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Lecture 8

PSYC 241 Lecture 8: Lesson 8: Introduction to Hypothesis Testing

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PSYC 241
Kristen Leighton

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find more resources at Lesson 8: Introduction to Hypothesis Testing ● Hypothesis Testing ○ Goal: rule out chance (sampling error) as a plausible explanation for results ○ Hypothesis testing helps determine whether a treatment has an effect ○ To evaluate research in which: ■ 1. A sample is selected from the population ■ 2. The treatment is administered to the sample ■ 3. The people in the sample are measured after treatment ○ If people in sample are noticeably different from those in original population, we have evidence of treatment effect ○ It is also possible, however, that the difference between sample and population is due to sampling error ○ A statistical hypothesis is an assumption about a population parameter ○ Best way to determine whether hypothesis is true would be to examine entire population ■ Impractical --> impossible ○ Random sample is proxy for population ○ Use this sample to test hypothesis ○ Two possible explanations: ■ 1. The difference between sample and population can be explained by sampling error ■ No treatment effect ■ 2. The difference is too large to be due to sampling error ■ Treatment effect ● Cannot "prove" things to be true ● Much easier to show that something is false ● Dilemma for researchers: ○ We want to support our hypotheses, but the techniques available are better for showing that something is false ● Null Hypothesis ○ Two types of statistical hypotheses: ■ 1. Null hypothesis: No difference ■ H0 ■ No difference between sample statistics and population parameters or ■ No difference between samples --> no difference between populations ● Any minor differences due to chance ● Alternative Hypothesis ○ 2. Alternative hypothesis: Difference ■ H1or Ha find more resources at find more resources at ■ Difference between sample statistics and population parameter or ■ Difference between two samples --> difference between populations ● Difference due to some non-random cause ● Even though we are using samples to test our hypothesis, the hypotheses are always stated based on populations ● Statistical Notation ○ H 0 µ0= µ1 ■ No difference in population means ○ H : µ doesn't equal µ 1 0 1 ○ H a µ0doesn't equal1µ ■ Population means are not equal (two-tailed, non-directional) ■ Non-directional tests are more stringent; more conservative ● Directional Tests ○ If researchers predicts a specific direction for the treatment effect (increase or decrease), can incorporate the directional prediction into the hypothesis test ○ The result is called a directional test or a one-tail test ○ Directional test includes directional prediction in statement of hypotheses and location of the critical region ○ For example, if the original population has a mean of 80 and treatment is predicted to increase the scores, the null hypothesis would state that after treatment: ■ H0: mean is equal to or < 80 (there is no increase) ● Statistical Notation ○ H : µ < µ 1 0 1 ○ H 1 µ0> µ1 ○ H a µ0< µ1 ○ H a µ0> µ1 ■ One mean is greater (or less than) the other (one-tailed, directional) ● The Null hypothesis, the Alpha Level, the Critical Region, and the Test Statistic (can be written on calculation sheet) ○ 5 steps in hypothesis testing: ■ Step 1: State Hypothesis ■ State the hypotheses; select an α (alpha) level ■ Null hypothesis0 H , always states that the treatment has no effect ■ Alpha level establishes a criterion, or "cut-off," for making a decision about the null hypothesis find more resources at find more resources at ■ Alpha level also determines risk of Type I error ■ Step 2: Set Criteria ■ Locate the critical region ■ The critical region consists of outcomes that are very unlikely to occur if the null hypothesis is true ■ Means that are almost impossible to obtain if the treatment has no effect ■ "almost impossible" means probability (p) that is less than the alpha level ■ Step 3: Collect and analyze data
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