# How to calculate the sample size of primary research?

The calculation of the sample size is to determine the number of units or items that a researcher needs to include in the sample. Sample size calculation is the fourth step of sampling design and comes after the identification of the population (from which the sample is to be drawn), selection of the sampling unit (geographical location), and the preparation of the source list.

It is important to calculate the size of the sample correctly mainly for two reasons. First, a sample intends to represent a population. Second, the data analysis and its interpretation to draw inferences of research that depends on the number of units for which the data is collected. These units can be responses from participants in a survey collected through a questionnaire.

While writing a research paper, researchers sometimes find it difficult to calculate the sample size. As mentioned by (Kothari, 2004), the sample should neither be too small nor too large. It should be optimum in size and fulfil the following criteria.

- Representativeness
- Efficiency
- Reliability
- Flexibility
- Precision

## Factors that determine the sample size

There are a number of factors that play an important role in calculating the sample. These include,

**Size of the population:**this is the size of the total population from which the sample is to be drawn.**Population variance:**this is the variation present in the population.**Population parameters:**the parameters on which inferences need to be drawn,**Confidence:**it refers to how well the selected sample will represent the population.**Research method:**It refers to a quantitative or qualitative method that the research adopts to answer the research questions.- Costs of collecting the data.
- Budget and time constraint of the researcher.

## Calculation of sample size

Once the above factors are determined, the samples can be calculated in a number of ways.

Using the recommended value of 385 as per Cochran’s sample size for a 5% level of significance or applying the below-stated formula.

n_0 = [z^{2 }*p*(1-p)]/ e^{2}

Where,

- n_0: Sample size
- z
^{2}: Z-score value at the selected confidence level of the study (i.e. 99%, 95%, or 90%) - p: estimated population proportion having an attribute of research
- e: desired precision level or margin of error

However, in the case of a small population, the sample size derived from Cochran’s formula could be adjusted i.e.

n = N*n_0/[N+n_0 – 1]

Where,

- n: adjusted sample size
- n_0: sample calculated via Cochran’s formula
- N: Population size

## Need for knowledge of statistics

In order to correctly calculate the sample, a researcher needs basic knowledge of the concepts of distribution and estimation in statistics along with knowledge of research methods. The following are the important books in this regard for further guidance.

- Research Methods for Business Students by Mark Saunders, Philip Lewis, and Adrian Thornhill. Seventh Edition, 2016, Pearson.
- An Introduction to Statistical Methods and Data Analysis by R. Lyman Ott and Michael Longnecker, Seventh edition, 2015, Cengage Learning.
- Sample Calculations in Clinical Research by Shein-Chung Chow, Jun Shao, Hanshen Wang, and Yuliya Lokhnygina, Third Edition, 2017, Taylor and Francis.

#### References

- Kothari, C. R. (2004).
*Research Methodology: Methods & Techniques*.*New Age International (P) Ltd*. https://doi.org/10.1017/CBO9781107415324.004

## Discuss