Statistics

Statistics

Chapter 7: Statistical Estimations

Statistical estimations are the given values for a set of known parameters. It is important to note that statistical estimations assume the data is random and the probability distribution is dependent upon the parameters of interest. The given parameters are derived from the measured data. The data set must include at least one component of randomness (usually in selecting the population or assigning a given treatment). The established parameters ultimately will define the distribution of the population of interest. We can further use our known parameters to identify and measure unknown parameters. This chapter will cover basic components and calculations of the Estimation Theory. It may be necessary to refer to previous chapters for terminology.

Learning Objectives

After reading Chapter 7 and completing the workbook, you should be able to:

1. Explain basic statistical estimation tests and predictions. 2. Calculate and define standard deviation of the sample and population.

3. Define and calculate variance. 4. Calculate the degree of freedom. 5. Define and calculate the standard error of the mean. 6. Define and calculate confidence interval.

Study Clues

A clear understanding of the basic statistical estimations presented in Chapter 7 will help prepare you to advance in this course and learn more complex statistical calculations and specific statistical tests. As you study, you should pay particular attention to the definitions, abbreviations and how to calculate each of the following: SEM, SE, and CI. You should refer to previous chapters as all chapters are designed to build from one another.

7.1 Needed Calculations for Estimates

Statistical estimations rely on several calculations defining the parameters. The Standard Deviation (SD) is also represented by the symbol σ (the lowercase Greek letter, sigma). The SD is a measure of how spread (or deviation from the mean). For SD, we are interested in determining how far our results or population is from the mean.

There are two types of standard deviation, each with their own calculation!

Let’s first address the standard deviation of a population : This can be calculation by fining the square root of the Variance. Variance is the average of the squared differences from the mean. That might sound confusing at first. There are three basic steps used to calculate variance.

1st find the sample mean.

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• 2nd find the difference. To do this, subtract the mean from each individual observation or value. Then you square the differences. • 3rd calculate the mean of the squared differences.

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