# Preknowledge

 Before looking at the details of different sampling methods you will need to be familiar with generating random numbers on your calculator on a spreadsheet package

## Systematic Sampling

Systematic sampling is a statistical method involving the selection of data elements from an ordered group (usually referred to as the population for the purposes of NCEA Level 2). The most common form of systematic sampling is an equal-probability method, where every kth element in the ordered group is selected, where k, the sampling interval, is calculated as:

$k = \frac {N}{n}$

where n is the sample size, and N is the population size. This means that you get the size of the data-set (population) and divide it by the size of your sample.  This gives you the sampling interval.

Using this procedure each element in the population has a known and equal probability of selection. This makes systematic sampling functionally similar to simple random sampling. It is however, much more efficient - i.e. faster and simpler to do.

The researcher must ensure that the chosen sampling interval does not hide any underlying pattern in the data such as an underground stream that may affect the size of fruit in a particular row of a plantation. Any pattern would threaten randomness.

A random starting point must also be selected.

Example: Suppose a supermarket wants to study buying habits of their customers, then using systematic sampling they can choose every 10th or 15th customer entering the supermarket and conduct the study on this sample.

This is random sampling with a system. From the sampling frame, a starting point is chosen at random, and choices thereafter are at regular intervals. For example, suppose you want to sample 8 houses from a street of 120 houses. 120/8=15, so every 15th house is chosen after a random starting point between 1 and 15. If the random starting point is 11, then the houses selected are 11, 26, 41, 56, 71, 86, 101, and 116.

Some advantages of systematic sampling are:

## Simple Random Sampling

This is the next step in writing up how to carry out a simple random sample.