1. Chapter 8 Introduction to Hypothesis Testing

2. 8.1 Hypothesis Testing Logic
A statistical method that uses sample data to evaluate the validity of a hypothesis about a population parameter

3. Logic of Hypothesis Test
State hypothesis about a …
Predict the expected characteristics of the sample based on the …
Obtain a random sample from the …
Compare the obtained sample data with the prediction made from the hypothesis
If consistent, hypothesis is …
If discrepant, hypothesis is …

4. Figure 8.1 Basic Experimental Design
FIGURE 8.1 The basic experimental situation for hypothesis testing. It is assumed that the parameter μ is known for the population before treatment. The purpose of the experiment is to determine whether the treatment has an effect on the population mean.

5. Figure 8.2 Unknown Population in Basic Experimental Design
FIGURE 8.2 From the point of view of the hypothesis test, the entire population receives the treatment and then a sample is selected from the treated population. In the actual research study, a sample is selected from the original population and the treatment is administered to the sample. From either perspective, the result is a treated sample that represents the treated population.

6. Four Steps in Hypothesis Testing
Step 1: Step 2: Step 3: Step 4:

7. Step 1: State Hypotheses
Null hypothesis (H0)
states that, in the general population, there is no change, no difference, or is no relationship
Alternative hypothesis (H1)
states that there is a change, a difference, or there is a relationship in the general population

8. Step 2: Set the Decision Criterion
Distribution of sample outcomes is divided
Those likely if H0 is true
Those “very unlikely” if H0 is true
Alpha level, or significance level, is a probability value used to define “very unlikely” outcomes
Critical region(s) consist of the extreme sample outcomes that are “very unlikely”
Boundaries of critical region(s) are determined by the probability set by the alpha level

9. Figure 8.3 Note “Unlikely” Parts of Distribution of Sample Means
FIGURE 8.3 The set of potential samples is divided into those that are likely to be obtained and those that are very unlikely to be obtained if the null hypothesis is true.

10. Figure 8.4 Critical region(s) for α = .05
FIGURE 8.4 The critical region (very unlikely outcomes) for alpha = .05

11. Step 3: Compute Sample Statistics
Compute a sample statistic (z-score) to show the exact position of the sample
In words, z is the difference between the observed sample mean and the hypothesized population mean divided by the standard error of the mean

12. Step 4: Make a decision
If sample statistic (z) is located in the critical region, the null hypothesis is …
If the sample statistic (z) is not located in the critical region, the researcher fails to …

13. 8.2 Uncertainty and Errors in Hypothesis Testing
Hypothesis testing is an inferential process
Uses limited information from a sample to make a statistical decision, and then from it …
Sample data used to make the statistical decision allows us to make an inference and …
Errors are possible

14. 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 …

15. Type II Errors
Researcher fails to reject a null hypothesis that is really false
Researcher has failed to detect a real treatment effect
Type II error probability is not easily identified

16. Table 8.1 Type I error (α) Type II error (β) Actual Situation
No Effect =
H0 True
Effect Exists =
H0 False
Researcher’s Decision
Reject H0
Type I error (α)
Decision correct
Fail to reject H0
Type II error (β)

17. Figure 8.5 Location of Critical Region Boundaries
FIGURE 8.5 The locations of the critical region boundaries for three different levels of significance: α = .05, α = .01, and α = .001.

18. Figure 8.6 Critical Region for Standard Test
FIGURE 8.6 Sample means that fall in the critical region (shaded areas) have a probability less than alpha (p < α). In this case, H0 should be rejected. Sample means that do fall in the critical region have a probability greater than alpha (p > α).

19. 8.3 Assumptions for Hypothesis Tests with z-Scores
Random …
Independent …
Value of σ is not changed …
Normally distributed …

20. Factors that Influence the Outcome of a Hypothesis Test
Size of difference between sample mean and original population mean
Variability of the scores
Number of scores in the sample

21. 8.5 Hypothesis Testing Concerns: 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
Cohen’s d measures effect size simply and directly in a standardized way

22. Cohen’s d : Measure of Effect Size
Magnitude of d
Evaluation of Effect Size
d = 0.2
Small effect
d = 0.5
Medium effect
d = 0.8
Large effect

23. Figure 8.8 When is a 15-point Difference a “Large” Effect?
FIGURE 8.8 The appearance of a 15-point treatment effect in two different situations. In part (a), the standard deviation is σ = 100 and the 15-point effect is relatively small. In part (b), the standard deviation is σ = 15 and the 15-point effect is relatively large. Cohen’s d uses the standard deviation to help measure effect size.