1. Chapter 3
Probability
Sampling Theory
Hypothesis Testing

2. Probability “On average” Distribution of outcomes
The extent to which something is likely to happen
“On average”
Distribution of outcomes

3. “On Average” Probability is based upon an infinite number of chances
The concept “on average” implies the likelihood, the probability, of a particular outcome given an infinite number of possible outcomes

4. Distribution of Outcomes
Permutations: the number of ways a result can occur where order is important
Combinations: the number of ways a result can occur without regard to order

5. Example
Coincidence game

6. Hypothesis Testing

7. What is a Hypothesis
Definition: A statement of relationship between variables.

8. Null Hypothesis A test of
Null hypothesis: a statement of no relationship between variables (a negation of the research hypothesis)
A test of
A null hypothesis can be rejected or not rejected

9. Significance
Before we test a hypothesis, we must decide how much error is acceptable
Social scientists generally accept 5%, on average
Something is considered significant when the chances that the relationship exists are 95% or greater (less than 5% chance of error)

10. Statements of Error
Type I Error: the error of rejecting a null hypothesis, rejecting coincidence, and claiming support for the research hypothesis
Type II Error: concluding that the result is due to random coincidence when it is actually not; fail to correctly reject the null hypothesis and support the research hypothesis

11. The Relationship Stated in the Research Hypothesis Exists in Reality
Figure 3.6. The Relationship Between Type I and Type II Errors in Hypothesis Testing 
The Relationship Stated in the Research Hypothesis 
Exists in Reality 
Does Not Exist In Reality 
The Null Hypothesis is Rejected 
OK 
Type I Error 
(α) 
You Failed to Reject the Null Hypothesis 
Type II Error 
(β) 
Rejecting a null hypothesis when we should not have, results in Type I error in which we claim a relationship that does not exist in reality. Failing to reject a null hypothesis when we should have because a relationship exists in reality, results in a Type II error. 

12. Significance and Error
Type I error, alpha (α): the acceptable level of error for rejecting the null hypothesis
Detecting an effect that is not present
False positive

13. Significance and Error
Type II error, beta (β): important for small sample sizes; failure to reject the null hypothesis when a relationship occurs
Not detecting an effect that is present
False negative
Power = 1 - β