School

York UniversityDepartment

PsychologyCourse Code

PSYC 3430Professor

Peter K PapadogiannisStudy Guide

MidtermThis

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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

about 51 heads? What about 52? What if you got 60 or 70 heads? At some point, you

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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