COMPARATIVE ANALYSIS OF THE EFFICIENCY OF SIMPLE RANDOM SAMPLING AND STRATIFIED RANDOM SAMPLING TECHNIQUES USING DATA FROM 2006 POPULATION FIGURES OF THE SIX SOUTH-SOUTH STATES OF NIGERIA

Igwe N.O, Bassey U and Oyah M.P Department of Maths/Statistics, AkanuIbiam Federal Polytechhic, Unwana, P.M.B 1007 Afikpo, Ebonyi State Nigeria. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History Received: 25 January 2020 Final Accepted: 27 February 2020 Published: March 2020


ISSN: 2320-5407
Int. J. Adv. Res. 8(03), 1056-1064 1057 are: it reduces cost, results in greater speed, accuracy and scope of the information that could be obtained. (Gitonga, et al., 2018) The overall population figure of Nigeria is made up of the sum of the sub-populations of the six (6) geographical Zones namely: North East, North West, North Central, South East, South West, and the South-South. Hence with sampling, it is argued that if one of the sub-populations could be isolated, and a random sample drawn there from, is used to estimate the total sub-population with high degree of success, then estimating the overall population figures of the country would be successfully attempted. In this regard, the 2006 population figures of the South-South geopolitical zone, made up of 6 States (AkwaIbom, CrossRiver, Delta, Edo, Rivers, and Bayelsa) is estimated using two (2) probability sampling techniques namely: simple random sampling and stratified random sampling. (Stuart, 1984).
The ultimate aim of this research is to compare the techniques of simple random sampling and stratified random sampling with a view to determining the one that efficiently provides good estimates and thereby serves as the best sampling plan for carrying out analysis on the population figures of the six South-South states.

Materials and Methods:-
For this research, data was collected from a secondary source precisely from the National Bureau of Statistics on the 2006 population figures of the six (South-South) states in Nigeria.

Method of determining sample size:
In the planning of a sample survey, a stage is always reached at which a decision must be made about the size of the sample. Sampling theory provides a frame work within which to think intelligently about the selection best sample size.
According to Stuart, 1984, the principal steps involved in the choice of a sample size are statement of the level of precision which shows the amount of error that we are willing to tolerate in the sample estimates, and the degree of variability in the attribute being measured.
An appropriate formula used in this regard is Taro Yamane formula which is given as: n= + ( ) , Where: n=Sample size, N=Population size, and e =Level of precision (%).
Since there are 246 units in the population using the above formula our sample size becomes (at 95%) n = + ( . )

= . =152
Therefore, we shall use as our sample size 152 units of the entire population of 246 units to carry out the necessary comparisons between the sampling techniques employed.

Method of random selection:
Generally, in sampling, if our conclusions are to be valid and dependable, then the sample selection must be done without any bias. Randomization technique which guarantees equal chances of being selected was used to select the required samples for this research. The use of table of random digits was adopted in this research.

Simple Random Sampling:
Let a sample of n units be drawn from a population of N units such that all the n distinct samples have an equal probability of being drawn, then the above method of selection is referred to as simple Random sampling. In practice, a simple random sample is drawn by first numbering all the units in the population from 1 to N. Then using a table of random digits or a computer program, a series of random digits from 1 to N is drawn one after the other until n digits are selected. The units' corresponding to the n selected digits gives the required sample size n. .
In other to facilitate the construction of strata before sample selection, two pieces of information are important: 1. The stratum frame and 2. The stratum weight The stratification factor also must be known. Stratification factor is the basis for dividing the heterogeneous population into homogenous sub-populations called strata. For this research, the states are used as the stratification factor.
When the population have been stratified, what follows is to determine the number of sub-sample (n h ) to be drawn from each stratum.
Proportionate stratified sampling can be achieved using the following formula:

Selection of simple random of size (n) = 152 units:
The method of using Table of Random digits for selecting the sample was adopted. Since there are 246 units in the population, we take first three digits random numbers on the table. The corresponding units of the random numbers selected give us our simple random sample.

Selection of stratified random sample of size n = 152 units:
Using state as the stratification factor, we proceed to obtain the sample n h (h=1,2,3,…6) for each stratum using the proportional allocation formula. Using equation 3.0 we obtain the following:      Table 3 clearly shows that stratified random sampling Techniques is more is more efficient than the simple random sampling technique.

Conclusion:-
From the foregoing, one can empirically conclude that stratified random sampling technique provides the best and most efficient estimators of the 2006 population figures of the six states in the South-South geopolitical zones of Nigeria.

Recommendation:-
There is the need to carry out a further research, which would involve the use of the estimators in stratified Random Sampling technique on the entire 2006 population figures of Nigeria made up of all the six (6) geopolitical zones.