Chapter 12 Hypothesis Testing Learning Objectives Examine the process of hypothesis testing Evaluate research and null hypothesis Determine one- or two-tailed tests Understand obtained values, significance, and critical regions Distinguish between Type I and Type II error Introduction Researchers compare groups of people Hypothesis testing Develop hypothesis and then research to find out if it is true One- and two-tailed tests, types of error, and statistical power Research hypotheses Typically state goals of research Derived from theory or primary question/research questions Place conceptual language in format for empirical examination Null hypotheses Research can be statistically validated or refuted No statistically significant difference between variables examined
Facilitate hypothesis testing Null hypotheses Important to inferential analyses since true parameters of population are unknown Cannot absolutely accept research hypothesis but can reject null hypotheses Hypotheses Requirements: Conceptually clear and specific Clearly spell out the research goals Conceptual framework defines operationalization Hypotheses Requirements: Empirically based with no moral judgments Free from emotional bias Related to a body of theory Should refute, qualify, or support existing theories Criteria established by Zetterberg (1963) Hypothesis testing results should disprove the null hypothesis with a certain probability Data arranged as predicted by hypothesis Alternate hypotheses should also be rejected Step 1: Developing research hypothesis
Research hypotheses are very similar to research questions or propositions Assumption that the difference is so large that it cannot be attributed to chance Must test empirically Step 2: Developing null hypothesis Reverse of the research hypotheses States difference is so small that it could have occurred by either chance or sampling error Goal is to reject null hypothesis Step 3: Drawing samples Samples taken from populations studied Samples must represent target population Preferably the theoretical population Step 4: Selecting the test Two-tailed test Without specifying a direction of the difference One-tailed test Directional difference Must have a reason to choose this over two-tailed test Step 5: Calculating the obtained value Use analysis procedure
Chi-square, Z-tests, t-tests, ANOVA Step 6: Determining significance and critical regions Critical value Level of certainty (probability of making Type I error), degrees of freedom, one- or twotailed test Level of significance Step 7: Making a decision Value obtained from the statistical test is compared to the critical value If obtained value is greater than critical value, reject null hypothesis If obtained value is less than critical value, null hypothesis cannot be rejected at that level of significance Type I and Type II Errors Reject null hypothesis when there is difference between variables Do not reject null hypothesis when no statistically significant difference between variables Errors: Null hypothesis that is true is rejected Fail to reject null hypothesis that should have been rejected Type 1 and Type 2 Errors Type I and Type II Errors Type I error Rejection of a null hypothesis that is true Probability associated with Type I error is the significance value of the test is α
Type II error Failing to reject a false null hypothesis Probability of committing a Type II error is Which Is Better, Type I or Type II Error? Depends on researcher s goal Type I errors are brought out in future research Type II errors can kill the research A 5% or 1% chance of making a Type I error is a reasonable risk At this level, there is an adequate level of protection from committing Type II Errors Power of tests Power of a statistical test Probability that it will reject H0 if false Linked with probability of a Type II error Sample size defines the power of the test Balance risk of committing Type II error and possibility of having a sample that is too large Alpha level, critical probability, or significance level influence power Determine falseness of null hypothesis Conclusion Decide what type of test to use and choose one- or two-tailed test Keep in mind statistical power and probability of making Type I or Type II errors