Part One – Hypothesis Testing

Read Lecture Four. Lecture Four starts out with the five-step procedure for hypothesis testing. What is this? What does it do for us? Why do we need to follow these steps in making a judgement about the populations our samples came from? What are the “tricky” parts of developing appropriate hypotheses to test? What examples can you suggest where this process might be appropriate in your personal or professional lives?

Part Two – T-tests

Read Lecture Five. Lecture Five illustrates several t-tests on the data set. What conclusions can you draw from these tests about our research question on equal pay for equal work? What is missing from these results to give us a complete answer to the question? Why?  

Part Three – F-test

Read Lecture Six. Lecture Six introduces you to the F-test for variance equality. Last week, we discussed how adding a variation measure to reports of means was a smart thing to do. Why does variation make our analysis of the equal pay for equal work question more complicated? What causes of variation impact salary that we have not discussed yet? How can you relate this issue to measures used in your personal or professional lives?

 

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Discuss the differences among the three major components of statistical methodology (descriptive statistics, statistical inference, and predictive statistics). Why might these distinctions be important to a manager? Refer to this week’s lecture before crafting your post.

Week Four Lecture

Statistical Thinking and Application

Chapter 10 describes concepts of statistics, statistical thinking, statistical methodology, sampling, experimental design, and process capability. 

Watch the following video for a few of the major reasons to study statistics: Statistics in Schools – Why Statistics?

The following video is an example of some of the ways statistics are used within the U.S. Census Bureau: World Statistics Day: Statistics All Around Us

Statistical Methods

• Descriptive statistics
• Statistical inference
• Predictive statistics

One of the biggest mistakes that people make in using statistical methods is confusing data sampled from a static population (cross-sectional data) with data sampled from a dynamic process (time series data).

• Enumerative study – analysis of a static population
• Analytic study – analysis of a dynamic time series

Analysis of Variance (ANOVA)

• ANOVA is a methodology for drawing conclusions about equality of means of multiple populations.
• ANOVA tests the hypothesis that the means of all populations are equal against the alternative hypothesis that at least one mean differs from the others.

Regression and Correlation

• Regression analysis is a tool for building statistical models that characterize relationships between a dependent variable and one or more independent variables, all of which are numerical.
• Correlation is a measure of a linear relationship between two variables, X and Y, and is measured by the (population) correlation coefficient.

Six Sigma and Process Improvement

Chapter 11 brings the Six Sigma concept into sharp focus, and builds on the need to integrate a performance management framework with operational requirements in managing quality. In this chapter, we introduce the statistical basis for Six Sigma, and outline the requirements for Six Sigma implementation. This chapter also extends the concepts of Chapter 10 on statistical thinking and introduces the 7 QC Tools used for kaizen — continuous improvement — Six Sigma and “lean” projects.

• Juran defined breakthrough as the accomplishment of any improvement that takes an organization to unprecedented levels of performance.
• The objectives of Six Sigma often focus on breakthrough improvements that add value to the organization and its customers through systematic approaches to problem solving. 
• “Six sigma” represents a quality level of at most 3.4 defects per million opportunities (dpmo). (In other words….99.99966% accuracy). Sigma (σ) is the Greek letter that is used to designate standard deviation.

A six sigma quality level corresponds to a process variation equal to half of the design tolerance while allowing the mean to shift as much as 1.5 standard deviations from the target.

DMAIC Methodology

1. Define
2. Measure
3. Analyze
4. Improve
5. Control

The “Seven QC Tools”

1. Flowcharts
2. Check sheets
3. Histograms
4. Cause-and-effect diagrams
5. Pareto diagrams
6. Scatter diagrams
7. Control charts

Run charts show the performance and the variation of a process or some quality or productivity indicator over time in a graphical fashion that is easy to understand and interpret. They also identify process changes and trends over time and show the effects of corrective actions.

Control Chart 

• Focuses attention on detecting and monitoring process variation over time
• Distinguishes special from common causes of variation
• Serves as a tool for on-going control
• Provides a common language for discussion process performance

A Pareto distribution is one in which the characteristics observed are ordered from largest frequency to smallest. A Pareto diagram is a histogram of the data from the largest frequency to the smallest.

Additional tools include Cause and Effect diagrams, scatter plots, checklists, histograms, pie charts, etc.

Forbes School of Business Faculty

 

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