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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;

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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

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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