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Which of the following is not true about stratified sampling?
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(A) Stratified random sampling is also called proportional random sampling.
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(B) Stratified random sampling allows researchers to obtain a sample population that best represents the entire population being studied.
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(C) Stratified sampling is the random selection of data from an entire population.
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(D) Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata.
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And (E) the stratified random sample is a statistical measurement tool.
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We’re asked which of the options (A), (B), (C), (D), and (E) is not true about stratified sampling.
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So let’s begin by recalling when and how we might use stratified sampling.
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Recall that we use stratified random sampling when the population subdivides into distinct, nonoverlapping smaller subgroups, which we call strata.
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Random samples are then taken from each stratum and combined to form the overall sample from the population.
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And the size of the sample from each stratum reflects the stratum proportion of the whole population.
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So now let’s examine each of our options (A), (B), (C), (D), and (E) to see if they match our definition of stratified random sampling.
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Beginning with option (A), this says stratified random sampling is also called proportional random sampling.
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We know that stratified random sampling is used when the population of interest is split into groups or strata.
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The size of the sample taken from each stratum reflects the proportion of the population represented by that stratum.
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It would therefore not be incorrect to give stratified random sampling an alternate name such as proportional random sampling.
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Option (A) is therefore true about stratified sampling.
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Now let’s consider option (B).
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This says that stratified random sampling allows researchers to obtain a sample population that best represents the entire population being studied.
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In stratified random sampling, we know that when random samples are taken from each stratum, the stratum sample size reflects the stratum proportion of the whole population.
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This means that each of the different groups are represented proportionally within the final combined sample.
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No subgroup is therefore over- or underrepresented, and the sample reflects the proportion or makeup of the whole population.
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Such a sample will then best represent the entire population being studied.
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Option (B) is then also true about stratified sampling.
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Now let’s consider option (C).
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This says stratified sampling is the random selection of data from an entire population.
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We know from our definition that stratified random sampling is used when the population subdivides into distinct nonoverlapping smaller subgroups or strata.
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Random samples are taken from each stratum and combined to form the overall sample.
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Option (C) however describes the random selection of data from an entire population that’s directly from the population.
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In this scenario then, there is no subdivision of the population before sampling.
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And this does not match with our definition of stratified random sampling.
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The statement in option (C) is therefore false about stratified sampling.
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So now let’s consider option (D).
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This says that stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata.
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In fact, this is exactly what’s specified in our definition of stratified random sampling.
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The population is subdivided into smaller groups or strata.
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We can then say that option (D) is true about stratified sampling.
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And finally, let’s look at option (E).
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This says the stratified random sample is a statistical measurement tool.
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When we take a stratified random sample from a population, the proportional makeup of the population is represented in the sample size for each stratum.
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This means that the true makeup of the population is represented in any predictions or results gained from the sample data.
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So by this token, the stratified random sample is indeed a statistical measurement tool.
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Option (E) is therefore true about stratified sampling.
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So we find that options (A), (B), (D), and (E) are true about stratified sampling and option (C) is not true about stratified sampling.
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Our answer is therefore option (C).