Stats chapter 1 - sampling

population

the whole set of items that are of interest

Census

measures/observes every member of a population

Sample

a selection of observations taken from a subset of the population and used to find out more information on the population as a whole

advantages of a census

results should be completely accurate

disadvantages of a census

• time consuming and expensive

• cannot be used when testing destroys process

• hard to process large quantity of data

advantages of sample

• less time consuming and cheaper

• fewer people have to respond

• less data needs to be processed

disadvantages of samples

• data may not be accurate

• sample may not be large enough to give information about small subgroups of the population

random sampling

• where each member of a population has an equal chance of being selected

types of random sampling

• simple random sampling

• systematic sampling

• stratified sampling

simple random sampling

a simple random sample of size n is one where every sample of size n has an equal chance of being selected

Methods of taking a simple random sample

• calculator/ random number generator

  number each member 1-n. generate random numbers between these intervals to select members

• lottery sampling:

  write the names of members on identical cards and place them in a hat, draw the cards and select members

systematic sampling

the required elements are chosen at regular intervals from an ordered list

advantages of simple random sampling

• free of bias

• easy and cheap for small samples and populations

• each sampling unit has a known and equal chance of selection

disadvantages of simple random sampling

• not suitable for large samples and populations

• sampling frame needed

how to take a stystematic sample

e.g. sample size of 20, required from a population of 100

• 100/20 = 5, so every fifth person is chosen

• first person is chosen at random

• then increment by 5 each time

advantages of systematic sampling

• simple and quick to use

• suitable for large samples and large populations

disadvantages of systematic sampling

• a sampling frame is needed

• bias is introduced if sampling frame is not random

stratified sampling

the population is divided into mutually exclusive strata and a random sample is taken from each

number sampled in a stratum = number in stratum/number in population x overall sample size

example of stratified sampling

advantages of stratified sampling

• sample accurately reflects population structure

• proportional representation of group within population

disadvantages of stratified sampling

• population must be clearly classified into distinct data

• same disadvantages as simple random sample within each stratum

types of non-random sampling

quota, opportunity/convenience

quota sampling

an interviewer or researcher selects a sample that reflects the characteristics of the whole population

advantages of quota sampling

• allows a small sample to still be representative of the population

• no sampling frame required

• quick, easy and inexpensive

• easy comparison between different groups within a population

disadvantages of quota sampling

• non-random sampling can introduce bias

• population must be divided into groups, which can be costly or inaccurate

• increasing scope of study increases number of groups, which adds time and expenses

• non-responses not recorded

opportunity sampling

sample is taken from people who are available at the time of study and who fits the criteria you are looking for

advantages of opportunity sampling

• easy and inexpensive

disadvantages of opportunity sampling

• unlikely to provide a representative result

• highly dependent on individual researcher