Introduction
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 that 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. 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 the smaller size, the more accurate 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 formulas-
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 inches.
The formula to determine the sample size is, n= ({Zα/2σ}/E)2
Where, E= 0.5 inch σ = 5 and α = 1 – 0.95 = 0.05
Hence, Zα/2 = Z 0.025 = 1.96
n = ({Zα/2σ}/E)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 there are a 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.
FAQs on Sample Size
1. What are the important terms related to Sample Size?
The important terms related to sample size are-
Population Size- Population size refers to the total number of people that you are trying to study. For example, if you want to get information about teachers in India, the population size will be the total number of teachers in India. The population size should be accurate; it should neither be too small nor too big.
Standard Deviation- The measure of the dispersion of data set from its mean is known as the standard deviation in the data. Determining the standard deviation is very important in order to anticipate the variation in the measures while studying. The standard deviation and the magnitude of the deviation is greater when the dispersion or variability is high.
Confidence level- Confidence level represents the accuracy of the data. The confidence level is aligned to the confidence interval and is represented in percentage. For example- if the confidence level is 95%, then the chances of your data being accurate will be 95%.
The margin of error or Confidence interval- There are very rare chances that any survey conducted is 100% correct. The confidence interval can be described as, for a certain proportion of time, the probability that a population parameter will fall between a certain value.
2. What are the limitations to the calculated sample size?
The limitations while calculating the sample size are-
Before initiating any study or research, the sample size always has to be calculated first as it is very important to know your target population first before you conduct a survey otherwise the survey would be of no use.
The sample size cannot be changed throughout the study course, if done there will be an error in the results.
Practical issues such as administrative issues and costs influence the sample size calculation.
3. What are the methods of sampling?
The process used to analyze a predetermined number of observations out of a large population is known as Sample. This predetermined number is also known as the sample size which is the first step of the sampling technique. There are two types of sampling techniques- probability and non-probability sampling.
Probability Sampling | Simple Random Sampling Systematic Sampling Cluster Sampling Stratified Random Sampling |
Non-Probability Sampling | Convenience Sampling Judgemental or Purposive Sampling Quota Sampling Snowball Sampling |
To study the above sampling techniques in detail, Vedantu has provided study material based on Sample Size and Sampling Techniques in Research.
4. Describe the thumb rule for sample size.
When you don’t have information on the population variability, the sample size is chosen according to the rule of thumb. The popular rule of thumb is the sample size 30 which means 30% of the population as the sample size. Therefore, for unknown population variability, sample size 30 is considered to be appropriate. If the sample size is greater than or equal to 30 then the distribution will be approximately normal and the sample size is said to be large enough.
5. Which sampling method is the easiest?
The sampling method which is considered to be the easiest is the convenience sampling method. The convenience sampling method is the one in which the participants are usually selected on the basis of their willingness to take part in the survey and their availability. Convenience sampling is very economical and less complicated. Researchers can observe the habits and opinions of the respondents in the easiest possible manner by using the convenience sampling method while conducting research.