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# PSYC 3430- Midterm Exam Guide - Comprehensive Notes for the exam ( 122 pages long!)

Department
Psychology
Course Code
PSYC 3430
Professor
Study Guide
Midterm

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York
PSYC 3430
MIDTERM EXAM
STUDY GUIDE

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Instructor Notes - Chapter 18 - page 265
Chapter 18: The Binomial Test
Chapter Outline
18.1 Overview
Hypotheses for the Binomial Test
The Data for the Binomial Test
The Test Statistic for the Binomial Test
18.2 The Binomial Test
Real Limits and the Binomial Test
In the Literature - Reporting the Results of a Binomial Test
18.3 The Relationship Between Chi-Square and the Binomial Test
18.4 The Sign Test
Zero Differences in the Sign Test
When to Use the Sign Test
Learning Objectives and Chapter Summary
1. Students should recognize binomial data and be able to identify situations where a binomial
test is appropriate.
Binomial data exist whenever individuals are classified into exactly two different
categories. A binomial test is appropriate when there is a question about the proportion
of individuals in each category.
2. Students should understand the normal approximation to the binomial distribution and when it
is appropriate to use the approximation.
When pn and qn are both greater than or equal to 10, the binomial distribution is
approximately normal with a mean of μ = pn and a standard deviation of σ = npq. In
this situation, individual scores can be converted to z-scores and probabilities can be
obtained from the unit normal table.
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Instructor Notes - Chapter 18 - page 266
3. Students should be able to conduct a binomial test using the normal approximation.
The null hypothesis specifies values for p and q in the population, usually values that
reflect the distribution that would occur simply by chance. The critical region for the test
is determined by using the alpha level to look up z-score boundaries in the unit normal
table. The sample data provide values for n and for X (the number of occurrences of one
specific outcome), and the X value is transformed into a z-score.
4. Students should understand that the sign test is simply a special application of the binomial
test. Specifically, the binomial test is being used to evaluate the results from a repeated-
measures study where the difference scores are categorized as increases or decreases.
The null hypothesis states that there is no consistent treatment effect, so increases and
decreases occur simply by chance and should occur equally often; p = q = 1/2.
Other Lecture Suggestions
1. The binomial distribution and the binomial test provide a very concrete and intuitive
demonstration of some of the basic aspects of statistics and hypothesis testing. For example,
(1) The concept of sampling error. In Chapter 1 we introduced the notion that the
statistics obtained for a sample are typically not identical to the corresponding parameters
for the population. When tossing a coin 100 times, for example, you do not expect
exactly 50 heads and 50 tails even if the coin is perfectly balanced (the population of
tosses contains exactly 50% heads and 50% tails).
(2) The concept of a critical region. If you toss a coin 100 times and obtain 50 heads
there would be no reason to suspect that something was wrong with the coin. But, what
have to draw a line and say, “Wait a minute, that is simply too many heads to occur by
chance.” In every hypothesis test, we draw a line marking the critical region. That is, the
test establishes a boundary, and declares that any result beyond the boundary is simply
too extreme to have occurred simply by chance.
2. The following values produce whole number answers for classroom demonstrations:
When p = q = 1/2, n = 36 produces whole number values of μ = 18 and σ = 3.
When p = q = 1/2, n = 64 produces whole number values of μ = 32 and σ = 4.
When p = q = 1/2, n = 100 produces whole number values of μ = 50 and σ = 5.
When p = 1/4 and q = 3/4, n = 48 produces whole number values of μ = 12 and σ = 3.
When p = 1/4 and q = 3/4, n = 192 produces whole number values of μ = 48 and σ = 6.
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