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OpenBook Sample Size Calculators
In order to generalize from a random sample and avoid sampling errors or biases, a random sample needs to be of adequate size. What is adequate depends on several issues which often confuse people doing surveys for the first time. This is because what is important here is not the proportion of the research population that gets sampled, but the absolute size of the sample selected relative to the complexity of the population, the aims of the researcher and the kinds of statistical manipulation that will be used in data analysis (Taherdoost, 2016). While the larger the sample the lesser the likelihood that findings will be biased does hold, diminishing returns can quickly set in when samples get over a specific size which need to be balanced against the researcher’s resources (Gill et al., 2010).
To put it bluntly, larger sample sizes reduce sampling error but at a decreasing rate. Several statistical formulas or calculators are available for determining sample size.
OpenBook Yamane Calculator (OY Calculator, 2022)
OpenBook Yamane Calculator (OY Calculator, 2022) is a free online sample size calculator developed to help research students or other researchers from various fields worldwide, having problem in calculation using Taro Yamane Formula manually, determine sample size accurately.
Taro Yamane Formula is written as
n = N / (1 + Ne2) simplified and adjusted, to be more accurate, from Cochran’s Sample Size Formula:
- n = Number of Samples,
- N = Total Population,
- e = Error Tolerance (level) or Margin of Error, 0.05
- p = Sample Proportion, 0.5
- z = z-value found in Z-score Table, 1.96
By substituting for z = 1.96 and p = 0.5 in the simplified formula above, Taro Yamane Formula can be proved as follows:
e could be 0.10, 0.05 or 0.01. They are margin of errors, that can be tolerated in determining sample size, at confidence level of 90%, 95% and 99% respectively. They are used in educational and social science research studies. The most commonly and widely used is 0.05. The sample proportion p, though varies, but by default is 0.5. If you are not familiar with confidence level, confidence interval or margin of error and sample proportion – the common terms in sample size and calculation, you can click here. The table below is Z-score Table for most use confidence level or confidence interval.
|Confidence Level||Confidence Interval||Area between zero and z-score||Z-score|
One of the advantages of using OpenBook Yamane Calculator, to accurately determine sample size, is when the total population is relatively large. Secondly, you don’t need to crack your brain of any complex formula and all its variables’ values especially if you don’t have relevant knowledge in statistics. Other advantage is that there are always excess samples of 16 or 15 at total population of 300,000 and above, when compared with other Sample Size Calculators, which is enough to gather much more information or data, from the respondents, about a study. To prove this, the highest sample you would ever get using OpenBook Yamane Calculator from total population of 300,000 and above is 400 and the highest sample you would ever get using other Sample Size Calculators from also 300,000 total population and above is 384 or 385. So, there are always excess samples of 16 or 15 to get much more information about a study using OpenBook Yamane Calculator.
However, the population N is to be determined first from the study area. When the population is relatively large and the exact number is unknown, then 300,000 or more can be used because any sample size gotten cannot be approximately greater than 400 or 385 (either Taro Yamane Formula at confidence interval of 0.05 or other Sample Size Formula at confidence level of 95%, confidence interval of 5% and sample proportion of 50%).
To calculate the Sample Size n, either with OY Calculator or OC Calculator below: enter the Total Population N, then calculate by clicking on Calculate Button. To enter different Total Population N, click Reset Button.
Using OY Calculator, you may also change the default 0.05 in the margin of error e placeholder to your desired confidence interval by selecting either 0.10 or 0.01 as alternate scenario. The 300,000 in the right field of population N placeholder is to be used when the exact number is unknown at confidence interval of 0.05. The common usage of 0.05 confidence interval for a specific sample size result is to bring balance against the researcher’s resources relative to the complexity of the population. Statistically, large samples must be equal to or greater than 30 (Murray, 1987). As sample size is used to validate research findings, it must not be too small. If too small, it will not yield valid results. At the same time, if it’s too large, may be a waste of money and time.
NOTE: You must round your answer to a whole number (because you can’t sample a fraction of a person or thing! For example, 399.990885 ≅ 400).
