1. Chapter 13: Understanding Results—Statistical Inferences Chapter 14: Generalizing Results

2. Descriptive Statistics
Used to present data in summary form.

3. Inferential statistics
Used to determine whether an independent variable had a reliable effect on a dependent variable
Replication: repeating experiment to try to get the same results second time
Groups must be equivalent
Achieved by experimental control and/or randomization

4. Random error
Variation due to differences among subjects within each group
Responsible for some difference in the means

5. Research and Null Hypotheses
Research hypothesis
H1: Population means are not equal
Null hypothesis
HO: Population means are equal
The assumption that the independent variable has had no effect

6. Statistical significance
The probability the difference in sample means is due to error
Statistically significant outcome: has a small likelihood of occurring if the null hypothesis is true

7. Level of significance Probability of error chosen by researcher
Usually set at .05 or less
Alpha level indicated by Greek letter α
Noted as p  .05; p  .01, etc
p: probability

8. Null-Hypothesis Significance Testing
Null-hypothesis significance testing assesses the probability of obtaining a given difference between sample means
t-test: commonly used significance test

9. The t-test Interpreting the t-test value:
If probability is high (over .05), fail to reject the null hypothesis
If probability is low (.05 or less), reject the null hypothesis

10. Do we have a winner? Data Analysis for an Experiment Comparing Means
Round Chopsticks?
Did the independent variable (shape of chopsticks) have an effect on the dependent variable (number of pasta pieces transferred)?
Square Chopsticks?

11. Null Hypothesis Significance Testing: The t Test
One-tailed versus two-tailed tests
One-tailed test = research hypothesis specified a direction of difference between the groups
Two-tailed test = research hypothesis did not predict direction of difference

12. Chopsticks Challenge
Hypothesis #1: Performance when using round chopsticks is different (better or worse) than performance when using square chopsticks
(two-tailed) = .19
Hypothesis #2: Performance when using round chopsticks is better than performance when using square chopsticks
(one-tailed) = .09

13. Do we accept the null hypothesis if the independent variable did not have an effect?
Instead we fail to reject the null hypothesis.

14. Type I and Type II Errors
Decision to reject the null hypothesis is based on probabilities rather than certainties.
Decision may or may not be correct

15. Type I error
Occurs when the null hypothesis is rejected, but the null hypothesis is true

16. Type II error
Occurs when the null hypothesis is false, but it is not rejected

17. Experimental sensitivity
Occurs when an experiment detects an effect of the independent variable (when, in fact, the independent variable truly has an effect)

18. Experimental power
Occurs when a statistical test allows researchers to correctly reject the null hypothesis
Determined by 3 factors:
Size of the effect
Sample size
Level of statistical significance