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Research Methods I

Different Tests of Significance. One-Sample z-test or t-testCompares one sample mean versus a population meanTwo-Sample t-testCompares one sample mean versus another sample meanIndependent t-tests (equal samples)Dependent t-tests (dependent/paired samples)One-way analysis of variance (ANOVA)Comparing several sample means.

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Research Methods I

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    1. Research Methods I More on Hypothesis Testing

    2. Different Tests of Significance One-Sample z-test or t-test Compares one sample mean versus a population mean Two-Sample t-test Compares one sample mean versus another sample mean Independent t-tests (equal samples) Dependent t-tests (dependent/paired samples) One-way analysis of variance (ANOVA) Comparing several sample means

    3. One-sample z-test One-sample z-test is like getting a z-score except that it is based on the sampling distribution of sample means. The formula is: z = (xbar - µ) / (s / vn) the value of the variable whose distance from the mean we wish to find minus the mean of our frequency distribution (of means) divided by the standard deviation of the frequency distribution

    4. One-tailed vs. Two-tailed Tests When means are compared and H1 is: µ1 ? µ2 it is a non-directional (two-tailed) test. When H1 is: µ1 < µ2 or µ1 > µ2 it is a directional (one-tailed) test. In a directional (one-tailed) test one possible alternative must have been excluded prior to collecting the data. Two-tailed tests are more conservative since it is harder to reject the null-hypothesis. z = 1.65 vs 1.96; z = 2.33 vs. 2.58; z= 3.09 vs. 3.29

    5. 4 Steps of Hypothesis Testing State the hypothesis Set the criteria for a decision Collect data and compute sample statistics Make a decision

    6. 1. State the hypothesis The null hypothesis (H0) states that in the general population there is no change, no difference, or no relationship (no effect of independent variable on dependent variable) The alternative hypothesis (H1) states that there is a change, a difference, or a relationship for the general population (independent variable has an effect on the dependent variable. H0 and H1 are mutually exclusive Gravetter and Wallnau

    7. 2. Set the Criteria for a Decision Examine all possible sample means that could be obtained if H0 was true. Alpha level or level of significance is a probability value that is used to define the very unlikely sample outcomes if the null hypothesis is true The critical region is composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true.

    8. Levels of significance Critical values of z Level of Significance 1.96 .05 2.58 .01 3.29 .001 Probability of falsely rejecting the true null hypothesis (type I error / alpha error) |z| < 1.96 – no rejection of H0 (the difference between the sample mean and the population mean is not significant, the difference was probably because of sampling error). |z| > 1.96 – reject H0 (accept H1) (the difference between the sample mean and the population mean is significant.

    9. 3. Collect data – sample statistics Select random sample Data is collected after researcher has stated hypotheses Compare data (sample mean) with hypothesis Compute z-score for sample mean

    10. 4. Make a decision If sample data fall in the ‘critical region’ of the distribution we must reject the null hypothesis The outcome that was found is very unlikely to be found if H0 was true. If sample data do not fall in the ‘critical region’ than we fail to reject H0. The outcome that was found can be found if H0 is true

    11. Type I and Type II Errors Type I Error Reject the null hypothesis even though it is true Null hypothesis should not be rejected Type II Error Fail to reject the null hypothesis even though it is false Null hypothesis should be rejected Alpha-level: the probability that the test will lead to a Type I error (probability of obtaining sample data in the critical region even though H0 is true)

    12. One-tailed vs. Two-tailed Tests When means are compared and H1 is: µ1 ? µ2 it is a non-directional (two-tailed) test. When H1 is: µ1 < µ2 or µ1 > µ2 it is a directional (one-tailed) test. In a directional (one-tailed) test one possible alternative must have been excluded prior to collecting the data. Two-tailed tests are more conservative since it is harder to reject the null-hypothesis. z = 1.65 vs 1.96; z = 2.33 vs. 2.58; z= 3.09 vs. 3.29

    13. Measuring Effect size Concerns about hypothesis testing: All-or-none decision – alpha level is arbitrary Idea of hypothesis is artificial (every treatment has some effect which is not considered in null hypothesis) Does not test if treatment has ‘substantial’ effect Sample size may determine if results are significant

    14. Measuring Effect Size Cohen’s d: mean difference / standard deviation The mean difference is being standardized Magnitude of D: 0 < d < 0.2 small effect 0.2 < d < 0.8 medium effect d > 0.8 large effect

    15. Statistical Power Power of a statistical test is the probability that the test will correctly reject a false null hypothesis. Or Power is the probability of obtaining sample data in the critical region when the null hypothesis is false. Power = p (reject a false H0) = 1 – ß Power also depends on Alpha level (.05 versus .01) Sample size (larger sample more power) One-tailed versus two-tailed test

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