OpenBook Cochran Calculator (OC Calculator, 2022)
(From Cochran’s Sample Size Formula without Adjustment or Modification of Z-score z, 1.96 at confidence interval or margin error e, 0.05 and sample proportion p, 0.5)
Using OC Calculator, you may also change the default 1.96 and 0.05 in their respective placeholder to your desired confidence level of either 90% or 99% by selecting 1.65 or 2.58 and 0.10 or 0.01 respectively as alternate scenarios. The 300,000 in the right field of population N placeholder is to be used when the exact number is unknown at confidence interval of 0.05 and z-score value of 1.96. The common usage of 0.05 confidence interval and 1.96 z-score value for a specific sample size result is to bring balance against the researcher’s resources relative to the complexity of the population. Statistically, large samples must be equal to or greater than 30 (Murray, 1987). As sample size is used to validate research findings, it must not be too small. If too small, it will not yield valid results. At the same time, if it’s too large, may be a waste of money and time.
For easy understanding and interpretation, you can use OC Calculator in percentage.
NOTE: You must round your answer to a whole number (because you can’t sample a fraction of a person or thing! For example, 383.6686994 ≅ 384).
Gotten Your Sample Size from OY Calculator or OC Calculator, What’s Next?
Now that you have gotten your sample size, from any of the calculators above, for the number of copies of your questionnaires, to be administered to your respondents, let OpenBook have the Questionnaire Reliability Checking and SPSS Data Analysis done for you. SPSS Data Analysis using Descriptive and Inferential Statistics.
Questionnaire Reliability Checking (Cronbach Alpha) is EXCLUSIVELY FREE! Distance is not a barrier; you can upload your already ticked FORM/QUESTIONNAIRE to whatsapp number: 2348028999115.
Service Price of SSPS Data Analysis ranges from 15,000 to 70,000 in Nigeria Naira (NGN) and 100 to 470 in US Dollar (USD).
BSc/BA Research Data Analysis: NGN15,000/USD100.
MSc/MA Research Data Analysis: NGN30,000/USD200.
PhD Research Data Analysis: NGN70,000/USD470.
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What is an Academic Project?
An academic project is a formal document whose major sections include an abstract, introduction, literature review, methodology, results, discussion, and conclusions and recommendations. The process of writing and presenting an academic project is guided by certain rules. These rules may vary depending on the level of education, institution, or the supervisor. OpenBook offers high standard academic project writing services strictly following the rules provided in order to represent the students’ contribution to the body of knowledge.
Formulating a Project Title of a Project
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Guidelines for Writing the Introduction
In the introduction section, the student should highlight the problem area and discuss its significance. A comprehensive introduction should contain the research questions, objectives, and hypotheses that will guide the academic project. Students should distinguish an introduction from a literature review. Whereas the introduction utilizes existing literature to highlight a problem area, the section does not synthesize the referenced studies.
Conducting a Literature Review
Literature review forms the second chapter of dissertations and theses. A comprehensive literature review highlights students’ ability to identify relevant scholarly works and synthesize their findings. Literature reviews should utilize current articles to inform future readers of the existing knowledge and establish a context for conducting their intended academic projects. The contents of a literature review should correlate to the formulated hypothesis and research questions. For example, an academic study may be intended to improve on the existing knowledge related to the implementation of bed alarms as a fall prevention intervention. Consequently, the accompanying literature review should synthesize the current knowledge related to the utilization of bed alarms in hospital settings. A student should highlight the existing knowledge gaps in the available literature that justify the proposed academic project. For instance, previous studies may have investigated the influence of bed alarms in preventing falls among geriatric patients. A student may identify a need to narrow the focus of their research to geriatric patients who have been diagnosed with chronic mental illnesses. A comprehensive literature synthesis should highlight the existing knowledge gap related to the limited studies that focused on a specific population.
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The methodology section should contain a discussion of the design and project implementation plan. The method section should be detailed and comprehensive to promote replicability. A project’s methodology comprises the intended population, setting, instrumentation, data collection, data analysis, and ethical considerations. A subsection may be introduced to discuss the formulated project procedure. The procedure should highlight all the executed steps and treatments performed on the independent variables to study the changes in the dependent variables. The methodology section should also highlight the proposed data analysis techniques. Students should identify the software used and data analysis tests conducted to guarantee the replicability of their academic projects.
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The length of the findings section often varies between qualitative and quantitative projects. The findings of a qualitative study may be lengthy because of the need to discuss the identified themes and their correlation to the formulated research questions. In the case of quantitative research, the findings ought to be tabulated because they fundamentally comprise statistics. The findings section should be followed by a discussion of the implications of the concluded academic project. The discussion section explains the observed outcomes. A comprehensive discussion should highlight the identified limitations and provide a basis for conducting future studies.
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