Chapter 8 Introduction to Hypothesis Testing

1. Chapter 8 Introduction to Hypothesis Testing PowerPoint Lecture SlidesEssentials of Statistics for the Behavioral SciencesSeventh Editionby Frederick J. Gravetter and Larry B. Wallnau

2. Chapter 8 Learning Outcomes

3. Concepts to review • z-Scores (Chapter 5) • Distribution of sample means (Chapter 7) • Expected value • Standard error • Probability and sample means

4. 8.1 Logic of Hypothesis Testing • Hypothesis testing is one of the most commonly used inferential procedures • Definition: a statistical method that uses sample data to evaluate a hypothesis about a population

5. Logic of hypothesis test • State hypothesis about a population • Predict the characteristics of the sample based on the hypothesis • Obtain a random sample from the population • Compare the obtained sample data with the prediction made from the hypothesis • If consistent, hypothesis is reasonable • If discrepant, hypothesis is rejected

6. Figure 8.1 Basic experimental situation

7. Figure 8.2 Unknown population in experimental situation

8. Four steps of Hypothesis Testing • State the hypotheses • Set the criteria for a decision • Collect data and compute sample statistics • Make a decision

9. Step 1: State hypotheses • Null hypothesis (H0) states that, in the general population, there is no change, no difference, or not relationship • Alternative hypothesis (H1) states that there is a change, a difference, or a relationship in the general population

10. Step 2: Set the criteria for decision • Distribution of sample means is divided • Those likely if H0 is true • Those very unlikely if H0 is true • Alpha level, or level of significance, is a probability value used to define “very unlikely” • Critical region is composed of the extreme sample values that are very unlikely • Boundaries of critical region are determined by alpha level.

11. Figure 8.3 Division of distribution of sample means

12. Figure 8.4 Critical regions for α = .05

13. Learning Check • A sports coach is investigating the impact of a new training method. In words, what would the null hypothesis say?

14. Learning Check - Answer • A sports coach is investigating the impact of a new training method. In words, what would the null hypothesis say?

15. Learning Check • Decide if each of the following statements is True or False.

16. Answer

17. Step 3: Collect data and Compute sample statistics • Data collected after hypotheses stated • Data collected after criteria for decision set • This sequence assures objectivity • Compute a sample statistic (z-score) to show the exact position of the sample.

18. Step 4: Make a decision • If sample data are in the critical region, the null hypothesis is rejected • If the sample data are not in the critical region, the researcher fails to reject the null hypothesis

19. Box 8.1: Proving the alternative hypothesis • Seems odd to focus on null hypothesis, which we do not believe to be true. • In logic, it is easier to demonstrate that a universal hypothesis is false than true.

20. Jury trial: an analogy • Trial begins with null hypothesis (innocent until proven guilty). • Police and prosecutor gather evidence (data) to show reject innocent plea and conclude guilt. • If there is sufficient evidence, jury rejects innocence claim and concludes guilt. • If there is not enough evidence, jury fails to convict (but does not conclude defendant is innocent).

21. Learning Check • Decide if each of the following statements is True or False.

22. Answer FF

23. 8.2 Uncertainty and Errors in Hypothesis Testing • Hypothesis testing is an inferential process • Uses limited information to reach general conclusion • Sample data used to draw conclusion about a population • Errors are possible

24. Type I Errors • Researcher rejects a null hypothesis that is actually true • Researcher concludes that a treatment has an effect when it has none • Alpha level is the probability that a test will lead to a Type I error.

25. Type II Errors • Researcher fails to reject a null hypothesis that is really false. • Researcher has failed to detect a real treatment effect.

26. Table 8.1

27. Figure 8.5 Location of critical region boundaries

28. Learning Check TF • Decide if each of the following statements is True or False.

29. Answer TF

30. 8.3 Example of a Hypothesis Test • Step 1: H0: alcohol exposure =18 (Even with alcohol exposure, the rats still average 18 grams at birth.) • Step 2: α = .05Critical region: z beyond ±1.96 • Step 3: z = 3.00 • Step 4: Reject H0

31. Figure 8.6 Structure of study in example

32. Figure 8.7 Critical region for Example 8.2

33. In the Literature • A result is significant or statistically significant if it is very unlikely to occur when the null hypothesis is true. • In APA format • State significance • Report value of test statistic • Report alpha level or p-value

34. Factors influencing hypothesis test • Size of difference between sample mean and original population mean • Appears in numerator of the z-score • Variability of the scores • Influences size of the standard error • Number of scores in the sample • Influences size of the standard error

35. Assumptions for hypothesis tests • Random sampling • Independent observations • Value of standard deviation is unchanged by the treatment • Normal sampling distribution

36. Figure 8.8 Rejection / critical region

37. Learning Check • A researcher uses a hypothesis test to evaluate H0 µ = 80. Which combination of factors is most likely to result in rejecting the null hypothesis?

38. Learning Check - Answer • A researcher uses a hypothesis test to evaluate H0 µ = 80. Which combination of factors is most likely to result in rejecting the null hypothesis?

39. Learning Check • Decide if each of the following statements is True or False.

40. Answer

41. 8.4 Directional (One-Tailed) Hypothesis Tests • The procedure in Section 8.3 is two-tailed because critical region is divided on both tails of the distribution. • Researchers usually have a specific prediction about the direction of a treatment effect before they begin. • In a directional hypothesis or one-tailed test, the hypotheses specify an increase or decrease in the population mean

42. Figure 8.9 Critical region for Example 8.3

43. Learning Check • A researcher is predicting that a treatment will decrease scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test

44. Learning Check • A researcher is predicting that a treatment will decrease scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test

45. 8.5 Concerns about Hypothesis Testing: Measuring Effect Size • Although commonly used, some researchers are concerned about hypothesis testing • Focus of test is data, not hypothesis • Significant effects are not always substantial • Effect size measures the absolute magnitude of a treatment effect, independent of sample size

46. Cohen’s d : measure of effect size

47. Figure 8.10 A 15-point difference in two situations

48. Learning Check • Decide if each of the following statements is True or False.

49. Answer

50. 8.6 Statistical Power • The power of a test is the probability that the test will correctly reject a false null hypothesis • It will detect a treatment effect if one exists • Power = 1 – β or 1 – p (Type II error) • Power usually computed before starting study • Requires assumptions about factors that influence power