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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.
Gill, J. Johnson, P. & Clark, M. (2010). Research Methods for Managers. Sage Publications
Taherdoost, H. (2016). Sampling Methods in Research Methodology; How to Choose a Sampling Technique for Research. International Journal of Advance Research in Management, 5(2), 18-27
OpenBook Yamane Calculator (OY Calculator, 2022)
Taro Yamane Formula is written as
n = N / (1 + Ne2) simplified and adjusted, to be more accurate, from Cochran’s Sample Size Formula:
Where:
- 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 |
90% | 0.10 | 90/2%=0.4500 | 1.65 |
95% | 0.05 | 95/2%=0.4750 | 1.96 |
99% | 0.01 | 99/2%=0.4950 | 2.58 |
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, 2009). 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.
Murray, R. Spiegel et al (2009). Probability and Statistics. The McGraw-Hill Companies Inc.
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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).
The use of OpenBook Yamane Calculator can be referenced in your thesis or dissertation as:
OpenBook Yamane Calculator, 2022. OpenBook Sample Size Calculators. OpenBook Communications and Technologies, Nigeria. https://www.openbookpage.com/
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, 2009). 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.
Murray, R. Spiegel et al (2009). Probability and Statistics. The McGraw-Hill Companies Inc.
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OR
For easy understanding and interpretation, you can use OC Calculator in percentage.
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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).
The use of OpenBook Cochran Calculator can be referenced in your thesis or dissertation as:
OpenBook Cochran Calculator, 2022. OpenBook Sample Size Calculators. OpenBook Communications and Technologies, Nigeria. https://www.openbookpage.com/
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.
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ACADEMIC PROJECT
What is an Academic Project?
Formulating a Project Title of a Project
A comprehensive project title should be brief and must identify the population of interest, and the independent and dependent variables. Students should also adhere to the stipulated requirements related to the length of the project title.
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An abstract should provide a summary of the academic project. Generally, an abstract is placed before the table of contents. A comprehensive abstract should highlight all the essential aspects of the project. Students should be cautious not to exceed the required length of the abstract that is estimated at 150-250 words. A comprehensive summary should highlight the project’s hypothesis, objectives, methodology, and findings.
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Conducting a Literature Review
Guidelines for Writing the Method/Approach Section
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