Associate Professor of Marketing
FGCU
MAR 3613 / 6646
CHAPTER 11
I. Definitions Of Important Terms:
A. Population (or Universe) Of Interest - the total group of people from whom information is needed.
B. Sample - a subset of the population of interest.
C. Census - data obtained from every member of the population of interest, rather than from a sample of that population.
II. Steps in Developing an Operational Sampling Plan:
A. Define the population of interest.
B. Choose the data collection method.
C. Choose a Sampling Frame - which is the list of the elements of the population to be sampled (i.e., the sample list);
Or, much less frequently, the sampling frame can be the specifications of a procedure for generating the list of the elements of the population to be sampled. (Snowball Sampling is a good example)
D. Select a Sampling Method:
1. Probability Sample - a randomly selected sample (where every element of the population has an equal, known, nonzero probability of selection).
2. Non-Probability Sample - samples that include the selection of specific elements from the population in a nonrandom manner.
III. Probability Sampling Methods:
A. Simple Random Sampling (SRS) - probability sampling in which the entire population is numbered, and the sample is selected by drawing from those numbers at random. (Note: This is how Lotto numbers are selected)
B. Systematic (Random) Sampling - probability sampling in which the entire population is numbered, and elements are drawn using a skip interval. (Such as selecting every 9th number beginning with a number between 1 and 10 which was selected randomly.
C. Stratified Sampling - probability sampling that forces a sample to be more representative of the population of interest.
This is done to minimize total (sampling) error (which is the difference between the sample results and those that would have been obtained by a census of the entire population of interest).
Stratified sampling minimizes sampling error because it eliminates a source of variation that "may" occur if a SRS does not happen to select a sample with the same "salient" dimensions as that of the population of interest.
1. Proportional Allocation - sampling in which the number of elements selected from a stratum is directly proportional to the size of the stratum relative to the population.
2. Disproportional (or Optimal) Allocation -- sampling in which the number of elements taken from a given stratum is proportional to the "relative" size of the stratum with the standard deviation of the characteristic under consideration.
But, what is a Stratum? Hint: Strata is plural for Stratum.
D. Cluster Samples - a sampling approach (often used with door-to-door interviewing) in which the sampling units are selected in groups (to reduce data collection costs).
E. Advantages of Probability Samples:
1. The researcher can be sure of obtaining information from a representative cross section of the population of interest.
2. Sampling error can be computed, which allows the calculation of how many usable responses to a survey must be obtained to generate reliable results.
3. The research results are projectable (generalizable) to the total population of interest with a small degree (+ or -) of error (which typically results from sampling error).
Of course you want to minimize bias such that most, if not all sampling error is only comprised of random error.
F. Disadvantages of Probability Samples:
Usually more expensive than nonprobability samples of the same size due to the added time required to develop the sample design, procedures, and especially the sampling frame, as well as the additional time required to collect the data.
IV. Non-Probability Sampling Methods:
A. Convenience Samples - samples used primarily for reasons of convenience. Used for exploratory research and speedy situations.
Often used for new product formulations or to provide gross-sensory evaluations by using employees, students, peers, etc.
B. Judgement Samples - sample in which the selection criteria are based upon the researcher's personal judgment that the members of the sample are representative of the population under study.
Used for most test markets and many product tests conducted in shopping malls.
C. Quota Samples - samples in which quotas are established for population subgroups.
Selection is by non-probability means and based upon the researcher's judgement of appropriate demographics.
This is the "non-probability" (i.e., non-random) equivalent of a Stratified Random Sample.
D. Snowball Sampling - samples in which the selection of additional respondents (after the first small group of respondents is selected) is based upon referrals from the initial set of respondents.
Used to sample low incidence or rare populations, and done for the efficiency of finding the additional, hard-to-find members of the sample.
