Module 5 Hypothesis Test for Multiple (>2) Groups

Lesson M05-03

Duration: 30 minutes

If the null hypothesis of equality of all group means is rejected, we can use a multiple comparisons procedure to investigate which pairs of groups are the same and which are different.  We cover the use of Tukey’s Paired Comparison test which allows us to control the overall type I error across all of the individual tests.  The Minitab output is explained and participants will practice with an exercise. 

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 5 pages 30-39

Module 5 Hypothesis Test for Multiple (>2) Groups

Lesson M05-02

Duration: 10 minutes

In Lesson 2, we cover some examples of performing ANOVA to test for the equality of means.  The assumptions to use this test are discussed as well as the methods used to verify the assumptions.  Residual plots are generally used to do this.

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 5 pages 19-29

Module 5 Hypothesis Test for Multiple (>2) Groups

Lesson M05-01

Duration: 16 minutes

In the first lesson, we introduce the problem of testing whether multiple (>2) means are equivalent.  The procedure typically used to do this is called Analysis of Variance (ANOVA).  While the technical details of ANOVA are a bit beyond the scope of this course, we introduce the key ANOVA table entries and how they relate to the performance of an F test which compares the variance between groups to the variance within groups as a way to test for equality of means.  The key ANOVA terminology and terms are briefly described for those interested, but the important thing is correctly applying the method using MINITAB. 

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 5 pages 1-18

Module 4 Hypothesis Tests for Two Groups

Lesson M04-05

Duration: 37 minutes

In this lesson we discuss testing for two proportions.  As with the 1-sample case, we first discuss the traditional approach of applying the normal approximation to the binomial distribution (and the conditions for which it applies).  We also discuss using the binomial distribution as well as Fisher’s Exact test which uses the Hypergeometric Distribution.  Minitab will perform the analysis using the Normal Approximation as well as Fisher’s Exact test.  Examples and exercises using these approaches are provided.  

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 4 pages 54-63

Module 4 Hypothesis Tests for Two Groups

Lesson M04-04

Duration: 31 minutes

Pairing implies that the data values in two groups have some element in common.  For example parts from two cavities on an injection molding machine that are produced in the same shot, or two measurements on the same part.  When pairing exists, the Paired t test should be performed because it allows us to test for differences without part to part or cavity to cavity differences affecting the error.  In other words, accounting for the paired nature of the data allows us to detect much smaller differences in the means since a potential source of nuisance error is controlled (e.g. sometimes referred to as blocking).  The paired t test approach is very different than the standard 2-sample t test.  The mechanics are explained and then an example and exercise follow.  

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 4 pages 41-53

Module 4 Hypothesis Tests for Two Groups

Lesson M04-03

Duration: 23 minutes

When we desire to show that two process means are equivalent, then the equivalence test should be used.  Here the null hypothesis is that the means are not the same, and rejecting the null hypothesis allows us to show that the means are equivalent (within a range of practice equivalence) with a specified confidence level.  So, we must be prepared to specify the largest difference in the means that would still be considered practically equivalent. As usual, after the test mechanics are explained, and example and exercise follow.

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 4 pages 36-40

Module 4 Hypothesis Tests for Two Groups

Lesson M04-02

Duration: 33 minutes

As in the one-sample case, a 2-sample Z test may be done if the variances happen to be known, although typically this is not the case.  The 2-sample Z test is presented for completeness.  The 2-sample t test is typically used to test for the equality of two process means.  There is a version of the test that may be used if the group Variances are not statistically different and a version that applies if the Variances are different.  The former has higher power, so it should be used when applicable.  Both tests are covered in this lesson.  Examples and exercises conclude this lesson.

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 4 pages 23-35

Module 4 Hypothesis Tests for Two Groups

Lesson M04-01

Duration: 41 minutes

Here, we learn the F test for testing the equality of two variances.  The F Distribution and its characteristics are introduced.  Under the null hypothesis (the variances are equal), the F statistic is just the ratio of the sample variances.  Some examples are presented.  The F-test requires that the data from each group can be well described by a Normal Distribution.  If this isn’t true, a nonparametric test may be performed.  After an example using Minitab is presented, the participants will practice with an exercise.

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 4 pages 1-22

Module 3 Hypothesis Testing Concepts and 1-Sample Tests

Lesson M03-09

Duration: 58 minutes

A Tolerance Interval the range that contains a specified proportion of the data from a process with a specified level of confidence.  The Natural Tolerance Limits are the bounds of the tolerance interval.  Different methods are available depending on if the distribution and parameters are assumed to be known (not likely) or not. Tolerance Intervals and Bounds based on the normal distribution are presented as well as those that make no distribution assumption (non-parametric approach)

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3 pages 63-82

Module 3 Hypothesis Testing Concepts and 1-Sample Tests

Lesson M03-08

Duration: 32 minutes

The Null Hypothesis of standard hypothesis tests for process parameters is a statement of equality.  Rejection of the null hypothesis results in a conclusion of inequality

Failure to reject the null hypothesis is not a conclusion of equality.  For example, the test may lack power to reject the null hypothesis even when the alternate is true.  Equivalence Tests allow us to set up the test to specifically test for equality.  This lesson covers the use of a sample equivalence test to determine if a process mean is equal to a target (or any constant) within a determine margin of practical equivalence. 

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3 pages 56-62

Module 3 Hypothesis Testing Concepts and 1-Sample Tests

Lesson M03-07

Duration: 24 minutes

In Lesson 7, we learn the 1-variance Chi-Square test to test a single process variance to determine if it is equal to a target value.  The Chi-Square distribution is presented and described.  As before, the test statistic/critical value method is introduced along with the use of a p-value and confidence interval.  An example is presented, and an exercise is performed. 

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3 pages 49-55

Module 3 Hypothesis Testing Concepts and 1-Sample Tests

Lesson M03-06

Duration: 35 minutes

When the normal approximation method is not applicable, an alternate approach is needed.  One option is to use the binomial distribution.  The binomial distribution is presented and the use of it to calculate p-values for the 1-sample proportions tests is described.  An example and exercise complete the lesson.  

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3 pages 42-48

Module 3 Hypothesis Testing Concepts and 1-Sample Tests

Lesson M03-05

Duration: 25 minutes

In lesson 5, we learn the traditional method of testing a single proportion using the normal approximation to the binomial distribution.  The conditions for which this method is valid are first presented.  Then, the critical value method (using a Z test), p-values, and confidence intervals are discussed.  The participants then perform an exercise.   

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3 pages 34-41

Module 3 Hypothesis Testing Concepts and 1-Sample Tests

Lesson M03-04

Duration: 40 minutes

Here, we learn the 1-sample t Test which is used to test the mean when the standard deviation is unknown.  The t-statistic is introduced along with its properties.  The three methods of performing a hypothesis test are covered (test statistics and critical values, p-values, and confidence intervals).  An example and exercise conclude the section.

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3 pages 22-33

Module 3 Hypothesis Testing Concepts and 1-Sample Tests

Lesson M03-03

Duration: 27 minutes

In this lesson we learn how to perform the hypothesis test using other approaches:

• Comparing the p-value to the significance level
• Using a confidence interval

We define p-values and learn how to calculate them for the 1-sample Z test.  We also learn how to calculate confidence intervals (2-sided) and also lower and upper confidence bounds around a sample mean which provides an interval (or bound) that is likely to capture the true value.  Examples and exercises using p-values and confidence intervals are included. 

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3 pages 12-21