Page 1 of 45
Advances in Social Sciences Research Journal – Vol. 11, No. 7
Publication Date: July 25, 2024
DOI:10.14738/assrj.117.17018.
Mweshi, G. K., & Muhyila, M. (2024). Determining a Statistical Analysis for the Quantitative Study. Advances in Social Sciences
Research Journal, 11(7). 187-231.
Services for Science and Education – United Kingdom
Determining a Statistical Analysis for the Quantitative Study
Geoffrey Kapasa Mweshi
School of Business, ZCAS University, Lusaka, Zambia
Mildred Muhyila
School of Social Sciences, ZCAS University, Lusaka. Zambia
ABSTRACT
The manner in which research will be conducted follows from the research
questions or hypotheses; the type of research must be in support of the project.
Several types of research are conducted in studies, including experimental, quasi- experimental, and observational research. Researchers must weigh the advantages
and drawbacks of each type of research to determine which design is best for their
specific research questions or hypotheses. Alternately, researchers can employ
several methods, known as triangulation, to provide a varied and complementary
perspective. The use of several methods, measures, or theoretical frameworks to
examine a particular phenomenon or behavior improves the robustness of study
and can corroborate findings across the various measures (Keyton 2014).
Quantitative Designs states the research questions the study will answer, identifies
the variables, and states the hypotheses (predictive statements) using the format
appropriate for the specific design. For a quantitative study, the theory(ies) or
models(s) guides the research question(s) and justifies what is being measured
(variables) and describes how those variables are related. Quantitative study:
Describes each research variable in the study discussing the prior empirical
research that has been done on the variable(s) and the relationship between
variables. The overall structure for a quantitative design is based on the scientific
method. It uses deductive reasoning, where the researcher forms a hypothesis
(Albers, 2017), collects data in an investigation of the problem, and then uses the
data from the investigation, after analysis is made and conclusions are shared, to
prove the hypotheses not false or false.
Keywords: quantitative research, numerical data, sample size determination,
correlations analysis, regression.
INTRODUCTION
Quantitative data is information that can be counted or measured and expressed as numbers.
Examples include: quantitative data analysis is a valuable tool for researchers and analysts
seeking to extract knowledge and insights from numerical data. Survey responses on a Likert
scale (1- strongly disagree to 5- strongly agree), scores on exams or tests, measurements like
height, weight, temperature, or reaction times, and sales figures, customer demographics, or
website traffic data; the process of quantitative data analysis: data collection which can involve
conducting experiments, surveys, or gathering data from existing sources; data cleaning and
preparation as the steps for ensuring the data is accurate and consistent. It might involve
identifying and correcting errors, handling missing values, and formatting the data for analysis;
Page 2 of 45
188
Advances in Social Sciences Research Journal (ASSRJ) Vol. 11, Issue 7, July-2024
Services for Science and Education – United Kingdom
exploratory data analysis (EDA): hypothesis testing for common tests that include: T-tests for
comparing means between groups, analysis of Variance (ANOVA) for comparing means of more
than two groups, Chi-square tests for analyzing relationships between categorical variables,
correlation analysis to measure the strength and direction of the relationship between two
variables, and regression analysis to model the relationship between a dependent variable and
one or more independent variables (Montgomery & Peck, 2021). Tools for quantitative data
analysis: spreadsheet software like Microsoft Excel or Google Sheets can be used for basic data
analysis tasks, and statistical software packages like SPSS, R, SAS, or Python offer a wider range
of statistical tests, data manipulation capabilities, and advanced visualizations. Quantitative
research relies heavily on statistical analysis to extract meaning from numerical data. But with
a vast arsenal of statistical tests available, selecting the most appropriate one can want to
navigate a maze.
The overall structure for a quantitative design is based in the scientific method. It uses
deductive reasoning, where the researcher forms a hypothesis (Creswell, 2014), collects data
in an investigation of the problem, and then uses the data from the investigation, after analysis
is made and conclusions are shared, to prove the hypotheses not false or false. Quantitative data
analysis simply means analysing data that is numbers-based. medians, modes, correlation, and
regression. If the researcher views quantitative design as a continuum, one end of the range
represents a design where the variables are not controlled at all and only observed.
