CHAPTER ONE
INTRODUCTION
1.1
Background of the study
Every population can be describe with certain characteristics to identify them either quantitative
or qualitative, statistically we called them parameter. These parameters are mean, variance,
proportion, precision estimate and so on
These parameter always exist but not always available and there maybe need to estimate for
them under different condition.
Accurate and precise estimates of population characteristics are essential for informed decision
making in a variety of fields, including public policy, marketing, and scientific research. One
method for obtaining these estimates is through stratified sampling, in which the population is
divided into strata or subgroups and a sample is drawn from each stratum. This approach can be
particularly useful when the characteristics of interest vary significantly within the population
(Gravetter & Wallnau, 2020).
Stratified sampling is a sampling technique that divides a population into distinct subpopulations
(strata) and then selects samples from each stratum. Stratified sampling is often used when a
population has significant differences among its subpopulations, so that a simple random sample
of the entire population would be unlikely to generate a representative sample. Stratified
sampling can be used to improve the precision of estimates from a sample survey.
The precision in of some probability samplings with emphasis on systematic sampling. Precision
is a measure of how close an estimator is expected to be to the true value of a parameter, which
is usually expressed in terms of imprecision and related to the standard error of the estimator.
Less precision is reflected by a larger standard error.( Valerie J. Easto & John ,1997). Sampling
error and bias relate to precision and accuracy. A measurement is precise if it obtains similar
results with repeated measurement (or repeated surveys).A measurement is accurate if it is close
to the truth with repeated measurement (or repeated surveys). Because bias in survey, may lead
to make inappropriate decisions about programmes based on invalid results, and lead to fail to
provide needed services or waste resources on providing unneeded services. Bias may lead to
grossly wrong conclusions, while having not quite enough precision may only decrease
confidence in the survey results. It is known that the precision of any estimate made from a
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sample depends both on the method by which the estimate is calculated from the sample data and
on the plan of sampling .Therefore, the paper provides a general discussion on the related
sampling methods with comparison on the basis of properties and precision. Comparisons of
Precision in systematic sampling and in other sampling methods is found in a wide range of
literature. Some of these references are (Vallian etal, 2000), (Brewer , 2002).
Recently used two major principles sample design to avoid bias in the selection procedure and to
achieve the maximum precision for a given outlay of resources. (Rose AM, Grais RF,
Coulombier D, Ritter H,2006) compared the results of two different survey sampling techniques
(cluster and systematic) where both survey methods gave similar results. Megan Deitchler,
Hedwig Deconinck and Gilles Bergeron ,2008) gave a comparison of three sampling designs in
an emergency setting ,and the paper considered the sampling precision of a systematic sampling
method for estimating total number of nerve fibers exposed on cross section of a nerve trunk.
The challenge of designing an educational intervention of any kind in higher education has been
of great interest to many a researcher and/or educator, over the years. Usoro (2006) carried out a
study on classification of students into various departments on the basis of their cumulative
results for a one year Foundation Programme otherwise known as Pre-National Diploma (PREND) in Polytechnics system. Charles and June (1970) carried out a study to determine if a
differentiation or separation among students graduating, withdrawing or failing could be
identified. Adebayo and Jolayemi (1998/1999), applied the statistics to investigate how
predictable the final-year result would be using the first year result or Grade Point Average
(GPA) of some selected University graduates. In the past 25 years, research in academic
prediction has centered on graduation, withdrawal, failure and selection of student’s on the basis
of either their collegiate success or cumulative results of Remedial or PREND; and literature to
date suggests no loss of interest.
1.2
Objectives of the study
The aim of this study is to comparison the precision of estimates obtained in stratified sampling
under different sampling plans. The specific objective are:
i.
To obtain required sample data under different plans
ii.
To estimate mean and proportion in stratified based on systematic and simple random
sampling plans
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iii.
A To obtain the variance of systematic and simple random sampling plans
iv.
To evaluate the precision of estimates in stratified sampling under identified sampling
plans
1.3
Statement of the Problem
In the practice we consider the problem of precision several population characteristics. The
problem is explored from a general point of view by estimating a fairly general class of
functional of the population distribution. A rising number of parents, school boards, lecturers and
civil rights organizations are beginning to question the fairness of the overreliance on
standardized tests. Research has shown that in spite of the progress made in advancing the
educational system, achievement in education continues to be very low and the uneven
distribution of education across different groups is related to social class differences,
socioeconomic background, gender, region, rural/urban location and school factors and others
1.4
SIGNIFICANCE OF THE STUDY
Comparison generally refers to the mapping of data items into predefined groups and classes.
The data comparison process involves learning and sampling. In learning phase, the training data
are analyzed by sampling and during sampling phase the test data are used to estimate the
accuracy of the classification rules. If we are able to see the difference in the two comparison
then any of them can used in order to safe us from using all measure of sampling techniques
1.5
SCOPE OF THE STUDY
This research was focused on comparison of precision in stratified sampling under different
sampling plans the data will be obtain from statistics department result of ND1 and ND2 (FT ,
DPT AND RPT) in federal polytechnic Ede, Osun state the term records in the year 2020/2021.
1.6
This
LIMITATIONS OF THE STUDY
study
covers
undergraduate
students
in
Federal
Polytechnic
Ede.
ND1&ND2(FT,DPT&RPT).
Utilizing stratified random sampling (SRS) requires strata to be carefully defined. The strata in
this case were described based on subgroups. Due to the limitations of subgroup sizes,
populations of limited could not be customized by ethnicity due to low sample sizes, which
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would automatically qualify for the prior recommendation to test all students in a sample less
than 30.
Employing stratified random sampling (SRS) to augment testing every student, to testing a
sample of students creates a cross-sectional, single point in time data and therefore does not
enable longitudinal analysis for comparisons over time at the student level.
Time constraint has shown on many research. The limited time has to be share among many
alternative uses, which include reading, attending lecture and writing the research.
Financial issue is another faced during the process of the research because we need to traveled to
during research and cost of printing and cost of browsing on internet
1.7
DEFINITION OF TERMS IN TERMINOLOGY
 Accuracy: Accuracy refers to how close a sample estimate is to population value on
average .
 Comparison: Comparison or comparing is the act of evaluating two or more things by
determining the relevant, comparable characteristics of each thing, and then determining
which characteristics of each are similar to the other, which are different, and to what
degree.
 Explicit stratification- Explicit stratification consists of building separate sampling
frames, according to the set of explicit stratification variables under consideration; used
for categorical variables
 Precision: The quality, condition or fact of being exact and accurate. refers to how close
the sample estimates from different sample are likely to be to each other.
 Sampling: Sampling means selecting the group that you eill actually collect data from in
your research
 Sub group: A subgroup is a group of units that are created under the same set of
conditions. .
 Stratified Random Sampling (SRS): Stratified Random Sampling also sometimes
called proportional or quota random sampling, involves dividing your population into
homogeneous subgroups and then taking a simple random sample in each subgroup
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 Stratified sampling: Stratified sampling is used to highlight differences among groups in
a population, as opposed to simple random sampling, which treats all members of a
population as equal, with an equal likelihood of being sampled.
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