# Small sample size

Small sample size |
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**Small sample size** is the practice of using a limited number of subjects or data points in a research study or experiment. In management, it refers to the selection of a relatively small number of individuals for use in a survey, experiment, or other study. Small sample sizes can provide a snapshot of a larger population, but the results may not be representative of the group as a whole and can be subject to bias. While a small sample size may be convenient and less costly, it can lead to inaccurate conclusions or generalizations.

## Example of small sample size

- In a survey of consumer preferences, a small sample size of 100 people may not accurately reflect consumer preferences for a particular product, especially if the target population is much larger.
- A study on the effects of a new drug may only use a small sample size of 10-20 people due to the cost and duration of the study. This small sample size may not provide enough evidence to accurately evaluate the efficacy of the drug.
- A market research study may only survey a small sample size of customers in order to gauge their reactions to a new product. The results from this small sample may not be reflective of the overall customer base, as the sample size is too small.

## Formula of calculating sample size

The formula for calculating the minimum sample size in a population study is:

n = (Zα/2)2 * PQ/d2

where,

n = minimum sample size

Zα/2 = z value corresponding to the confidence level (e.g. for a 95% confidence level, Zα/2 = 1.96)

P = estimated proportion of the population with the characteristic of interest

Q = 1 - P

d = desired precision/margin of error (e.g. if the desired precision is ±3%, d = 0.03)

For example, if we wanted to estimate the proportion of people who support a particular political party in a population of 100,000 with a 95% confidence level and a margin of error of ±3%, the minimum sample size would be:

n = (1.96)2 * 0.5 * 0.5 / 0.03^2

n = 384.8

Therefore, the minimum sample size for this study would be 385 people.

## When to use small sample size

Small sample sizes can be used in situations where time, cost, or other constraints limit the ability to conduct a larger study. For example, small sample sizes can be used when:

- Conducting pilot studies, where a smaller study is used to test the feasibility and effectiveness of an experiment before committing to a larger study;
- Conducting exploratory research, where the main objective is to gain an understanding of a new phenomenon or topic;
- Testing hypotheses, where a small sample size can provide evidence of a relationship between two variables;
- Generating ideas and gathering feedback, where small sample sizes can be used to test new products, services, and ideas;
- Evaluating interventions, where small sample sizes can be used to measure the effectiveness of a strategy or program; and
- Monitoring changes, where small sample sizes can be used to track changes in a population over time.

In all of these situations, small sample sizes can provide useful information, but care should be taken to ensure that the results are not overgeneralized or used to draw conclusions about the larger population.

## Types of small sample size

Small sample sizes can take on a variety of forms, depending on the needs of the researcher. The following are some of the most common types of small sample sizes:

- Convenience Sampling: This type of sampling involves selecting a small group of participants who are conveniently available to the researcher. This type of sample may not be representative of the population as a whole and can be subject to bias.
- Purposive Sampling: This type of sampling involves selecting a small sample of individuals who are specifically chosen for their unique characteristics or experiences. It can be used to focus on specific groups or demographics, but the sample may not be representative of the population as a whole.
- Quota Sampling: This type of sampling involves selecting a small sample that is representative of the population in terms of certain characteristics, such as age, gender, or ethnicity. This type of sampling can be less prone to bias, but it can be difficult to ensure that the sample accurately reflects the population.
- Random Sampling: This type of sampling involves selecting a small sample of individuals from a population using a random process. This type of sampling can reduce bias and can provide a more accurate representation of the population, but the sample size may be too small to provide reliable results.

## Limitations of small sample size

A small sample size can lead to inaccurate conclusions or generalizations, due to several limitations. These include:

- Limited Representativeness: With a small sample size, it is difficult to ensure that the sample is representative of the population as a whole. This can lead to bias and skewed results.
- Increased Variability: With a small sample size, the variance or standard deviation of the data can be greater than with a larger sample size. This can affect the reliability of the results.
- Limited Statistical Power: With a small sample size, the power of a statistical test is reduced. This means that it is more difficult to detect significant differences between groups or to detect relationships in the data.
- Limited Generalizability: With a small sample size, it is difficult to make general conclusions about the population as a whole. This makes it more difficult to draw meaningful conclusions from the research.

## Suggested literature

- McNeish, D. M., & Stapleton, L. M. (2016).
*The effect of small sample size on two-level model estimates: A review and illustration*. Educational Psychology Review, 28, 295-314.