## Saturday, 16 June 2018

Systematic sampling is a statistical method which involves the selection of elements from the regular sampling framework. The most common form of systematic sampling is an equal-probability method, in which every kth element in the frame selects.

Is calculated as: 

k = N/n

Where,

k = the sampling interval

N = the population size.

n = The sample size.

## Overview to Systematic sampling

Use this procedure to each element in the population has a known and equal possibilities of selection. This makes systematic sampling functionally similar to simple random sampling. Nevertheless, it is much more efficient (if variance within systematic sample was more than the variance of a population).

Researchers must ensure that the chosen sampling interval will not hide a pattern. Each pattern would threaten randomness. Random point must also be select.

## Logical Method: systematic sample process

### Introduction Steps

Systematic sampling should be applying only if certain populations logically homogeneous, because systematic sample units are uniformly distributing over the population.

Example: suppose that a supermarket would like to study buying habits of their customers. Then using systematic sampling, they can pick any 10 or 15 customers entering the supermarket and did a study of this sample.

### Random Sampling

This is a random sampling with the system. From the sampling frame, the starting point is chosen at random, and then the options are at regular intervals.

Example, you want to sample 8 houses from the road consisting of 120 houses. 120/8 = 15, so every 15 houses were select after a random starting point between 1 and 15.

If the random starting point is 11, then the houses select are 11, 26, 41, 56, 71, 86, 101, and 116.

### Analysis

If, as is more common, the population is not evenly divisible (suppose you want to sample 8 houses from 125, where 125/8 = 15.625). You should take any home or home every 15 16? If you take every 16th House, 8 * 16 = 128. So there is a risk that the last House chosen does not exist.

On the other hand, if you take every 15th House, 8 * 15 = 120, so the last five houses will not be select. Random starting point should be select as a non-integer between 0 and 15.625 (inclusive on only one end point). To ensure that every home has the same opportunities for select:

• The interval should now be non-integral (15.625), and each non-integer select should be rounded up to the next integer.

• If a random point is 3.6, then the houses selected are 4, 19, 35, 51, 66, 82, 98, 113 and, where there are 3 cycle interval of 15 and 5 intervals 16.

• To illustrate the danger of systematic skip concealing a pattern, suppose we plan to sample the street environment in which each has ten houses on every block.

• This place is the home of the # 1, 10, 11, 20, 21, 30 ... at the corner of the block; corner blocks may be less valuable. Because more of their territory taken up by street front etc.

That are not available for the purpose of building. If we then every 10 households sample, the samples we will either be made only from the corner of the House (if we start at 1 or 10) or have no corner houses (start); either way, it will not be representing.

### Probability

Systematic sampling can also be used with the same non-selection probability. In this case, rather than simply counting through elements of the population and selecting every kth unit. We allocate each element spaces along the line numbers in accordance with the probability of selection. We then generate a random uniform distribution ranging from between 0 and 1, and move along the line on step number 1.

Example: we have a population of as many as 5 units (A #). We want to give the unit A A 20% probability of selection, unit B 40% probability, so on until the unit E (100%).

### On Conclusion

Assuming we maintain alphabetical order, we allocate each unit to the following intervals:

A: 0-0.2
B: 0.2-0.6 (= 0.2 0.4)
C: 0.6-1.2 (= 0.6 0.6)
: 1.2-2.0 D (= 1.2 0.8)
E: 2.0-3.0 (= 2.0 1.0)

If we start was 0.156 random, we would first select the unit of the interval that contains the number of this (i.e. A). Next, we will choose the interval containing 1.156 (element C), then 2.156 (element E). If not our random start was 0.350, we will select from points 0.350 (B), 1.350 (D), and 2.350 (E).

## Final Conclusion

Systematic Sampling is typically involves first selecting a fixed starting point in the larger population and then obtaining subsequent observations by using a constant interval between samples taken.

It is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed periodic interval. It is to be applied only if the given population is logically homogeneous, because systematic sample units are uniformly distributed over the population.