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Chapter 12

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


Department
Marketing
Course Code
MKT 3413
Professor
Al Burns
Chapter
12

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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
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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
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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
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