Hypothesis Testing Probability The extent to which something is likely to happen On average Distribution of outcomes On Average Probability is based upon an infinite number of chances ID: 652762
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Slide1
Chapter 3
Probability
Sampling Theory
Hypothesis TestingSlide2
Probability
The extent to which something is likely to happen
“On average”
Distribution of outcomesSlide3
“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 outcomesSlide4
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 orderSlide5
Example
Coincidence gameSlide6
Hypothesis TestingSlide7
What is a Hypothesis
Definition: A statement of relationship between variables.Slide8
Null Hypothesis
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 rejectedSlide9
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)Slide10
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 hypothesisSlide11
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
The Relationship Stated in the Research Hypothesis
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)
OK
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.
Slide12
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 Slide13
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