# Understanding The Relationship Between Sample Size And Accuracy Of Results

## Introduction

When conducting research or experiments, it is critical to ensure that the results are reliable and accurate. One way to achieve this is by ensuring that the sample size is appropriate. The sample size refers to the number of observations or measurements taken from the population under study. The accuracy of the results is directly proportional to the sample size. In this article, we will explore the relationship between sample size and accuracy of results.

## The Importance of Sample Size

Sample size is crucial in research and experiments because the findings obtained from a small sample may not be representative of the entire population. A small sample size may result in biased results, leading to inaccurate or unreliable conclusions. On the other hand, a large sample size provides a more accurate representation of the population, reducing the chances of biased results.

## Determining Sample Size

The determination of sample size depends on the research question, type of study, and the population under study. A general rule of thumb is that the larger the population, the larger the sample size required. Additionally, the level of accuracy desired and the statistical power of the study also affect the sample size determination.

### Statistical Significance

Statistical significance refers to the probability that the results obtained in a study are not due to chance. The level of statistical significance is determined by the significance level or alpha level set at the beginning of the study. A higher significance level requires a larger sample size to achieve the desired level of accuracy.

## The Relationship between Sample Size and Accuracy

A larger sample size provides a more accurate representation of the population, reducing the chances of biased results. This is because a larger sample size leads to a smaller sampling error, which is the difference between the sample and population values. A smaller sampling error means that the sample is more representative of the population, leading to more accurate results.

### Margin of Error

Margin of error refers to the range of values within which the population parameter is expected to lie. A larger sample size results in a smaller margin of error, indicating a greater level of accuracy. A smaller sample size leads to a larger margin of error, indicating a lower level of accuracy.

## Examples of Sample Size Determination

Let us consider two examples to illustrate the relationship between sample size and accuracy of results.

### Example 1: Survey on Student Preferences

Suppose we want to conduct a survey on the preferences of students regarding online learning. The population under study is all college students in the United States. To determine the sample size, we need to consider the level of accuracy desired and the margin of error. Suppose we want a margin of error of 5% with a 95% confidence level. Using a sample size calculator, we find that a sample size of 385 is required.

### Example 2: Medical Trial

Suppose a pharmaceutical company wants to conduct a medical trial to test the effectiveness of a new drug. The population under study is all patients with a particular medical condition. To determine the sample size, the company needs to consider the level of statistical significance, the margin of error, and the effect size. Suppose the level of statistical significance is set at 0.05, the margin of error is 5%, and the effect size is 0.5. Using a sample size calculator, we find that a sample size of 393 is required.

## Conclusion

In conclusion, the sample size is a critical factor in research and experiments. A larger sample size leads to more accurate and reliable results, while a smaller sample size may lead to biased results. The determination of sample size depends on the research question, type of study, and the population under study. Therefore, it is essential to consider the level of accuracy desired, the margin of error, and the level of statistical significance when determining the sample size.