Sampling and statistical diagrams

Definition of: Population

The whole set of items that are of interest

Definition of: Census

Observes or measures every member of a population

Definition of: a Sample

A selection of observations taken from a subset of the population which is used to find out information about the population as a whole

1 advantage of a census

• It should give a completely accurate result

3 disadvantages of a census

• Time consuming and expensive

• Cannot be used when the testing process destroys the item

• Hard to process large quantity of data

3 advantages of a sample

• Less time consuming and expensive than a census

• Fewer people have to respond

• Less data to process than in a census

2 disadvantages of a sample

• The data may not be as accurate

• The sample may not be large enough to give information about small sub-groups of the population

You would need a larger sample if:

The population were varied

Definition of: Sampling Units

The individual elements or items selected from a population to constitute a sample for study.

Definition of: a Sampling Frame

A complete list of all the sampling units in a population from which a sample is drawn.

What are the 3 methods of random sampling?

• Simple random

• Systematic

• Stratified

In random sampling, every member of the populations has:

an equal chance of being selected

Random sampling is:

Representative of the population and helps to remove bias from a sample

Simple random sampling is when:

Every individual in the population has an equal chance of being selected

How are individuals chosen in simple random sampling?

Need a sampling frame, each individual allocated a unique number and a selection of numbers are chosen at random. You can choose these numbers either by generating random numbers or lottery sampling (drawing numbers out of a ‘hat’)

How are individuals chosen in systematic sampling?

Individuals are chosen at regular intervals from an ordered list (divide population by sample size and choose that number as the interval)

How are individuals chosen in stratified sampling?

The population is divided into mutually exclusive strata (e.g males and females) and a random sample is taken from each

Formula for calculating number of individuals in each stratum (they need to be proportional)

The number sampled in a stratum = (number in stratum / number in population (total of stratum’s) ) x overall sample size

3 advantages of simple random sampling:

• Free of bias

• Easy and cheap to implement for small populations and small samples

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

2 disadvantages of simple random sampling:

• Not suitable when population or sample is large as it can be time consuming, disruptive and expensive

• A sampling frame is needed

2 advantages of systematic sampling:

• Simple and quick to use

• Suitable for large samples and large populations

2 disadvantages of systematic sampling:

• A sampling frame is needed

• Can introduce bias if the sampling frame is not random

2 advantages of stratified sampling:

• Sample accurately reflect the population structure

• Guarantees proportional representation of groups within a population

2 disadvantages of stratified sampling:

• Population must be clearly classified into distinct strata

• Selection within each stratum suffers from the same disadvantages as simple random sampling

2 types of non-random sampling:

• Quota sampling

• Opportunity sampling

What happens in quota sampling?

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

How is quota sampling carried out?

The population is divided into groups according to a given characteristic. The size of each group determines the proportion of the sample that should have that characteristic

What happens in opportunity sampling?

(AKA convenience sampling) Consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for

Method to quota sampling:

Interview people and then allocate them into the appropriate quota. This continues until all the quotas have been filled, if person ignores or quota they fit into is full, simply ignore them and move on to the next person

Example of opportunity sampling:

First 20 people you meet outside a supermarket on a Monday morning who are carrying shopping bags

4 advantages of quota sampling:

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

• No sampling frame required

• Quick, easy, and inexpensive

• Allows for easy comparison between different groups within a population

4 disadvantages of quota sampling:

• Non-random sampling can introduce bias

• Population must be divided into groups, can be costly or inaccurate

• Increasing scope of study increases number of groups, which adds time and expense

• Non-responses are not recorded as such

2 advantages of opportunity sampling:

• Easy to carry out

• Inexpensive

2 disadvantages of opportunity sampling:

• Unlikely to provide a representative sample

• Highly dependent on individual researcher

What are quantitative variables/data?

Variables/data associated with numerical observations

e.g. shoe size is quantitative because you can give numbers to them

What are qualitative variables/data?

Variables/data associated with non-numerical observations

e.g. hair colour is qualitative because you can’t give a number to it

What is a continuous variable?

A variable that can take any value in a given range

e.g. time can take any value like 2 secs, 2.1 secs, 2.2 secs…

What is a discrete variable?

A variable that can take only specific values in a given range

e.g. number of girls in a family is a discrete variable as you can’t have 2.65 girls

Important things to consider with the large data set: (7)

• Which locations are near the equator

• Which locations are near a coast

• Which locations are in each hemisphere

• Which variables are discrete or continuous

• You can use 0 or 0.25 for variables listed as “tr”

• The great storm of 1986 happened in October in UK

• Number of days in each month

What locations in the large data set are near a coast?

• Jacksonville

• Camborne

• Hurn

• Leuchars

• Perth

Significance of different hemispheres:

Perth is in the Southern Hemisphere, meaning it has its summer while the UK has its winter

Significance of which variables are discrete or continuous:

Cloud cover is discrete, this means …

Significance of the Great Storm of 15 and 16th October 1986:

• Wind speed was high at this time

• South and south-east of UK was affected

• Will skew some variables such as wind, gust, rainfall

• Won’t skew other variables such as (sunshine/cloud cover) as October in the UK is normally like that anyways

Significance of the number of days in each month:

• 30 days in June and September

• 31 days in May, July,August and October

• In total the Large Data Set covers 184 days