POPULATION AND SAMPLE

While population parameter and sample statistics may appear to be similar and even represent the same element, they are quite different in reality. A population parameter describes a characteristic of the entire population. On the other hand, sample statistics describe a sample drawn from a certain population. The population parameters are difficult to obtain the exact figure unlike the sample statistics, which can be established to exact figure. Every population parameter has a corresponding statistic that can be measured. The population parameter is a fixed number compared to sample statistics that is dependent on the sample size (Taylor, 2018).

Methods of Estimating Population Parameters

Among the common methods for estimating population parameters is the method of Ordinary Least Squares. This method is based on the idea of selecting a line that represents an average relationship of the observed data. The OLS regression line is placed in a such a way that the sum of the squared distances between the dots and the regression line becomes minimized as much as possible. 

Another method of estimation population parameter is the maximum likelihood estimation. This method attempts to find the parameters values that maximize the likelihood function from a particular observation. This method yields a maximum likelihood estimate.

Confidence Interval

This refers to a type of interval estimate that is calculated from the statistics of the observed data that includes a true value of an unknown population. It indicates the frequency of potential confidence intervals that may hold the value of the unknown population parameter. It is, therefore, comprised of a range of possible values representing an unknown population parameter (Greenland et al. 2016).

Margin of Error

This represents the range of values below and above the sample statistic in a confidence interval. The margin of error indicates how many percentage points the results acquired will differ from the real population value. 

E= z_α/₂ (ϭ/√ n)

The formula above calculates the margin of error for the confidence level of a population mean.

The margin of error = Critical value x Standard deviation of the statistic

This formula represents the margin of error for sample statistics. 

References

Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European journal of epidemiology, 31(4), 337-350.Taylor, C. (2018). Learn the Difference Between a Parameter and a Statistic. Thoughtco. Retrieved from https://www.thoughtco.com/difference-between-a-parameter-and-a-statistic-3126313