Stats - Populations and Sampling
What is a population?
The whole set of items that are of interest when collecting data.
What is a sample?
A subset of a population that is intended to represent the populations.
What’s an example of a population?
- All humans in the UK
- All light bulbs in a factory
- All the cars in Europe
What is a sampling unit?
Each individual thing in the population that can be sampled.
What is a sampling frame?
A list/record of sampling units.
What is a census?
A collection of data over a whole population.
What is the advantage of a census?
It should give a completely accurate result.
What are the three disadvantages of a census?
- Time comsuing and expensive
- Can not be used when testing involves destruction
- Large volume of data to process
Why can’t you use a census when the testing involves destruction?
Because if you destroy everything in the population, nothing will be left.
What are the three advantages of a sample?
- Cheaper
- Quicker
- Less data to process
What are the two disadvanatages of a sample?
- Data may not be accurate
- Data may not large enough to represent small subgroups.
Would you use a census or a sample for testing the ripeness of avocados?
A sample.
Why would you use a sample instead of a census for testing the ripeness of avocados?
Because to test them you’d have to cut them in half and you would destroy all the avocados in the process.
What are the three types of random sampling?
- Simple random sampling
- Systematic sampling
- Stratified sampling
What are the two types of non-random sampling?
- Quota sampling
- Opportunity sampling
What is the definition of random sampling?
Everything has an equal chance of being chosen, to avoid bias.
What is simple random sampling?
Where everything in the sampling frame has an equal chance of being chosen.
How do you do simple random sampling?
- Assign each item in the sampling frame a number
- Pick a random number between 1 and the length of list as many times as you want samples
What’s another name for simple random sampling?
Lottery sampling.
What are the three advantages of simple random sampling?
- Bias free
- Easy and cheap to implement
- Everything has an equal chance of being selected
What are the two disadvantages of simple random sampling?
- Not suitable when the population is a large size.
- Need a sampling frame.
Why is simple random sampling not suitable for a large population?
You have to assign everything in the population a number which may be time consuming.
What is systematic sampling?
Where the samples are chosen at regular intervals in a list.
Systematic sampling is a type of which sampling?
Random sampling.
What’s an example of a systematic sample?
Taking every 10th phone number in a phone book.
What is the formula for taking $k$ samples in systematic sampling?
If you take a sample every $k$ elements, where should you start in systematic sampling?
At a random number between 1 and $k$.
What are the two advantages to systematic sampling?
- Simple and quick to use
- Suitable for large samples/populations
What are the two disadvantages to systematic sampling?
- A sampling frame is needed
- Can introduce bias if sampling frame is not random.
How can you introduce bias to systematic sampling?
If the list is not randomly ordered, bias may be introduced. For example, ordering people by wealth.
What is a strata?
A distinct group or category in a popluation.
What’s the singular form of “strata”?
Stratum.
What is stratified sampling?
Where you divide the population into distinct groups/categories (strata) and randomly sample from each group.
Stratified sampling is a type of which sampling?
Random sampling.
What is the main advantage for stratified sampling?
It guarantees a proportional representation of groups within a popluation.
What are some examples of strata in a population?
- Age
- Year group
- Gender
What are the two disadvantages of stratified sampling?
- Population must clearly be divided into distinc groups
- Selection from each stratum has same disadvantages to a random sample.
What is quota sampling?
Where you take a sample by filling a quota that’s in proportion to some characteristic of the population.
Quota sampling is kind of like what other type of sampling but in reverse?
Stratified.
How do you take a quota sample?
- Divide the population into the groups you wish to study (e.g. gender, age)
- Set a quota for each group, proportionate to that group’s representation in the wider population
- Take N samples from each group where N is the quota for that group.
What is the main advantage of a quota sample?
It allows a small sample to be representative of a population.
An advantage of quota sampling is that you don’t need a…?
Sampling frame.
Quota sampling is a type of what sampling?
Non-random sampling.
Why can a quota sample introduce bias?
Because it’s not completely random.
Why is quota sampling difficult for large studies?
Because there will be more groups, which could be costly or inaccurate.
What is opportunity sampling?
A sample taken from people who are available at the time of study and who meet criteria.
What’s another name for opportunity sampling?
Convience sampling.
What is the main advantage of opportunity sampling?
Very easy and inexpensive.
What is the main disadvantage of opportunity sampling?
It’s unlikely to provide a representitive sample.
What’s the issue with a study of how many people go to the cinema where an opporunity sample is taken outside of the cinema?
The people around the researcher likely go to the cinema regularly, so there will be bias.
What is a common source of bias?
Inappropriate sampling groups.
A researcher is surveying shopping habits of different age groups. They have a list of the amount of samples they wish to get per age bracket that’s proportional to their representation in the population as a whole. This is a type of what sampling?
Quota sampling.
A researcher is doing an exit poll of everyone who comes out of a polling station. This is a type of what sampling?
Opportunity sampling.