# Random sampling and sampling methods

## In a nutshell

The main point to consider when deciding on a sampling method is that it should be random.

## Random sampling

The aim of sampling is to take a small group from a population that represent the entire population, therefore the sampling of the participants should be random to achieve this.

The areas in which the samples are taken from should be in a random order to accurately represent those in the population and the distribution of them. This is often done by setting out a grid of the area and using a number generator to randomly select the areas of where to sample within the grid.

A shows an area that isn't selected at random. B shows areas that are selected at random.

When collecting health data, the sampling should again be random and this is achieved by numbering all of the population and using a random number generator.

##### Example

*A medical study investigating the proportion of people with ADHD that also have Dementia. Hospital records show that there are $18,320$ patients with Dementia.*

*The patients are numbered $1-18,320$. A random number generator, generates a sample of random patients that are cross-referenced to find if they also have ADHD.*

*The proportion can be calculated and an estimate of the total number of patients with both ADHD and Dementia is produced.*

## Sampling methods

### Using a quadrat

A quadrat is a one square metre frame used to isolate an area in order to count samples of plant or wildlife.

In order to take a random sample, the quadrat must be thrown onto an area at random and not placed. Alternatively a $10 \, m\times 10 \, m$ surveying area can be constructed and a random number generator can be used to generate a set of coordinates to place the quadrat.

The number of specimens in the quadrat can then be counted and the data extrapolated to cover the whole of the area being investigated.

Below is an image showing a $1 \, m \times 1 \, m$ quadrat being use to sample a larger area.

##### Example

*A quadrat is used to investigate how many daffodils are growing in a $350 \, m^2$ field. A number generator is used to generate a random set of coordinates. The quadrat is placed and the number of daffodils are counted. *

*The number of daffodils is found to be $23$ in the quadrat. The approximation can then be made that there are:*

*$23\times 350 =8050$ daffodils in the field. *

### Using a transect line

A transect line is a line which is placed at an area of study. The number of wildlife or plants are counted and recorded each side of the transect.

The transect is normally placed across a differing habitat in order to see the change in plant or wildlife samples as the habitat changes.

##### Example

*A piece of rope is tied to the base of a tree into a clear opening in a field. The number of woodlice is counted at regular intervals along the transect.*

*A kite diagram is then drawn with the results. A conclusion can then be drawn and matched with the theory. *

### Using capture-recapture

A variety of different methods to capture live wildlife, like pooters, pit-fall traps and nets are used to capture wildlife. Once caught the wildlife is marked harmlessly and released back into the population.

| 1. | Jar | 2. | Cover propped up with stones | 3. | Food or bait | |

A set time later, the same method is used to capture another sample of wildlife from the same location. The following formula can be used to estimate the population size:

$Population \ size =\frac {number \ in \ first \ sample \times \ number \ in \ second \ sample}{number \ in \ second \ sample \ which \ are \ marked}$

##### Example

*A pooter is used to collect a sample of woodlice living within $1\,m^2$ of a wooden log. The $23$ woodlice were marked using a harmless paint and released back into their habitat. At the same time the next day $29$ woodlice were caught with $6$ woodlice having a mark. *

*Estimating the population size:*

*$population \ size =\frac {23 \times 29}{6}$*

*Woodlice population size: *

*$population \ size=111$*