13-1 Chapter 13 Sampling: Final and Initial Sample-Size Determination.

13-1

Chapter 13

Sampling: Final and Initial

Sample-Size Determination

Copyright © 2011 Pearson Education, Inc.

Figure 13.1 Relationship of Sample Size Determination to the Previous Chapters and the Marketing Research Process

Chapter 13 - 2

Focus of this Chapter

Relationship toPrevious Chapters

• Statistical Approach to Determining Sample Size

• Adjusting the Statistically Determined Sample Size

• Research Design Components (Chapter 3)

• Sampling Design Process (Chapter 12)

Approach to Problem

Field Work

Data Preparation and Analysis

Report Preparationand Presentation

Research Design

Problem Definition

Relationship to MarketingResearch Process


Figure 13.2 Final and Initial Sample Size Determination: An Overview


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Opening Vignette

Application to Contemporary Issues (Fig 13.5)

International Social Media Ethics

Definitions and Symbols (Table 13.1)

The Sampling Distribution(Figs 13a.1-13a.3) (Appendix 13a)

Statistical Approach to Determining Sample Size (Fig 13.3)

Confidence Interval Approach(Fig 13.4) (Table 13.2)

Adjusting the Statistically Determined Sample Size

Means Proportions

Chapter 13 - 4


Parameter: A parameter is a summary description of a fixed characteristic or measure of the target population.A parameter denotes the true value which would be obtained if a census rather than a sample was undertaken.

Statistic: A statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter.

Random sampling error: The error when the sample selected is an imperfect representation of the population of interest.

Definitions and Symbols

Chapter 13 - 5


Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter.

Confidence interval: The confidence interval is the range into which the true population parameter will fall, assuming a given level of confidence.

Confidence level: The confidence level is the probability that a confidence interval will include the population parameter.

Definitions and Symbols (Cont.)

Chapter 13 - 6

Chapter 13 -7

Table 13.1Symbols for Population and Sample Variables

Variable Population Sample

Mean μ

Proportion π p

Variance

Standard deviation σ s

Size N n

Standard error of the mean

Standard error of the proportion

Standardized variate (z)



Figure 13.3 The Confidence Interval Approach and Determining Sample Size

Confidence IntervalApproach

Means Proportions

Chapter 13 - 8

.

The Confidence Interval Approach

Chapter 13 - 9

z



The Confidence Interval Approach (Cont.)

Chapter 13 - 10


The Confidence Interval Approach (Cont.)

Chapter 13 - 11

The confidence interval is given by

We can now set a 95% confidence interval around the sample mean of $182.

The 95% confidence interval is given by

= 182.00 + 1.96(3.18) = 182.00 + 6.23

Thus the 95% confidence interval ranges from $175.77 to $188.23.


Figure 13.4 95% Confidence Interval

0.475 0.475

Chapter 13 - 12

𝑋 𝑋𝑈𝑋𝐿

Chapter 13 - 13Copyright © 2011 Pearson Education, Inc.

Table 13.2Sample Size Determination for Means and Proportions

Steps Means Proportions

1. Specify the level of precision.

2. Specify the confidence level (CL).

CL = 95% CL = 95%

3. Determine the z value associated with the CL.

Z value is 1.96 Z value is 1.96

Chapter 13 -14Copyright © 2011 Pearson Education, Inc.

Table 13.2 (Cont.)Sample Size Determination for Means and Proportions

Steps Means Proportions

4. Determine the standard deviation of the population

Estimate σσ = 55

Estimate ππ = 0.64

5. Determine the sample size using the formula for the standard error

6. If necessary, reestimate the confidence interval by employing s to estimate σ

4-15

A sample size of 400 is enough to represent China’s more than 1.3 billion people or the more than 300 million American people.

The sample size is independent of the population size for large populations.

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Adjusting the Statistically Determined Sample Size

Incidence rate refers to the rate of occurrence or the percentage of persons eligible to participate in the study.

In general, if there are c qualifying factors with an incidence of Q1, Q2, Q3, ...QC, each expressed as a proportion,

Incidence rate = Q1 x Q2 x Q3....x QC

Initial sample size = Final sample size

Incidence rate x Completion rate

Chapter 13 - 16


International Marketing Research

When conducting marketing research in foreign countries, statistical estimation of sample size can be difficult, because estimates of the population variance might be unavailable.

When statistical estimation of sample size is attempted, the differences in estimates of population variance should be recognized and factored in, if possible.

When the goal is to examine differences across countries or international markets, it is desirable to have the same sample size across countries.

Chapter 13 - 18


Marketing Research & Social Media

It is feasible to have large, even very large, sample sizes when conducting marketing research in social media.

In many social media projects, the sample size can far exceed that required by statistical considerations.

It is important to address the issues of the appropriateness and representativeness of social media as outlined in Chapter 12.

Chapter 13 - 19


Ethics in Marketing Research

The researcher has the ethical responsibility to not use large estimates of the population variance simply to increase the cost of the project by inflating the sample size.

When the sample standard deviation varies widely from that which is assumed, the researcher should disclose the larger confidence interval to the client and jointly arrive at a corrective action.

Incorrectly reporting the confidence intervals of survey estimates based on statistical samples is unethical.

Chapter 13 - 20


Acronym: Size

The statistical considerations involved in determining the sample size can be summarized by the acronym SIZE:

S ampling distribution

I nterval (confidence)

Z value

E stimation of population standard deviation

Chapter 11 - 21


Figure 13A.1 Finding Probabilities Corresponding to Known Values

Area is 0.3413Area between µ and µ + 1 s = 0.3413Area between µ and µ + 2 s = 0.4772Area between µ and µ + 3 s = 0.4986

Chapter 13 - 22

X Scale μ-3σ μ-2σ μ-1σ μ μ+1σ μ+2σ μ+3σ

(μ=50,σ=5) 35 40 45 50 55 60 65

Z Scale -3 -2 -1 0 +1 +2 +3


Figure 13A.2 Finding Values Corresponding to Known Probabilities

Area is 0.500Area is 0.450

Area is 0.050

X 50X Scale

Z = -1.645 0Z Scale

Chapter 13 - 23


Figure 13A.3 Finding Values Corresponding to Known Probabilities:Confidence Interval


X 50X Scale

Z = -1.96 0Z Scale


Z = 1.96

Chapter 13 - 24

13-1 Chapter 13 Sampling: Final and Initial Sample-Size Determination.

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