Sampling means choosing random values.
Consider the bubble gum jar below with various colors of bubble gums.
If you ‘randomly’ select a few gums from the jar, it is very likely that the selected ones will have gums of all colors.
Hence, you can say that the randomly selected sample is a representative of all the gums present in the jar.
In statistical language, these randomly selected gums are known as the sample, and the jar is known as the population.
A randomly selected sample is a representative of the population
The stress on randomness is high because if it is not random selection then it may not represent the whole group aka population. You may select most of the red color gums or green color gums and other colors will not be seen in the sample.
Effect of Size on Sampling
The bubble gum jar contained 200 gums with 6 different colors.
If you select only 10 gums there is a chance that few colors may NOT be present.
If you select 50 gums then there is a high chance of all colors being present.
If you select 100 gums then there is a very high chance of all colors being present.
if you select all 200 gums then its sure that all colors will be present. This is the case where the sample is the same as the population. That means you simply selected all!
As sample size increases, the properties of sample start becoming more similar to the population
Sampling Theory Numeric Example
Let us say you have 100 numbers and you need to choose any 12 numbers from it randomly. The result consisting of those 12 numbers is a sample.
These 12 numbers will have the similar properties as exhibited by the 100 numbers.
Specifically, the mean of those 12 numbers will be close to the mean of all the 100 numbers. The distribution of those 12 numbers will be similar to the distribution of all the 100 numbers.
Mean of the sample is close to the mean of the population
What are the types of sampling?
There are four major types of sampling techniques listed below.
- Simple Random Sampling
- Stratified Sampling
- Systematic Sampling
- Biased sampling
Simple Random Sampling has two types. One allows repetitions in values and the other does not allow any repetitions.
1.1) Simple Random Sampling Without Replacement (SRSWOR)
This form of sampling is used most frequently. The idea is, once you select a number you cannot select it again. Hence the name ‘Without’ Replacement.
For example, in
1.2) Simple Random Sampling With Replacement (SRSWR)
This type of sampling is used when the total(Population) number of values are small. We allow repetitions in the selected values.
In below scenario, the numbers 62 and 94 got selected twice while selecting the values randomly.
2) Stratified Sampling
Strata means group.
Stratified sampling makes sure that there are few values selected randomly from each group.
Consider below example where 3 types of numbers are present. 10 series, 100 series and 500 series.
If you randomly select 5 numbers, there is a possibility that any one of the series is completely missed. In the below scenario the 10 series numbers are completely missed.
If you perform the stratified sampling in this scenario, it will make sure there are numbers from each series. As shown in the below diagram, numbers from each group are selected. Basically, you are performing simple random sampling on each group separately.
Next obvious question should be, ‘How many to pick from each group?’
The answer is ‘it depends on the size of the group’. The bigger the group is, the higher the number of values in sample.
3) Systematic Sampling
Systematic Sampling is when you select every ‘
There is a simple system in place. which picks the index of values.
In the below scenario Systematic sampling of every 5th number is shown
4) Biased Sampling
As the name suggests, this is when you selected values based on your choice purposefully.
This type of sampling is also known as purposeful sampling or convenience sampling.
The choice will depend upon the specific requirements of individual and case. For example you may sample all 100 series values only or pick all 500 series numbers in below scenario.
Conclusion
- Sampling means choosing random values.
- A randomly selected sample is representative of the whole group (population).
- Stratified sampling makes sure that there are few values selected randomly from each group.
- Systematic Sampling is when you select every ‘
i’ th value. - Biased Sampling is when you select values based on your choice purposefully.
