Question

Explain how you would choose 8 for a dinner party: (2 pts each)

NOTE: I am grading your explanation of the process. If you answer with a list of names only, you will not receive credit. You may include both, however, if you wish.

a. Using the Systematic Sampling type

b. Using the Stratified Sampling type

c. Using the Cluster Sampling type

d. Using the Convenience Sampling type

e. Using the Random Sampling type

William Shakespeare

Agatha Christie

Barbara Cartland

Danielle Steel

Harold Robbins

Georges Simenon

Enid Blyton

Sidney Sheldon

J. K. Rowling

Gilbert Patten

Dr. Seuss

Eiichiro Oda

Leo Tolstoy

Corín Tellado

Jackie Collins

Horatio Alger

R. L. Stine

Dean Koontz

Nora Roberts

Akira Toriyama

Alexander Pushkin

Stephen King

Paulo Coelho

Louis L'Amour

René Goscinny

Erle Stanley Gardner

Edgar Wallace

Answer 1

Let, N= total population size

n= sample size

a) In Systematic Sampling, we have k= (N/n).

The general criterion is of choosing every ith member from n number of strata of size k each, so formed from the total number of N observations. We divide the population units in n strata based on the value of k obtained from the above mentioned formula, where random start, i<=k. Therefore, in the given example, we have N=27 and n=8, and that does not comply to N=nk, and therefore, we use the Lahiri approach (Circular Sampling for cases when nk doesn't equal N, 1952) to obtain the sample size in which the sample is specified by the units:

i+jk, if i+jk<N

i+jk-N, if i+jk>N {for all j = 0,1,2,3,4,....(n-1)}

(Note that Lahiri Method provides a constant sample size with any random start i chosen)

b) In Stratified Sampling, we form h small internally homogeneous strata (but mutually heterogeneous) of the authors based on certain features which they do possess in common, keeping in mind, that these strata are mutually exclusive and exhaustive. Now, with the population divided into h small strata each of size Nh (Stratum Size), we can apply the random sampling within these strata, keeping in mind what would be the strata sample size (nh), based on certain pre-requisites of the experimenter. Therefore, out of the Nh units in a strata, nh units are picked up randomly from each strata to create the necessary sample.

Say if we divide 27 authors in 3 strata and select 3 from 1st strata, 2 from 2nd and 3 from 3rd strata.

Note that stratified sampling is used when the data available to the researcher is heterogeneous, (and sample is needed to be highly representative), and random selection of it would inflate the error.

c) Cluster Sampling involves stratification of the population units into mutually homogeneous, but internally heterogeneous. Therefore, these strata, commonly known as the clusters would be small representations of the population data as it would contain image of all the population elements. Therefore, in the given example, it is essential that 9 small clusters of size 3 (say) each would be created, which are homogeneous to each other. Now, select 3-4 clusters randomly, and then select from these clusters a total of 8 authors in either two stage sampling (sampling from the cluster itself), or one stage sampling (selecting all the units of the cluster).

Note that the researcher can choose non equal size of clusters as well.

d) Convenience Sampling is a type of non probabilistic sampling scheme which is highly simple. It necessarily implies that the researcher would select those authors who are easy to contact or reach out to. Therefore, no strict probabilistic principle would be put to use, and those who could be easily contacted would be called for the party.

e) In Random Sampling, place a number against each author (preferably starting from 1-27). A lottery system could be adopted in which 27 chits with the names of the authors on it are put into a bowl, and only 8 chits are picked up to select 8 authors for the party.

Or, a randomization technique of generating 8 numbers from 1-27 could offer a list of 8 authors to be picked up for the party.