# Sample Size

The sample size is a measure of the number of individual samples that are present or have been observed during an experiment or a survey conducted. To understand it a little better, we can take an example. If we test 100 plants for a certain type of disease-causing virus, the sample size is 100. To carry out the survey, you received a 30,500 complete set of questionnaires, then the size of the sample is 30,500. The sample size in statistics is represented by the letter ‘n.’ Hence, the Sample Size definition is a measure of the number of samples for a particular study or research.

Factors Contributing To Sample Size Collection

There are certain factors which are taken into consideration before determining the sample size of a particular experiment or a study. These are-

• Size of the population– The size of the population that is being studied is the first thing that is considered to. The study that involves the conclusion from a larger area says an entire country will require a larger sample size in comparison to studying that includes smaller areas like a state or a city. The margin of error- Is another thing that is considered. Given the fact that the data that has been collected is accurate to what extent? There are high chances of errors in the data, so the margin of error is always considered.

• Standard deviation – Standard deviation refers to the amount of deviation seen in the individual sample and the whole group of samples. Let’s say, for example, if the samples of soil are collected from a park, they are likely to show lesser deviation in the amount of nitrogen content in them, as opposed to the samples of soil that have been collected from across the nation.

What Dangers Are Related to Small Sample Size?

It has been said that smaller the smaller size, more in the accuracy of the findings!/Let us understand this by an example. A team decided to study how many people exercise daily in a country and what they did was pick up 5 people and interviewed them regarding the same. Two of them said that they exercise regularly. The outcome of the study would be that 40% of the population exercise regularly, and this would represent the country as a whole. The data does carry a lot of inaccuracy, and the Margin of error is quite high. So smaller the sample size, the higher are the margins of error and vice versa. Hence, it is advisable to select a large sample size to conduct any given experiment or study.

Calculating the Sample Size

To calculate the size of the sample, the figures you need are- Desired confidence level, margin or error, the total number of people in the population. There are two sample size formula-

1. Sample Size Calculation is Done In the Following Manner

Sample size can be calculated by (Percentage Distribution of 50)/ (?percentage of Margin of error/ Score of confidence level) squared)

2.  Finite Population Correction-

True Sample is equal to –(Size of sample*Population)/ (Size of sample+Population-1)

Understanding the concept of Sample Size better

The Sample Size examples would let us understand the concept even better. So here is one

In a given society the height of its residents is normally distributed at a standard deviation of 5 inches. Then, how will we find the minimum sample size required to construct a case study with the confidence level being 95% and the margin of error being 0.5 inch

The formula to determine the sample size is, n= [Zα2σE ]

Where, E= 0.5 inch σ = 5 and α = 1 – 0.95 = 0.05

Hence, Zα/2 = Z 0.025 = 1.96

n=(Zα2σE)2

Putting the values, we get

N=[1.96(5)0.5]2

Which comes out to be 384.16 and if we round it off, it is 385.

Conclusion

Not only a small sample size, but even the larger one is a problem. The interpretation with such large samples makes it difficult for the research and also affects the figures. Hence, it is not recommended to take larger samples. A moderately good amount of sample is what should be taken in order to obtain accurate results. Though there is no specified limit to decide the sample size but there are few thumb rules that can be followed. One of them says a minimum of 30 samples should be taken, and another says 12 minimum samples should be considered before carrying out a study.

1. What is sample size justification?

Sample size justification is as important as sample size itself. If a researcher is not able to justify the sample size, he cannot validate a valid study at all.

2. What are the main factors influencing the sample size?

The main factors are the total size of the population, the margin of error, the level of confidentiality, and the standard deviation.

3. What does an ideal sample size look like?

The size of an ideal sample should neither be too small nor too big because both these tend to influence the accuracy of the result and hence the study reveals inaccurate conclusions.

4. How to determine the sample size for a pilot study?

When you are estimating the sample size for a pilot study, the simplest methods are to apply the thumb rules. These are-

According to Browne, the thumb rule is to take at least 30 subjects or greater to derive to a conclusion and Julius states that 12 samples per arm should be taken as a minimum count.

5. Is 30 a good sample size?

This is a question that has created confusion among many. Yes, 30 is supposed to be a good sample size but other factors total population of the area should also be considered before coming to a conclusion of deciding the sample size as 30.

6. What is the percentage of the confidence level that is generally used by the researchers?

It is often seen that researchers during a study use 95% as their confidence level.

7. How is the margin of error related to sample size?

The margin of error and sample size are inversely proportional to each other. As the margin of error increases, sample size decreases, and with the decrease in margin of error, sample size tends to increase.