Module 11 Introduction

Lesson M11-00

Duration: 3 minutes

Advanced Hypothesis Testing & Regression Reference Textbook – Section 3

In the last module, we discuss regression models that handle discrete responses (binary, ordinal, nominal responses).  Logistic regression is the most common approach although other “link functions” are possible that would result in Probit regression or Gompit regression.  Logistic regression is the most common approach since it has nice interpretive qualities.  

Module 10 Introduction

Lesson M10-00

Duration: 3 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 9

Module 10 expands the Regression models to allow multiple predictors in the model.  With multiple potential predictors, we need to test each one to determine whether they are statistically significant.  We can use p-values to determine whether terms belong in the model or not.  We consider some model building strategies including some automated routines that help determine the best models using various criteria and avoid issues like multi-collinearlty.  We discuss the potential issues of multi-collinearity and highly influential data points and how to detect these issues.  Finally, we learn how to model categorical predictors through the use of indictor variables.  Of course, examples and exercises allow us to fully understand how to develop models in Minitab.  

Module 9 Introduction

Lesson M09-00

Duration: 4 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Sections 7,8

This module covers the development of (linear) predictive models from data with one response and one predictor.  We start with characterizing the strength of the linear relationship between variables through the use of the correlation coefficient.  After introducing some of the key concepts in modeling, we learn the method of use least squares regression to find the best fit line to data where one variable is the predictor and one is the response (output).  Testing the model for validity may be done by analyzing the residuals (differences between the actual responses and predicted responses).  We review an example and also look at how we use models for prediction purposes (along with the inherent uncertainty in such predictions).  We complete the module with an application of Simple Linear Regression, where we develop a model to predict the shelf life of a product.

Module 8 Introduction

Lesson M08-00

Duration: 3 minutes

Advanced Hypothesis Testing & Regression Reference Textbook – Section 5

This Module covers Hypothesis Tests that may be used when specific assumptions of parametric / standard Hypothesis Tests do not hold.  These tests have fewer requirements however they also have less statistical power.  We cover some common nonparametric 1-sample, 2-sample, and multiple sample tests.

Module 7 Introduction

Lesson M07-00

Duration: 5 minutes

Advanced Hypothesis Testing & Regression Reference Textbook – Section 1,2

In Module 7, we prepare for some hypothesis test involving categorial data by first reviewing some common distributions that describe discrete data. Then we cover the chi-square test of independence is used to test whether a relationship exists between categorical variables.  Finally, we learn some of the details of the Fisher’s Exact test which uses the Hypergeometric Distribution and is useful when we have small sample sizes for the Chi-Square test.

Module 6 Introduction

Lesson M06-00

Duration: 4 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 6

So far, we have learned about performing hypothesis tests without major concern about sample sizes.  In this section, we will understand how the sample size affects the Type II error probability (the probability that we fail to reject the null hypothesis when the alternate is actually true).  While several things affect the Power, the only one that we can easily control is the sample size.  It’s important that the sample size be appropriate.  If it’s too small, the power will be low (high probability of making a Type II error).  On the other hand, if the sample size is too large, we run the risk of concluding significant differences exist when they are not actually different from a practical standpoint.  That is, the test can become to sensitive and we may conclude differences exists when they are not meaningful.  So, here we learn how to compute an appropriate sample size for hypothesis tests. We also cover sample size calculations when we are simply estimating a statistic like a mean or standard deviation (so that the margin of error in our estimate is reasonably small).  Finally, we also cover sample size calculations for Equivalence Tests so that if practical equivalence actually exists, we are likely to conclude that based on our test.  

Module 5 Introduction

Lesson M05-00

Duration: 4 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 5

In Module 5, we cover testing multiple process means and variances for equality.  When the groups are not all equal, we may use multiple comparison’s procedures to determine which groups (if any) are equivalent.  Data transformations are sometimes needed to either satisfy normality assumptions or constant variance assumptions.

Module 4 Introduction

Lesson M04-00

Duration: 3 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 4

In Module 4, we cover hypothesis tests for two groups.  That is, we are comparing whether two variances, two means, or two proportions are statistically different with a specified level of confidence.  Because the appropriate two sample means test depends on whether the group variances are equal or not, we start by learning how to test two variances.  In some situations, the data in the two groups is paired (where the first measurement in one group is related to the first measurement in the second group).  In these situations, it is much more powerful to use the paired test to test for differences.  As with the single process hypothesis tests we can use the test statistic/critical value method, use the p-value, or use confidence intervals to test the hypothesis.  

Module 3 Introduction

Lesson M03-00

Duration: 5 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 3

In general, hypothesis testing is used to test any conjecture or theory. Usually, a statistical hypothesis is a statement about the parameter values of some probability distribution. For example, we may hypothesize regarding values of means, variances, or distribution shapes. The idea is that we establish a hypothesis and then we collect a random sample of data from the population or process under study. Then, we use the data to compute an appropriate test statistic which tells us whether enough evidence exists to support the hypothesis given an established level of error. 

To illustrate, we begin by considering hypothesis tests for process/population averages.  The concepts involved in hypothesis testing will be explained in the context of the testing a population mean.  Subsequently, other types of hypothesis tests will be covered such as testing proportions and variances.  Equivalence Tests are introduced in the case of 1-sample.  Finally, the use of Tolerance Intervals is discussed.  Note that the hypothesis tests covered in this first module all involve a single process and the hypothesis involves testing whether a process parameter is equal to a target value (constant).  

Module 2 Introduction

Lesson M02-00

Duration: 7 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 2

Exploratory Graphical Analysis is useful place to begin when analyzing datasets.  Unusual data points may reflect errors in data collection or transcription.  Additionally, obvious patterns may be seen graphically, which can help uncover issues to explore further.  Many types of graphs may be created to explore data over time, relationships between variables, distribution fits, etc.  Graphical Methods are used to:

• Quickly summarize data
• Visually represent descriptive statistics (e.g. mean, median, std. deviation, etc.)
• Prioritize quality problems
• Identify sources of variability
• Study processes over time
• Understand relationships between variables 

Module 1 Introduction

Lesson M01-00

Duration: 3 minutes

Statistics, Hypothesis Testing, & Regression Reference Textbook – Section 1

This module reviews some of the basic ideas and concepts related to statistics and distributions.  Data has various types (e.g., continuous vs. attribute), and the type of data is important for using the right analysis method.  Much of this course deals with statistics that describe central tendency and variation, so they are reviewed here.  The Normal distribution plays an important role in many of the methods discussed in this course, so it is also introduced/reviewed here.  Finally, the Central Limit theorem is useful for understanding some of the differences between raw individual data and averages that are calculated from the raw data.  These ideas related to statistics and distributions will be used throughout the rest of this course.