Part One: Probability

Case Study #1.1: Sampling Schemes:

A well-defined sampling design is essential to the successful execution of a statistical design. Everything begins with a good sample obtained by use of a sampling design / plan.

Case Description: We will try out different sampling schemes on an actual bowl.

Case Objectives:

Try sampling with replacement - draws with replacement (WR):

That is, draw a color from the bowl, note the color, put it back into the bowl. Mix the bowl. Repeat this process 50 times. Tabulate your results for your bowl. Did the color on one draw tell you anything about the next draw ? List the colors in your sample. What does this tell you about the colors in the bowl, how do you know this, and can you be sure that your list of colors is complete ? How common is each color?

Try census sampling:

That is, draw every single chip from the bowl, that is, draw each chip, note the color, and lay it aside, that is, do not put it back into the bowl. Tabulate your results for your bowl. List the colors in your sample. What does this tell you about the colors in the bowl, how do you know this, and can you be sure that your list of colors is complete ? How common is each color?

There are many different methods of sampling. The choice of sampling used in a design carries with it consequences in the execution of the design, and in the available analysis methods when the design is completed.