True or False: When obtaining a stratified sample, the number ...

Question

True or False: When obtaining a stratified sample, the number of individuals included within each stratum must be equal.

Accepted Answer

Hello there. Today we are going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. True or false, in stratified sampling, the researcher is required to allocate the same sample size to each stratum, regardless of stratum population sizes, or variances. OK. So it appears for this particular problem. Asked to take the statement, which once again the statement is in stratified sampling, the researcher is required to allocate the same sample size to each stratum, regardless of stratum population sizes, or variances, and we're asked to determine if this particular statement will be a true. B false or C cannot tell or D only when the strata are hoogeneous. So With that said, we're ultimately trying to determine whether or not this statement is true or false. So with that in mind, our first step that we need to take in order to solve this problem is we need to recall and define what stratified sampling is. So as we should recall, stratified sampling partitions the population into non-overlapping strata and then selects samples from each stratum. So with that in mind, our second step now is we need to recall and write what the proportional allocation formula is, which states that lowercase n subscript H is equal to lowercase n multiplied by N subscript H divided by capital N. And we need to note that this makes lowercase n subscripth proportional to the stratum size N subscript H. OK. So our third step now is we need to recall and write the equal allocation formula, which states that lowercase n subscript H is equal to lowercase n divided by capital H. For capital H strata, and we need to note that this is an optional choice but not in a requirement. So that will mean that we now for our 4th step, we need to recall and state the Niemann allocation formula, which states that Lowercase n subscript h is equal to n multiplied by subscript H multiplied by sigma subscript H all divided by the sum evaluated from K equals 1 to H of Nk multiplied by sigma subscript k. Fantastic. And we need to note that this uses stratum. So once again, this will use stratum standard deviations Sigma subscript H to allocate the sample sizes. So that means for our 5th and final step we can make our final conclusions and we can therefore conclude that the equal allocation is not required because proportional or Niemann allocation methods are valid alternatives. Therefore, the particular statement made in our practice prom is going to be, without a doubt, be false. So our final answer once again is be false. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

True or False: When obtaining a stratified sample, the number of individuals included within each stratum must be equal.

Key Concepts

Stratified Sampling

Proportional vs. Equal Allocation

Purpose of Stratification

Watch next