How to calculate sample size

How to calculate sample size

In statistics, calculating the sample size is an essential step when conducting research or surveys. This article discusses how to calculate sample size using writing patterns.

sample size, statistics, research, surveys, writing patterns


In statistics, calculating the sample size is an essential step when conducting research or surveys. The sample size determines the number of participants that you need to include in your study to achieve a certain level of accuracy or confidence. The sample size is influenced by several factors, such as the population size, the confidence level, the margin of error, and the variability of the data. In this article, we will discuss how to calculate sample size using writing patterns.

Step 1: Define Your Population

The first step in calculating sample size is to define your population. This refers to the group of individuals or objects that you want to study. You need to have a clear idea of who your target audience is before you can begin selecting your sample. For example, if you are conducting a survey to find out about the eating habits of college students, your population would be college students.

Step 2: Select a Confidence Level

The next step is to select a confidence level. This refers to the level of accuracy that you want to achieve in your research. The most common confidence level used in research is 95%, which means that you can be 95% confident that your results are accurate. However, you can select a higher or lower confidence level depending on your needs.

Step 3: Determine the Margin of Error

The margin of error is the amount of error that you are willing to accept in your research. This is usually expressed as a percentage. For example, if you want to have a margin of error of ±5%, this means that your results can be off by 5% in either direction. You need to determine the margin of error that you are willing to accept before you can calculate the sample size.

Step 4: Choose a Writing Pattern

There are different writing patterns that you can use to calculate sample size. The most common patterns are the “Taro Yamane” formula, the “Slovin’s formula,” and the “Krejcie and Morgan” formula. Each formula has its advantages and disadvantages, and you need to choose the one that is most appropriate for your research. We will be using the Taro Yamane formula in this article.

Step 5: Calculate the Sample Size

The Taro Yamane formula is as follows: n = N / (1 + Ne^2). In this formula, n represents the sample size, N represents the population size, and e represents the margin of error. To use this formula, you need to multiply your population size by your desired sample size. Then, divide the result by the sum of 1 plus the product of your population size and the square of your desired margin of error.

Step 6: Apply the Formula to an Example

Let’s say that you want to conduct a survey about the job satisfaction of employees in a company with a population size of 1000. You want to achieve a 95% confidence level and a margin of error of ±5%. Using the Taro Yamane formula, you can calculate the sample size as follows: n = 1000 / (1 + 1000(0.05)^2) = 278. You need to select a sample size of 278 employees from the company.

Step 7: Verify the Sample Size

After calculating the sample size, you need to verify that it is appropriate for your research. One way to do this is to use a sample size calculator, which can help you determine if your sample size is large enough to achieve the desired level of accuracy. You also need to consider other factors that may affect your research, such as the homogeneity of your population and the complexity of your research questions.

Step 8: Select Your Sample

Once you have calculated your sample size, the next step is to select your sample. You need to ensure that your sample is representative of your population and that it is selected randomly. This means that every member of your population should have an equal chance of being selected for your sample. You can use different sampling methods, such as simple random sampling, stratified sampling, or cluster sampling, depending on your research design.

Step 9: Collect Data

After selecting your sample, you need to collect data from your participants. This can be done through surveys, interviews, questionnaires, or other research methods. You need to ensure that your data collection tool is reliable and valid, which means that it measures what it is supposed to measure and produces consistent results.

Step 10: Analyze Data

Once you have collected your data, the next step is to analyze it. You can use different statistical methods, such as descriptive statistics, inferential statistics, or regression analysis, depending on your research questions. You need to ensure that your data analysis is appropriate for your research design and that it produces meaningful results.

Step 11: Interpret Results

After analyzing your data, you need to interpret the results. This means that you need to draw conclusions from your data and explain what they mean in the context of your research questions. You also need to consider the limitations of your research and the implications of your findings for future research or practice.

Step 12: Report Findings

Finally, you need to report your findings. This can be done through a research paper, a presentation, or other means. You need to ensure that your report is clear, concise, and well-organized, and that it follows the standard conventions of academic writing. You also need to acknowledge the contributions of others and provide references for your sources.

Step 13: Revise and Improve

After reporting your findings, you may receive feedback from your peers, reviewers, or supervisors. You need to revise your work based on their comments and suggestions and improve the quality of your research. This may involve conducting further analysis, collecting more data, or refining your research questions.


Calculating sample size is a crucial step in conducting research or surveys. By following these steps and using writing patterns, you can ensure that your sample size is appropriate for your research design and that your results are accurate and reliable. Remember to select a representative and random sample, collect reliable and valid data, analyze your data appropriately, and report your findings clearly and concisely.

Related video of How to calculate sample size