Sampling and data collection
Qualitative data is data that is usually given in words not numbers to describe something
For example: the colour of a teacher's car
Quantitative data is data that is given using numbers which counts or measures something
For example: the number of pets that a student has
Discrete data is quantitative data that needs to be counted
Discrete data can only take specific values from a set of (usually finite) values
For example: the number of times a coin is flipped until a tails is obtained
Continuous data is quantitative data that needs to be measured
Continuous data can take any value within a range of infinite values
For example: the height of a student
Age can be discrete or continuous depending on the context or how it is defined
If you mean how many years old a person is then this is discrete
If you mean how long a person has been alive then this is continuous
The population refers to the whole set of things which you are interested in
For example: if a vet wanted to know how long a typical French bulldog slept for in a day then the population would be all the French bulldogs in the world
A sample refers to a subset of the population which is used to collect data from
For example: the vet might take a sample of French bulldogs from different cities and record how long they sleep in a day
A sampling frame is a list of all members of the population
For example: a list of employees’ names within a company
A population parameter is a numerical value which describes a characteristic of the population
These are usually unknown
For example: the mean height of all 16-year-olds in the UK
A sample statistic is a value computed using data from the sample
These are used to estimate population parameters
For example: the mean height of 200 16-year-olds from randomly selected cities in the UK
Sampling Techniques
A census collects data about all the members of a population
For example: the Government in England does a national census every 10 years to collect data about every person living in England at the time
The main advantage of a census is that it gives fully accurate results
The disadvantages of a census are:
It is time consuming and expensive to carry out
It can destroy or use up all the members of a population when they are consumables (imagine a company testing every single firework)
Sampling is used to collect data from a subset of the population
The advantages of sampling are:
It is quicker and cheaper than a census
It leads to less data needing to be analysed
The disadvantages of sampling are:
It might not represent the population accurately
It could introduce bias
Simple random sampling: if a sample of size is taken then every group of members from the population has an equal probability of being selected for the sample
Simple random sampling is carried out by uniquely numbering every member of a population and randomly selecting n different numbers using a random number generator or a form of lottery (where numbers are selected randomly)
Systematic sampling: a sample is formed by choosing members of a population at regular intervals using a list
To carry this out you would calculate the size of the interval k=size of population (N)size of sample (n) and choose a starting point between 1 and then select every kth member after the first one
Stratified sampling: the population is divided into disjoint groups (called strata) and then a random sample is taken from each group (stratum)
The proportion of a sample that belongs to a stratum is equal to the proportion of the population that belongs to the stratum
The number of members sampled from a stratum = size of sample (n)size of population (N) x number of members in the stratum
The population could be split by age ranges, gender, etc
Quota sampling: the population is split into groups (like stratified sampling) and members of the population are selected until each quota is filled
If a member does not want to be included then another member is chosen instead
The members do not have to be selected randomly
Opportunity (convenience) sampling: a sample is formed using available members of the population who fit the criteriaSampling Critique
Simple random sampling: this should be used when you want a random sample to avoid bias
Useful when you have a small population or want a small sample (such as children in a class)
This can not be used if it is not possible to number or list all the members of the population (such as fish in a lake)
Systematic sampling: this should be used when you want a random sample from a large population
Useful when there is a natural order (such as a list of names or a conveyor belt of items)
In order for the sample to be random the sampling frame needs to be random
This can not be used if it is not possible to number or list all the members of the population (such as penguins in Antarctica)
Stratified sampling: this should be used when the population can be split into obvious groups of members (where members within a group have a common characteristic)
Useful when there are very different groups of members within a population
The sample will be representative of the population structure
The members selected from each stratum are chosen randomly
This can not be used if the population can not be split into groups or if the groups overlap
Quota sampling: this should be used when a small sample is needed to be representative of the population structure
Useful when collecting data by asking people who walk past you in a public place or when a sampling frame is not available
This can introduce bias as some members of the population might choose not to be included in the sample
Opportunity (convenience) sampling: this should be used when a sample is needed quickly
Useful when a list of the population is not possible
This is unlikely to be representative of the population structure
Most sampling techniques can be improved by taking a larger sample
Sampling can introduce bias - so you want to minimise the bias within a sample
To minimise bias the sample should be random
A sample only gives information about those members
Different samples may lead to different conclusions about the population
