets of people with different levels of the IV for each (EXP, control groups design)

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t test for dependent means Difference between one test to the next ▫Role of IV ▫If null is true, then difference = ? ▫pg 238 Communication scores before and after premarital counseling 1.State null and alternative 2.Select appropriate t 3.Determine critical value 4.Compute 5.Decide 6.Tell your Babushka

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t test for independent means Pooled estimate of the population SD ▫Weighted average of s for each sample ▫pg 279 Effects of writing on health 1.State null and alternative 2.Select appropriate t 3.Determine critical value 4.Compute 5.Decide 6.Tell your Nai nai

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Let’s give it a whirl…. 1. Siegel (1990) found that elderly people who owned dogs were less likely to pay visits to their doctors after upsetting events than those who did not own pets. Similarly, consider the following data: A sample of elderly dog owners is compared to a similar group of elderly persons who do not own dogs. The researcher records the number of visits to the doctor during the past year for each person. For the following data, is there a significant difference in the number of doctor visits between dog owners and control subjects? Use the.05 level of significance. CONTROL GROUP: 12, 10, 6, 9, 15, 12, 14 DOG OWNERS: 8, 5, 9, 4, 6 WHAT KIND OF TEST IS THIS???

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A psychologist tests a new drug for its painkilling effects. Pain threshold is measured for a sample of subjects by determining the intensity (in milliamperes) of electric shock that causes discomfort. After the initial baseline is established, subjects receive the drug and their pain thresholds are once again measured. The data are listed below. Do these data indicate that the drug produces a significant increase in pain tolerance? Use a one tailed test with the.05 level of significance. PAIN THRESHOLDS (milliamperes) without drug with drug 2.1 3.2 2.3 2.9 3.0 4.6 2.7 2.7 1.9 3.1 2.1 2.9 2.9 2.9 2.7 3.4 3.2 5.3 2.5 2.5 3.1 4.9

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A group of students recently complained that all of the statistics classes are offered in the morning. They claim that they "think better" later in the day and, therefore, would do better if the course was offered in the afternoon rather than in the morning. To test this claim, the instructor scheduled the course at the 2:40 time slot one semester. The afternoon class is given the exact same course as during prior semesters, including the same final exam. The instructor knows that, for previous students the final exam scores had been normally distributed with a mean of 70. The afternoon class, with 16 students enrolled, got a mean of 76 with a sample standard deviation of 8. Did the students in the afternoon section perform significantly better? a. Test with p=.05 with a one tailed test. b. Identify the dependent and independent variables

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1 Statistical Inference. 2 The larger the sample size (n) the more confident you can be that your sample mean is a good representation of the population.

1 Statistical Inference. 2 The larger the sample size (n) the more confident you can be that your sample mean is a good representation of the population.

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