Statistical research and surveys require data collectors to draw the right inferences by studying their populations. In most cases, it is considered inefficient, time taking, and uneconomical. Hence, samples are derived by using statistical procedures and demographic indicators. Determining sample size and understanding the data can further help draw relevant insights for your research.
One of the conservative strategies to study the population is by forming a good sampling frame and thereby arriving at the most precise sample.
Why Determining Sample Size is Important?
Different studies correlate to different populations. This brings us to the consideration that for different populations, the sample size would also differ. In fact, determining sample size is one of the most crucial steps in statistical studies because the quality of your sample would determine the quality of your study.
The better the study, the more the results would predict the actual responses if the survey was to be conducted on the whole population. In the process of determining sample size for an experiment, it is important to consider these age-old inferences.
- Samples that are too small often become unrepresentative of the population being studied. It is important that for each type of person in the main population, an adequate proportion be maintained in the sample.
If this proportion is changed in order to diversify the sample, the researcher will fail to paint the correct image of the population.
- Samples that are large otherwise prove to be more accurate. However, forming big samples comes at the cost of time and money. It defeats the entire point of sampling at the same time.
- No sample can be drawn in the correct manner if the researcher does not study the population first. Knowledge of the demographics of the main population is the key to arriving at the most meticulously drawn sample.
Determining Sample Size For Quantitative Research
Quantitative research requires enumerators to utilize multiple statistical measures in order to draw a representative sample size. Various sample size determining methods make use of a set of variables that help in arriving at the mathematical figures, which are then substituted in the formula for calculating the correct sample size.
These variables are-
- Size of the population being studied.
- Confidence Interval
- Confidence Level
- Standard Deviation
Let’s dive deeper and take a closer look at them!
- Size Of The Population Being Studied:
Estimating the right population size makes the study all the more reliable. In many cases, it is difficult to ascertain or calculate how big our population is. This limitation is usually overcome by determining a certain range within which the population would fall or taking an approximate figure for the formula.
The population’s size depends on the study’s goal; hence researchers are required to accurately know the scope of their study, i.e., who will and will not become the ‘population’ for that particular research.
- Confidence Interval or Margin Of Error:
This is a ± figure which points out the degree of reliability of the study. Researchers must define a range within which the sample’s responses would correspond if the study was conducted on the whole population.
This means that if the confidence interval lies at 5 and 70% of the population marks an answer, then in the main population, 65% (70-5) to 75% (70+5) are expected to pick the same answer.
- Confidence Level:
How would you know that your confidence interval is valid for your chosen sample and any random samples made from the population?
The confidence level, which is a % figure, tells the researcher how representative the sample is and how accurate the decided margin of error is. This value mostly ranges from 80% to 99%. So if your confidence level is 85%, then as you choose different samples and conduct the same study 85 times, there would be an 85% correspondence between the inferences drawn from your 85 studies.
We thus see a direct relation between the sample size and confidence level, while there is an indirect relation between the sample size and the confidence interval.
- Standard Deviation:
The standard deviation of the sample gives an idea about the standard deviation of the population. It shows how scattered or close the various responses obtained are from each other and also from the mean.
Low standard deviations tell that responses are close to the mean, while high SDs show that they are scattered from high to low values. In research, a standard deviation of 0.5 is considered ideal and safe to draw a sample that is large and more representative of the population.
While there are a number of online sample size calculators available nowadays, we’ll show how a basic sample can be derived if the values are known. The sample size determination formula for an unknown population is –
Sample size = (Z score)2 x Standard Deviation x (1-Standard Deviation) / (Confidence Interval)2
Z-scores are numerical equivalents of the confidence level. For a confidence level of 95%, the Z- score is 1.96.
How To Determine Sample Size Of A Known Population?
The below formula accurately determines the size of the sample when the population size is known :
n = Nx [ Z^2 x p x (1-p) / e^2 ] / [ N – 1 + ( Z^2 x p x (1-p)/ e^2 ]
Sample Size Formula With Example
- Confidence Interval = 95% => Z = 1.96
- Standard Deviation = 0.5
- Confidence Interval = ±7%
Sample Size = (1.96)2 x 0.5 x 0.5 / (0.07)2
Sample Size = 3.8416 x 0.25 / 0.0049
Sample size = 0.9604 / 0.0049
=> Sample Size = 196
This means that 200 would be the required sample size for your study. In empirical studies, though, samples ranging from 400-500 are suggested as the populations are unknown.
On the other hand, if one’s sample is coming out to be very large, then decreasing the confidence level or increasing the confidence interval is suggested.