Lesson 7: Understanding Uncertainty

Lesson Overview Section

Figure 7.1 illustrates key aspects of the Statistical Paradigm.  We are interested in the characteristics of a population or how it might behave under different real-world conditions.  To investigate, we take an appropriate sample or compare samples under different conditions (Lessons 1 and Lesson 2).  Our samples then produce data that must be described and/or compared using appropriate measures, statistical summaries, and pictures (Lesson 3 to Lesson 6). Next, in order to use those statistics to make inferences about the population, we must consider what types of samples or differences between groups might happen just by chance - that is the topic of probability that we examine in this lesson.

 

Statistical Paradigm

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Probability

The rules of probability can tell us the likelihood of different types of samples that might arise from a particular population.

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Inference

We want to infer what parameter values are most consistent with the sample statistic at hand.

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Conclude

What does our knowledge of the parameter values tell us about the population?

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Describe and Compare

Data is collected from the samples and, with sample data in hand, we attempt to create statistical summaries and pictures that give the salient features of the data collected.

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Samples

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Statistical Summaries and Pictures

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Population

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Parameters

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Figure 7.1 Key Components of the Statistical Paradigm

 

Life is riddled with decisions that must be made in the face of uncertainty.  What time should your friend pick you up at the airport given the uncertainty in the arrival time of your flight? Should you take an umbrella on your hike given the uncertainty in the weather forecast? Is it better to have the surgery or take the new medication given the uncertainty in the clinical outcome? Should you bet on the favorites or go for the underdogs in your office March Madness basketball pool?  Statistics help us to address the myriad of problems of this type by directly quantifying the uncertainties in life.  Probability is the language of certainty.  This lesson provides insights into this language's basic grammar - the rules that govern the quantification of uncertainty.

Objectives

After successfully completing this lesson you should be able to:

  • Identify and apply the relative frequency interpretation of probability.
  • Apply the basic rules of probability.
  • Set up a calculation for and interpret an expected value.
  • Interpret how proportions and averages converge when the chance process generating them is repeated independently.
  • Set up and interpret a random simulation to estimate a probability.