Probability, Sampling, and Hypothesis Testing

The First Session

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The First Session

Probability, Sampling, and Hypothesis Testing (and the subsequent module, Statistical Experiments) focuses on applying statistics to test for differences between a proposed “model” of a “process” and the real “process.”

The modeling (learning) process is accomplished through repeated inductive and deductive steps. Inductive model development (i.e. a hypothesis, a conjecture, or a theory) based on data (facts or observations) is used first, then model testing where new data is collected, with either an acceptance of the model, or the inductive creation of a modified or new model followed by new testing. This process is discussed in detail in Chapter One of the text Statistics for Experimenters and in Box's article "Scientific Method: The Generation of Knowledge and Quality" which discusses the Wright Brothers application of this deductive-inductive process in hundreds of experiments that made it possible for the first flight. Moen, Nolan and Provost in their book discuss this deductive-inductive improvement cycle in the more familiar context of the Shewhart or Deming cycle, or as we typically know it the Plan-Do-Study-Act Cycle.

The typical five questions to be answered while creating and testing a theory are:

1. How can I describe this population? (Descriptive Statistics)
2. How certain am I about the reported results? (Confidence Limits)
3. Are there differences in some indicator(s) between groups that belong to certain categories or were treated differently? (Hypothesis testing)
4. Are there relationships between variables in the sense that they tend to vary together? (Correlation)
5. Is there a causal relationship among one or more independent variables and a dependent variable? (Regression)

ALT #1: Tired Paper Clips provides you with visual tools to help you describe the population. In ALT #2: A Trip to Pennyville and ALT #3: Return to Pennyville, you explore reported certainty about our results. In the final four ALTs, you apply various statistical tools to answer the question of whether there are differences between two populations.

The module that follows, Statistical Experiments, addresses differences among multiple populations and determining relationships among variables.

For more information about the statistical methods/tools presented within this module, seek guidance by reading works by Sir Ronald Fisher, A. J. Duncan, W. E. Deming, D. J. Wheeler, W. A. Shewhart, and appropriate ANSI standards.

On-Line Statistical “Textbooks":

The solutions provided in this module extensively use the data analysis package in Excel.

References:

  • Box, G.E.P. (1997). Scientific Method: The Generation of Knowledge and Quality. Quality Progress, 30, 47-50.
  • Box, G.E.P., Hunter, W.G., & Hunter, J.S. (1978). Statistics for Experimenters. New York: John Wiley & Sons.
  • Duncan, A.J. (1986). Quality Control and Industrial Statistics (5th ed.). Irwin: Homewood, IL.
  • Moen, R.D., Nolan, T.W., & Provost, L.P. (1999). Quality Improvement Through Planned Experimentation (2nd ed.). New York: McGraw-Hill.
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