Qualitative data is data that is usually given in words not numbers to describe something
For example: the colour of a teacher's car
Quantitative data is data that is given using numbers which counts or measures something
For example: the number of pets that a student has
Discrete data is quantitative data that needs to be counted
Discrete data can only take specific values from a set of (usually finite) values
For example: the number of times a coin is flipped until a tails is obtained
Continuous data is quantitative data that needs to be measured
Continuous data can take any value within a range of infinite values
For example: the height of a student
Age can be discrete or continuous depending on the context or how it is defined
If you mean how many years old a person is then this is discrete
If you mean how long a person has been alive then this is continuous
The population refers to the whole set of things which you are interested in
For example: if a vet wanted to know how long a typical French bulldog slept for in a day then the population would be all the French bulldogs in the world
A sample refers to a subset of the population which is used to collect data from
For example: the vet might take a sample of French bulldogs from different cities and record how long they sleep in a day
A sampling frame is a list of all members of the population
For example: a list of employees’ names within a company
A population parameter is a numerical value which describes a characteristic of the population
These are usually unknown
For example: the mean height of all 16-year-olds in the UK
A sample statistic is a value computed using data from the sample
These are used to estimate population parameters
For example: the mean height of 200 16-year-olds from randomly selected cities in the UK
Sampling Techniques
A census collects data about all the members of a population
For example: the Government in England does a national census every 10 years to collect data about every person living in England at the time
The main advantage of a census is that it gives fully accurate results
The disadvantages of a census are:
It is time consuming and expensive to carry out
It can destroy or use up all the members of a population when they are consumables (imagine a company testing every single firework)
Sampling is used to collect data from a subset of the population
The advantages of sampling are:
It is quicker and cheaper than a census
It leads to less data needing to be analysed
The disadvantages of sampling are:
It might not represent the population accurately
It could introduce bias
Simple random sampling: if a sample of size is taken then every group of members from the population has an equal probability of being selected for the sample
Simple random sampling is carried out by uniquely numbering every member of a population and randomly selecting n different numbers using a random number generator or a form of lottery (where numbers are selected randomly)
Systematic sampling: a sample is formed by choosing members of a population at regular intervals using a list
To carry this out you would calculate the size of the interval k=size of population (N)size of sample (n) and choose a starting point between 1 and then select every kth member after the first one
Stratified sampling: the population is divided into disjoint groups (called strata) and then a random sample is taken from each group (stratum)
The proportion of a sample that belongs to a stratum is equal to the proportion of the population that belongs to the stratum
The number of members sampled from a stratum = size of sample (n)size of population (N) x number of members in the stratum
The population could be split by age ranges, gender, etc
Quota sampling: the population is split into groups (like stratified sampling) and members of the population are selected until each quota is filled
If a member does not want to be included then another member is chosen instead
The members do not have to be selected randomly
Opportunity (convenience) sampling: a sample is formed using available members of the population who fit the criteriaSampling Critique
Simple random sampling: this should be used when you want a random sample to avoid bias
Useful when you have a small population or want a small sample (such as children in a class)
This can not be used if it is not possible to number or list all the members of the population (such as fish in a lake)
Systematic sampling: this should be used when you want a random sample from a large population
Useful when there is a natural order (such as a list of names or a conveyor belt of items)
In order for the sample to be random the sampling frame needs to be random
This can not be used if it is not possible to number or list all the members of the population (such as penguins in Antarctica)
Stratified sampling: this should be used when the population can be split into obvious groups of members (where members within a group have a common characteristic)
Useful when there are very different groups of members within a population
The sample will be representative of the population structure
The members selected from each stratum are chosen randomly
This can not be used if the population can not be split into groups or if the groups overlap
Quota sampling: this should be used when a small sample is needed to be representative of the population structure
Useful when collecting data by asking people who walk past you in a public place or when a sampling frame is not available
This can introduce bias as some members of the population might choose not to be included in the sample
Opportunity (convenience) sampling: this should be used when a sample is needed quickly
Useful when a list of the population is not possible
This is unlikely to be representative of the population structure
Most sampling techniques can be improved by taking a larger sample
Sampling can introduce bias - so you want to minimise the bias within a sample
To minimise bias the sample should be random
A sample only gives information about those members
Different samples may lead to different conclusions about the population
