The proper selection of the sample size and probability distribution techniques is crucial to epidemiological studies because the two factors significantly influence imperative variables such as variability, frequency, p-values, and significance level in a statistical study. Statisticians combine an array of mathematical models to guide the estimation of the chief factors used to test the hypothesis in a statistical experiment. Collaboration between clinicians and biostatisticians enables clinical experiments to provide feasible results. The essay will analyze the relationship between the fundamental variables in clinical statistical experiments.

The width of a confidence interval depends on the sample size, population variability, and confidence-level in a statistical experiment. Variability describes the difference between data points in a population. It decreases with the increase in the sample size because a small sample provides limited information for statistical analysis. A visual depiction of data in interactive media enhances the analysis of variability levels for different datasets. The visualization of the sporadic distribution of data provides either a representative or distorted picture of the population. Variability introduces challenges in the estimation of the sample size because statisticians can only determine the true variability of a population after conducting a test. Although statisticians can estimate variability using previous tests, assumptions regarding similar trials can lead to poor experimental results.

The practical sample size is essential to the determination of the effect of a treatment. An Overestimation of the sample size leads to a clinically or economically unviable outcome. On the other hand, underestimating the sample size leads to insufficient evidence to demonstrate the effectiveness of a test. Insufficient evidence is likely to influence the abandonment of treatment or healthcare policies that could benefit the healthcare sector.

The calculation of a probability distribution helps to determine the likelihood that an event will have the expected outcome. Statisticians can estimate a probability by dividing the frequency of observation with the total number of observations (sample size). Similarly, multiplying the sample size with a probability produces the expected frequency. Statisticians can modify important variables and obtain the desired value using the mathematical relationship between frequency, probability, and sample size (Faltin, 2012).

For example, a high frequency of alleles enhances the probability of determining the risks associated with DNA mutations. When the alleles under study are rare, biostatisticians can increase the sample size accordingly to gain the desired frequency to detect the risks of diseases. The p-values are significant in hypothesis testing. The values illustrate the probability that the results of a statistical experiment are due to a chance rather than an effect. A low p-value indicates a high probability that the observed outcome is due to a substantial effect. The statisticians will reject the null hypothesis for a low p-value. On the other hand, a p-value that is greater than the predetermined significance level leads to the acceptance of the null hypothesis. Statisticians obtain the p-values by dividing the frequency of each outcome with the sample size. Each p-value symbolizes the portion of the total dataset represented by a score.

## Conclusion

The detection of an effect in a statistical experiment depends on the variability, probability distribution, frequency, sample size, p-values, and the significance level in the evaluation of datasets. Statisticians can determine one variable by initializing the other variables. For example, initializing the population variability, probability distribution, frequency, and significance level for a dataset enables statisticians to evaluate the appropriate sample size for an experiment.

## Reference

Faltin, F. (2012). *Statistical methods in healthcare*. Chichester, West Sussex: Wiley. Web.