# MKT 3413 Chapter Notes - Chapter 12: Confidence Interval, Estimation Theory, Sampling Error

This

**preview**shows pages 1-3. to view the full**12 pages of the document.**MKT 3413, Alvin Burns

Chapter 12 Textbook Notes: Generalizing Your Findings

Chapter 12 Textbook Notes: Generalizing Your Findings

Ipsos Forward Research

oClients often forget that a sample finding is at best an approximation

of the truth

oEvery finding is subject to sampling error

oIn fact, we will always have sampling error; it’s inherent to the

sampling process

oSampling error exists in every sample, that number is going to vary

virtually every time we conduct a study

oMeasures of central tendency and measures of variability adequately

summarize the findings of a survey.

However, when a probability sample is drawn from a

population, values that we want to know about

Every sample contains error meaning that the averages and

percentages will not fall on the population values

So it is best to report a range that the client understands

defines the true population value or what would be found if a

census were feasible

In other words, every sample provides some information about

its population, but there is always some sample error that must

be taken into account

oParameter estimation, where the population value is estimated with a

confidence interval using specific formulas and knowledge of areas

under a normal or bell-shaped curve

Generalizing a Sample’s Finding

oUsing summarization analysis is perfectly acceptable when the

researcher wishes to quickly communicate the basic nature of the

central tendency and variability of the findings in the sample

oGeneralizing is using the sample error, that is the (plus or minus)

value, so as to determine an interval for the average or percentage

The researcher is then confident that this interval includes the

true population average or percentage

oWe refer to sample finding whenever a percentage or average or

some other analysis value is computed with a sample’s data

However because of the sample error involved, the sample

finding must be considered an approximation of the

population fact, defined as the true value when a census of the

population is taken and the value is determined using all

members of the population

find more resources at oneclass.com

find more resources at oneclass.com

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

To be sure, when a researcher follows proper sampling

procedures and ensures that the sample is a good

representation of the target population, the sample findings

are indeed, best estimates of their respective population facts-

but they will always be estimates that are hindered by the

sample error

oGeneralization is the act of estimating a population fact from a

sample finding

Generalization is a form of logic in which you make an

inference about an entire group based on some evidence about

that group.

When you generalize, you draw a conclusion from the available

evidence

oWith generalization analysis, there are just two types of evidence:

1. The variability (less is more evidence) and

2. The sample size (more is more evidence)

oPopulation facts are estimated using the sample’s findings*

oGeneralization is the act of estimating a population fact from a sample

finding*

oGeneralization is “stronger” with larger samples and less sampling

error*

oWith a larger sample size, you should expect the range used to

estimate the true population value to be smaller

Intuitively, you should expect the range for y to be smaller than

the range for x because you have a larger sample and less

sampling error

oWhen we make estimates of population values, such as the percentage

(pi) or average (u), the sample finding percent (p) or average (x) is

used as the midpoint, and then a range is computed in which the

population value is estimated, or generalized, to fall

Table 12.1

o100 randomly selected respondents

Sample finding: 33% of respondents report they are

dissatisfied

Estimated Population Fact: Between 24% and 42% of all

buyers are dissatisfied

o1,000 randomly selected respondents

Sampling finding: 35% are dissatisfied

Estimated Population Fact: Between 32% and 38% dissatisfied

Estimating the Population Value

oEstimation of population values is a common type of generalization

used in marketing research survey analysis

find more resources at oneclass.com

find more resources at oneclass.com

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

oThis generalization analysis is often referred to as parameter

estimation, because the proper name for the population value is the

parameter, or the actual population value being estimated

Typically, population parameters are designated by Greek

letters such as (pi) (percent) or (u) (mean or average), while

sample findings are relegated to lowercase Roman letters such

as (p) (percent) or (x) (average or mean)

oGeneralization is mostly a reflection of the amount of sampling error

believed to exist in the sample finding

oPopulation facts or values are referred to as parameters*

How to Estimate a Population Percentage (Categorical Data)

oA Confidence interval is a range (lower and upper boundary) into

which the researcher believes the population parameter falls with an

associated degree of confidence (typically 95% or 99%)

Percentages are proper when summarizing categorical

variables

oTypically marketing researchers rely only on the 95% or 99% levels

of confidence, which correspond to (plus or minus) 1.96 and (plus or

minus) 2.58 standard errors, respectively

By far the most commonly used level of confidence in

marketing is the 95% level corresponding to 1.96 standard

errors

95% level of confidence is usually the default level found in

statistical analysis programs

So if you wanted to be 95% confident that your range included

the true population percentage, you would multiple the

standard error of the percentage by 1.96 and add that value to

the percentage, p, to obtain the upper limit, and you would

subtract it from the percentage to find the lower limit

For a 99% confidence interval, substitute 2.58 for 1.96

oMost marketing researchers use the 95% level of confidence*

Table 12.2: Steps used to estimate the population percentage

1. P is the percentage of times respondents chose one of the categories

in a categorical variable

a. The sample percent is found to be 33%, so p=33%

2. Q is always 100% - p

a. Q= 100%-33%= 67%

3. Standard error of the percentages (Sp): divide p times q by the sample

size, n, and take the square root of that quantity

a. Sp= 4.7%

4. Multiply the standard error by 1.96. Call it the limit.

a. Limit = 9.2%

5. Subtract the lmit from p to obtain the lower boundary. Then add the

limit to p to obtain the upper boundary. These boundaries are the 95%

confidence interval for the population change

find more resources at oneclass.com

find more resources at oneclass.com

###### You're Reading a Preview

Unlock to view full version