E. Advantages of Nonprobability Samples:
1. Usually sower cost than probability samples.
2. Acceptable when the level of accuracy of the research results is not of utmost importance.
3. Less research time required than probability samples.
4. Often produces samples quite similar to the population of interest when conducted properly.
F. Disadvantages of Nonprobability Samples:
1. Sampling error cannot be calculated. Thus, the minimum required sample size cannot be calculated which suggests that the researcher may sample too few or too many members of the population of interest.
2. The researcher does not know the degree to which the sample is representative of the population from which it was drawn.
3. The research results cannot be projected (generalized) to the total population of interest with any degree of confidence.
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CHAPTER 12
Other things equal, the larger the sample, the less the total sampling error (which is the differences in the sample from the population).
This is especially true because one element of total error--random error--automatically decreases.
So, why do we want to decrease total error?
Because lower total sampling error increases the accuracy of the statistical inferences made about the population of interest based upon the data gathered from a small but representative sample.
However, the costs of sampling increase faster than the sampling error falls.
Therefore, there is a limit to how large a sample can or should be, and that limit is based upon the cost versus desired accuracy level of the research project.
When a researcher uses a non-probability sample, the size of the required sample cannot be calculated accurately.
Thus, the researcher must rely on judgement to determine the appropriate sample size. In this case, s/he would be wise to make the sample as large as the budget will allow.
In contrast, when a researcher uses a probability sample, the required size of the sample can be calculated in advance of drawing the sample.
Three pieces of information are required to estimate the sample size:
1. An estimate of the population variance (actually need the population's standard deviation which is the square root of the population variance) which may be determined from a prior survey, a pilot survey, secondary data, or executive opinions.
2. The specified level of sampling error (E) that the researcher is willing to accept (or allow).
3. The desired (or acceptable) level of confidence (Z) that the actual sampling error does not exceed the specified (allowable) sampling error (i.e., that it is within an acceptable interval expressed by Z scores which are calibrated in standard errors).
DEFINITIONS:
Normal Distribution - a continuous distribution which is symmetrical about the mean (a bell shaped distribution curve).
THREE Characteristics of a Normal Distribution:
1. Mean = Median = Mode.
2. 68% of the observations fall within + or - 1 standard deviation of the mean;
95% fall within + or - 2 standard deviations of the mean;
99.5% fall within + or - 3 standard deviations of the mean.
3. The mean of the distribution of responses can be any number, it doesn't have to be zero.
Standard Normal Distribution (Z) - a normal distribution (as described above), with a standard deviation of 1, but with a mean of 0.
A standardized normal distribution mathematically creates the equivalent of a normal distribution with a mean of zero, rather than the real mean of the observations in our sample.
Population Distribution - a frequency distribution of all the elements of a population.
Sample Distribution - a frequency distribution of all the elements of an individual sample.
Sampling Distribution of Sample Means - a frequency distribution of the means of many (all possible) samples drawn from a particular population.
It is assumed normally distributed due to the central limit theorem.
Central Limit Theorem - a distribution of a large number of sample means (or sample proportions) will approximate a normal distribution regardless of the "actual" distribution of the population from which the samples were drawn.
Sampling Distribution of the Proportion - a frequency distribution of the proportions (percentages) of many samples drawn from a particular population.
It is also assumed normally distributed due to the central limit theorem.
Standard Deviation (of a sample) (S) - (a measure of dispersion) equal to the square root of the sum of all the squared deviations (i.e., variances) of all observations from the mean of those observations.
Standard Error Of The Mean - the standard deviation of a Sampling Distribution of Sample Means.
Population Standard Deviation - the standard deviation of a variable for the entire population.
Point Estimates - inferences regarding the sampling error associated with a particular numeric estimate of a population value.
Interval Estimates - inferences regarding the likelihood that a
particular numeric population value will fall within a certain range.
Interval Estimates are always expressed as a range, and that range is stated with a certain degree (level) of confidence (such as with 95% confidence).
Allowable Sampling Error - the amount of sampling error the researcher is willing to accept. It is expressed as ALPHA.
Confidence Level - the probability that a particular confidence interval will include the true population value.
It can only be calculated with probability samples.
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