Sampling Methods

[Name of the Author]

Table of Contents

Case Assignment1

Case 11

Stratified Random Sampling1

Case 23

SRS3

Case 34

Cluster Sampling4

Case 45

Systematic Random Sampling5

Case 56

References8

Session Long Project (SLP)9

References10

Case Assignment

Case 1

In this case the stratified random sampling is used as the population consisted of three distinct subgroups

Stratified Random Sampling

In this type of sampling the population is divided into homogenous subgroups and after that a simple random sample from each group is taken. The sub groups in which the population is divided are called strata.

Mathematically,

Nh:- Total number of population units in stratum h.

nh:- Total number of sample units in stratum h.

N: Total number of population

n: sample size

f=n/N : sampling fraction

The stratified random sampling not only represents the whole population but also represents the sub groups within the population through strata. In simple random sampling, a sample from the whole population is taken, but it does not show the exclusivity of subgroups within the population. For this reason stratified random sampling is used. In each strata of the stratified random sampling every nh unit has equal chance of occurring (through simple random sampling) and that is why stratified sampling is random. There are two types of stratified sampling, proportional sampling and disproportional sampling. In proportional stratification the sampling fraction is equal in each strata and in disproportional stratification the sampling fraction in not equal across strata.

In this case the stratified random sampling is used as the population consisted of three distinct subgroups namely, Sophomore, Junior and Senior classes.

Here:N: 1325n: 131f=n/N = 131/1325=0.99, The sampling fraction is 10%Nh: N1 = Sophomore, N2=Junior, N3=Seniornh: n1=49, n2=34, n3=48

The data and the statement itself suggest that the sample has been stratified for including the impact of different sup groups (Sophomore, Junior and Senior in this case) on the sample. The sampling fraction for each stratum has turned out to be equal which means that proportional stratification method is used.

The stratified random sampling is used in this case because the population consists of distinct homogenous sub groups. The students in sophomore, junior and senior classes differ from each other in age, mental ability, education level, grade structure and many others. All of the three sub groups have one trait in common which is all for them being student. This is the main reason stratified random sampling method is used in this case. Stratified random sampling also provided more accuracy to the sample as distinct characteristic of a sub group will effect only that specific group.

Case 2

In this case the simple random sample selection method is used

SRS

Simple random sampling is the simplest sampling method in statistics. It consists of three factors:

The population from which sampling is done is N

The sample that is taken from the population is n

Every value of n has an equal chance or probability of occurring.

The simple random sample can be obtained by a variety of mechanical and computerized methods. The major factor for selecting a simple random sample is that the selector (whether a machine or a person) should be blindfolded against the population, there should not be any biasness for ...