Connections amongst variable are only described. At the other end of the spectrum, however,
are designs which include a very close control of variables, and relationships amongst those
variables are clearly established. In the middle, with experiment design moving from one type
to the other, is a range which blends those two extremes together.
Determining of Sample Size for Quantitative Study in A research Study
Population Size:
Determine the population size (if known). The other important consideration to make when
determining your sample size is the size of the entire population you want to study. A
population is the entire group that you want to draw conclusions about. It is from the
population that a sample is selected, using probability or non-probability samples (Albers,
2017). The population size may be known (such as the total number of employees in a
company), or unknown (such as the number of pet keepers in a country), but there’s a need for
a close estimate, especially when dealing with a relatively small or easy to measure groups of
people.
How to Determine Sample Size for a Research Study:
The sample size references the total number of respondents included in a study (Albers, 2017),
and the number is often broken down into sub-groups by demographics such as age, gender,
and location so that the total sample achieves represents the entire population. A consideration
for the concept of a minimum sample size of 100 in providing a starting point being a rule of
thumb is applied for quantitative study based on suggestions that a minimum sample size of
100 for studies is statistically reliable, justifiable with a larger sample, whereas also the chance
of results is accurately reflecting the whole population increases (Qureshi et al, 2018), and that
limitation does not account for factors like desired precision (margin of error) or the type of
study (surveys vs. experiments). A large enough sample size has a high probability (power) of
detecting a worthwhile effect, as larger studies have greater power to detect a beneficial (or
Page 3 of 45
189
Mweshi, G. K., & Muhyila, M. (2024). Determining a Statistical Analysis for the Quantitative Study. Advances in Social Sciences Research Journal,
11(7). 187-231.
URL: http://dx.doi.org/10.14738/assrj.117.17018
detrimental) effect of a given size, where the probability of making such an error is designated
and commonly known as the significance level, and that the risk of missing an important
difference (Type II error) decreases as the sample size increases. The statistical sample size is
done with the calculation as a more robust approach that considers: desired confidence level
(typically 90% or 95%), margin of error (how much difference you're willing to accept between
the sample and the population), expected variability in the data (population standard
deviation), and study design (comparing means, proportions, etc.).
Confidence Interval and Confidence Level:
When thinking about sample size, the two measures of error that are almost always
synonymous with sample sizes are the confidence interval and the confidence level.
Confidence Interval (Margin of Error):
Determine the confidence interval. Confidence intervals measure the degree of uncertainty or
certainty in a sampling method and how much uncertainty there is with any particular statistic.
In simple terms (Albers, 2017), the confidence interval tells you how confident you can be that
the results from a study reflect what you would expect to find if it were possible to survey the
entire population being studied. The confidence interval is usually a plus or minus (±) figure.
For example, if your confidence interval is 6 and 60% percent of your sample picks an answer,
you can be confident that if you had asked the entire population, between 54% (60-6) and 66%
(60+6) would have picked that answer.
Confidence Level:
Convert the confidence level into a Z-Score. The confidence level refers to the percentage of
probability (A 95% confidence level means that 95% of the intervals would include the
population mean), or certainty that the confidence interval would contain the true population
parameter when you draw a random sample many times. It is expressed as a percentage and
represents how often the percentage of the population who would pick an answer lies within
the confidence interval (Albers, 2017). For example, a 99% confidence level means that should
you repeat an experiment or survey over and over again, 99 percent of the time, your results
will match the results you get from a population. The larger your sample size, the more
confident you can be that their answers truly reflect the population. In other words, the larger
your sample for a given confidence level, the smaller your confidence interval.
Standard Deviation:
Determine the standard deviation (a standard deviation of 0.5 is a safe choice where the figure
is unknown). Another critical measure when determining the sample size is the standard
deviation, which measures a data set’s distribution from its mean (Albers, 2017). In calculating
the sample size, the standard deviation is useful in estimating how much the responses you
receive will vary from each other and from the mean number, and the standard deviation of a
sample can be used to approximate the standard deviation of a population. The higher the
distribution or variability, the greater the standard deviation and the greater the magnitude of