SAMPLING FOR STATISTICS GCE O LEVEL/IGCSE

SAMPLE SURVEY

The term survey has been defined as a means of collecting information to meet a definite need.

When a survey is carried out by a sampling method, it is called a sample survey. The main steps in a sample survey are to:

Clearly state the objectives of the survey;

1. Define the population we wish to study as clearly as possible;
2. Construct the sampling frame by clearly defining the sampling units;
3. Choose an appropriate sample design and proper sample size;
4. Organize a reliable field work to achieve the objectives of the survey;
5. Summarize and analyses the data.

SAMPLING BIAS

The word bias means a systematic component of error which deprives a survey result of representativeness. Bias is different from a random error in the sense that the random errors balance out in the long run while bias is cumulative and does not become less as the sample size increases. Bias may rises due to:#

1. Negligence and carelessness during sampling procedure.
2. Faulty planning of sampling.
3. Wrong selection of sample units.
4. Incomplete investigation and survey.
5. Framing of wrong questionnaire.

RANDOM SAMPLE

A sample is called a random sample if the probability of selection for each unit in the popub is known prior to sample selection.

SIMPLE RANDOM SAMPLING

A sample is defined to be a simple random sample (SRS) if it is selected in such a manner that (i) each unit in the population has an equal chance of being included in the sample. And (ii) each possible sample of the same size has an equal chance of being the sample selected. For example, in a class of 20 students, every student has an equal chance of getting A-grade exam.

SELECTION OF SIMPLE RANDOM SAMPLES (SRS)

A simple random sample can be selected by the following methods.

For example, in a class of 30 students, if we want to choose only one student for any particular sports. We place the slip of the name of each student in the bowl and then draw one from it. Therefore it is random.

STRATIFIED RANDOM SAMPLE

A sample is defined to be a stratified random sample if it is selected from a population which has been divided into a number of non-overlapping groups or sub-populations, called strata (the plural of stratum), such that part of the sample is drawn at random from each stratum.

MARKS	NUMBER OF STUDENTS
Below 50	70
50-75	80
75-100	100
TOTAL	250

A survey is to be taken to find methods to improve the local bus services. Show how to select a sample of 100 students from this population for the survey.

STRATA	MARKS	SAMPLE SIZE FROM EACH STRATUM
1	Below 50	70 x 100/250=28
2	50-75	80 x 100/250=32
3	75-100	100 x 100/250=40
	TOTAL	100

SYSTEMATIC RANDOM SAMPLE

A sample is defined to be a systematic sample if it is obtained by choosing one unit at random from the first k units and thereafter selecting every k^th unit in the population, serially numbered from 1 to N. The letter k is called the sampling interval.

Example: a particular type of bulb is made on a production line. Show how to select a systematic sample of 100 bulbs from 2000 bulbs produced on this production line on a certain day.

Solution: here we find the interval is of length 20, i.e. (2000/100). We begin buy selecting a bulb at random from the first 20 bulbs produced. If the 5^th bulb is chosen, then the other bulbs are selected at regular intervals, i.e. the 25^th, 45^th, 65^thi and so on until we have 100 bulbs.

QUOTA SAMPLING

A quota sample is a type of judgment sample. It is a sample, usually of human being, in which the information is collected purposively from the segments of a population (the quotas), e.g. the quota of men and women; urban and rural; upper, middle and lower income groups; etc.

For example, the class teacher may select the `well behaved' or `ill behaved^' from a particular class by their personal judgment.