1.2 Random Sampling

Question 1

What would we want from random sampling

Answer 1

Each thing in our sampling frame to have an equal chance of being chosen, in order to avoid bias

Question 2

3 types of random sampling

Answer 2

• Simple random sampling
• Systematic sampling
• Stratified sampling

Question 3

Method of simple random sampling

Answer 3

• To carry out a simple sample, size n, from a population size N, firstly, we need a sampling frame
• Each item is assigned a different number from 1 to N. Use a random number generator to select ‘n’ unique numbers
• Choose the items corresponding to these numbers to form the sample

Question 4

Advantages of simple random sampling

Answer 4

• Avoids bias as each sampling unit has a known equal chance of being selected
• Easy and cheap to implement for a small population and samples

Question 5

Disadvantages of simple random sampling

Answer 5

• Not suitable when population size is large
• A sampling frame is needed
• Sample may not accurately reflect the population (could by chance be all girls, eg in bluebook)

Question 6

Full marks layout of simple random sampling question

Answer 6

• Using the [list, eg register] as a sample frame, assign the [items] a number from [1 to (total number of items)]
• Use a random number generator to get [whatever sample asked for in Q] unique numbers
• Choose the [items] corresponding to those numbers to form the sample

Question 7

What is systematic sampling

Answer 7

In systematic sampling, the required elements are chosen at regular intervals from an ordered list

Question 8

Method of systematic sampling

Answer 8

To carry out systematic sampling (size n, from population size N) again you need a sampling frame.

• Each item is assigned a different number from 1 to N. Starting at a random item (number chosen by random number generator) between 1 and k (k=pop size, N/samp size, n). Take every kth element to from the sample

eg Q in bluebooks

Question 9

Advantages of systematic sampling

Answer 9

• Simple & quick to use
• Suitable for large samples & populations

Question 10

Disadvantages of systematic sampling

Answer 10

• Can introduce bias if sampling frame is small & not random as patterns can be picked up in the data
• A sampling frame is needed

Question 11

Full marks layout of systematic sampling questions

Answer 11

• Using the [list] as a sample frame, assign each name a number from 1 to [total pop]
• total pop size/sample size asked for = k
• Use a random number generator to obtain a number between 1 and k. Starting with that number , select every kth name to form the sample

Question 12

What is stratified sampling

Answer 12

Population is divided into groups (strata) & a simple random sample is carried out in each group

Question 13

Method of stratified sampling

Answer 13

• To carry out a stratified sample (size n from population size N) we need a sampling frame and distinct strata. The same proportion n/N is to be sampled from each strata
• Within each strata, each item is assigned a different number & a random number generator is used to select the number of unique numbers required
• Choose the items corresponding to these numbers to form the sample

Question 14

Advantages of stratified sampling

Answer 14

• Sample reflects population structure
• Guarentees proportional representation of groups within population

Question 15

Disadvantages of stratified sampling

Answer 15

• Sampling frame is needed & population must be clearly classified into distinct strata
• Selection within each stratum suffers from same disadvantages as simple random sampling

Question 16

Full mark layout of stratified sampling questions

Answer 16

• [1st group, male size]/[total pop] = k males
  [2nd group, female size]/[total pop] = b females
• Assign each [1st group, males] a number from 1 to [male size] & [2nd group, females] a number from 1 to [female size]
• Use a random number generator to get k unique numbers of [males] and b unique numbers of [females]
• Select the [people] corresponding to those numbers to form the sample