PSYC227_fall09_week9 - EXAM 2 onThursday Hypothesis Testing...

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on Thursday EXAM 2
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Learning Objectives: 1. Effect size 2. Power Was it due to chance, or something else? Hypothesis Testing
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Hypothesis Tes8ng Step 1: state the hypothesis Step 2: set the criteria for a decision Step 3: Collect data and compute sample sta8s8cs Step 4: make a decision A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population. Was it due to chance, or something else? Standardized method for evalua8ng the results of a research study.
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Step 1: state the hypothesis The Null hypothesis (H 0 ) : observed difference reflects chance varia8on ( zero effect ) The Alterna1ve hypothesis (H 1 ) : observed difference is real ≠, two‐tailed <, > one‐tailed (direc8onal) H 0 and H 1 are mutually exclusive! No change
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Select an alterna1ve hypothesis as that which the sampling experiment is intended to establish . There are 3 possibili8es One‐tailed, upper‐tailed > One‐tailed, lower‐tailed < Two‐tailed Select the null hypothesis as the status quo. One‐tailed: parameter value closest to the alterna8ve Two‐tailed: complementary (only unspecified) value Step 1: state the hypothesis No change
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Example The population of 2 year old children has an average weight of 26 lb. The distribution of weights is normal with standard deviation 4 . Researcher selects a sample of 4 infants and instructs the parents to provide each child with extra handing. The researcher predicts that extra handling will stimulate growth and produce an increase in their weight at age 2. The researcher records the weight of each child at age 2 and obtains a sample mean of 29.5 lb.
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H 0 : µ 26 (there is no increase in weight) H 1 : µ > 26 (there is an increase in weight) Step 1: hypothesis Step 2: critical region α =0.05
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Step 3: compute sample statistic Step 4: make a statistical decision Sample mean is in the critical region (1.75 > 1.65) or p-value = 0.0401 < 0.05 = α Reject the null hypothesis. Conclude that extra handling does result in increased body weight for infants. 1.75 p-value = 0.0401 Compare z-values or Compare probabilities Sample mean Hypothesized population mean Standard error test statistic
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Decisions in hypothesis testing: 1. The sample data provide sufficient evidence to reject the null hypothesis. Conclude that the treatment has an effect . 2. The sample data do not provide enough evidence to reject the null hypothesis. Conclude that the treatment does not appear to have an effect . Uncertainty and Errors in Hypothesis Testing
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Uncertainty and Errors in Hypothesis Testing Fail to reject α β
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Level of significance: the alpha level: A researcher is conducting a hypothesis test to determine whether a treatment produces a significant increase in scores. The sample data produces z = 2.3. What would be the decision for a Critical region boundary 1. two-tailed test with α = 0.05 1.96 2. one-tailed test with α = 0.05 1.64 3.
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