mid-semester feedback in-class exercise. chapter 8 introduction to hypothesis testing
TRANSCRIPT
Mid-semester feedback
In-class exercise
Chapter 8Introduction to Hypothesis Testing
Logic of hypothesis testing
Use sample data to evaluate a hypothesis about a population parameter
Begin with known population and evaluate whether a sample that receives a treatment represents the known population or some other population Did the treatment have an effect?
Logic of hypothesis testing 4 steps in hypothesis testing
1. State hypotheses Null hypothesis Alternative hypothesis
Directional (one-tailed) Nondirectional (two-tailed)
2. Set criteria for a decision Probability that sample comes from population Alpha level
Defines critical region(s) (region(s) of rejection) Visualizing the boundaries for making a
decision
Logic of hypothesis testing 4 steps in hypothesis testing
1. State hypotheses2. Set criteria for a decision3. Collect data and compute sample stats
Compute M and convert to z-score
4. Make a decision Reject the null hypothesis
Z-score in critical region Probability of sample mean < alpha level
Fail to reject null hypothesis (retain null hyp) Z-score not in critical region Probability of sample mean > alpha level
Examples of hypothesis testing
I have taught statistics many times. Across all the students and all the tests the have taken, the mean score on my stat tests=80 with SD=10. Let’s assume that these represent known population parameters.
I decide to try something different in one of my stat classes. Twice a week, the students attend a tutoring session. I believe that the tutoring sessions will improve test scores.
Examples of hypothesis testing
4 steps1. State hypotheses2. Set criteria for decision
Two-tailed test; =.05
3. Collect data M=85; n=25
4. Make a decision (evaluate hypotheses) Reporting results in the literature Re-run analysis with a one-tailed
test
Examples of hypothesis testing
In-class exercises Are you guys really working harder (ste
p 1) Are you guys really working harder (ste
p 2) Are you guys really working harder (ste
p 3) Are you guys really working harder (ste
p 4) Reporting results in the literature Re-run analysis with a one-tailed
test
Uncertainty and errors in hypothesis testing
Inferences and sampling error Type I error
Conclude an effect when there really isn’t one
Probability of Type I error = alpha level ()
Type II error Conclude no effect when there really is
one Probability of Type II error = beta ()
Assumptions for hypothesis test with z-scores
Random sampling Independent observations
Data obtained from each individual not influenced by other individuals in sample
SD (variability) not changed by treatment
Normal sampling distribution
Effect size
Hypothesis testing indicates whether an effect is significant but does not indicate the absolute size of an effect Large sample sizes can lead to
statistical significance with small effects
Effect size
Cohen’s d is one measure of effect size d=size of treatment effect in SD units d=(M-)/ Interpretation
0 < d < 0.2 small effect 0.2 < d < 0.8 medium effect d > 0.8 large effect
Calculate effect size for tutoring study =80; =10; M=85
Power
Power=probability of finding an effect assuming that one exists
Influenced by: Size of effect Alpha level Sample size
Often used to determine appropriate sample size