Sample Size report
Sample size refers to the number of units in a sample, generally represented by n, a critical concept in sampling inference. The sample size is directly related to the accuracy of the inference; that is, in a given overall situation, the larger the sample size, the smaller the representative error of the statistic, and vice versa, the smaller the sample size, the larger the error.
There are various formulas for calculating the required sample size based upon whether the data collected is categorical or quantitative (e.g., estimating a proportion or a mean). These formulas require the population size, margin of error, and maximum deviation.
In general, the sample size is mainly determined by precision, budget, sampling type, type of analysis, etc. In sampling surveys, the determination of sample size is very important. Because the sample size is too large, it will cause a great waste of time, labor, and financial resources. The below post explains more details about sample size.
What is Sample Size
Have you thought about why researchers spend much of their time planning how their studies will be carried out? As the outstanding researchers tell you, a study's results are only as good as its design. Sample size and power are critical elements of study design.
Sample size refers to the number of participants or observations included in a study. This number is usually represented by n. The sample size influences two statistical properties: the precision of our estimates and the power of the study to conclude. Sampling error, though unavoidable, can be eased by sample size. Larger samples tend to be associated with a smaller margin of error.
- If your sample is too small, you may include a disproportionate number of outliers and anomalies. These skew the results, and you don't get a fair picture of the whole population.
- If the sample is too big, the entire study becomes complex, expensive, and time-consuming to run, and although the results are more accurate, the benefits don't outweigh the costs.
The effect survey values have on the accuracy of its results
| Value increased | Value decreased | |
|---|---|---|
| Population size | Accuracy decreases | Accuracy increases |
| Sample size | Accuracy increases | Accuracy decreases |
| Confidence level | Accuracy increases | Accuracy decreases |
| Margin of error | Accuracy decreases | Accuracy increases |
Sample Size Guide
If you would like to do the calculation sample size by hand, use the following formula: N0 = Z2pq divided by e2
- N = population size
- e = margin of error (percentage in decimal form)
- z = z-score.
Z-Score
The z-score is the number of standard deviations a given proportion is away from the mean. A low standard deviation means that all the values will be clustered around the mean number. In contrast, a high standard deviation means they are spread out across a wider range with very small and very large outlying figures. To find the right z-score to use, refer to the table below:
| Desired confidence level | z-score |
|---|---|
| 80% | 1.28 |
| 85% | 1.44 |
| 90% | 1.65 |
| 95% | 1.96 |
| 99% | 2.58 |
Tips for calculating sample size
- If you want a smaller margin of error, you must have a larger sample size given the same population.
- The higher the sampling confidence level you want to have, the larger your sample size will need to be.
To choose the correct sample size, you need to consider a few different factors that affect your research and understand the statistics involved. You will be able to use a sample size formula to bring everything together and sample confidently, knowing that there is a high probability that your survey is statistically accurate.
