To find out the potential X'sInstructor : OK, we've know where we're starting from and where we're going, so now the real detective work starts. What are the variables that are preventing us from reaching our goal? Remember, we're looking for the Vital X's that can influence our Y, what the customer cares about.
Instructor : So we now know where our process currently is and what our eventual goal will be. Let's look at the learning objectives for Step 6. By the time you finish this section, you will be able to:
> Explain the purpose of a hypothesis test
>Define the terms random sample, null hypothesis, alternative hypothesis, type I error, type II error, p-value, and confidence interval
>You will be able to Identify and explain the tools (for each data type) that can be used to analyze the influence of the X's on a Y (1 and 2 sample T tests, homogeneity of variance, 1-way ANOVA (analysis of variance), Scatter plot, and Simple Regression)
>You will be able to evaluate the results of a T test.
>Finally, you will be able to identify potential sources of variation in a process, which is the primary reason for this step in the overall D M A I C process.
Instructor : Hypothesis testing provides a statistical comparison of two samples and of one sample to the population.
Instructor : It provides an objective basis for concluding whether there is a difference between them.
Instructor : There are a number of reasons to do hypothesis testing.
Instructor : There are a number of reasons why hypothesis testing is a fundamental concept in executing a DMAIC project.
Instructor : First of all, determine if there is a significant difference between processes. In those cases, the formal hypothesis test will indicate objectively whether or not there is a difference, thus leading all parties to come to the same conclusions and make the same decisions in a collaborative manner.
Instructor : Once we have identified these factors and made adjustments for improvement, we need a way to validate that improvement.
Instructor : Finally, we need to identify factors which impact the Mean or standard deviation of the process.
Instructor : A hypothesis is a statement of assumptions. You can make a hypothesis about virtually anything and then statistically test it. For every hypothesis there is an alternate hypothesis. Hypothesis testing is done by applying a number of statistical tools to the data to compare alternative explanations, which we call the Null Hypothesis and the Alternative Hypothesis. In order to proceed, we must be very clear concerning definitions.
Instructor : A Null Hypothesis, often referred to as H-sub zero, is a statement of status quo. It presumes no change. If you are comparing two product lines, processing machines, or other industrial processes, a null hypothesis claims that there will be no difference if observed over time.
Instructor : Let's take as a Null Hypothesis, the following statement:
Instructor : GE's nut removal time is equal to the competitor's nut removal time. Remember, this is the hypothesis which we are looking to reject.
Instructor : An Alternative Hypothesis, often referred to as H-sub-A, is a statement of difference. It is often a statement of something we want to prove. An example would be that if we observe the production of a given part with two different kinds of machine tool, there will be a significant difference over time.
Instructor : GE's nut removal time is not equal to the competitor's nut removal time.
Instructor : We now have our hypotheses defined, but before we actually start the testing, we should look at the risks associated with this process.
Instructor : There are a number of other tools and terms which address various aspects of hypothesis testing depending on the circumstances involved.
Instructor : The risks associated with hypothesis testing are divided into two categories of potential errors.
Instructor : A Type I error is rejecting the Null Hypothesis when the Null Hypothesis is true.
Instructor : A Type II error is failing to reject the Null Hypothesis when in fact the Null Hypothesis is false.
Instructor : Alpha expresses the probability of committing a type one error
Instructor : While beta expresses the probability of committing a type two error.
Instructor : In the
Instructor : So we can use the statement "The defendant is innocent" as a null hypothesis.
Instructor : It follow that the alternative must be "The defendant is guilty."
Instructor : Convicting an innocent person would be a Type I, or alpha, error.
Instructor : While freeing someone who is truly guilty would be a Type II, or beta, error.
Instructor : Another way to look at the two types of error is in this format. In this case we are looking at whether or not to accept and stock finished goods
Instructor : The Null Hypothesis states the usual status quo; the products meet specifications and are accepted and stocked
Instructor : The Alternative Hypothesis states that the finished goods fail to meet specifications and are rejected.
Instructor : If you reject goods when in fact, the goods meet specifications, you are committing a Type I error.
Instructor : If you stock goods, when in fact they do not meet specifications, you are committing a Type II error.
Instructor : There are five basic steps to hypothesis testing
>The first step is to confirm that the samples you test are representative of the process, and that they have normal distribution.
>Then you must lay out clear statements of your Null and Alternative Hypotheses.
>Next you must determine which test to use. Some choices include the T Test and the Analysis of Variance, or ANOVA for difference in means, and Homogeneity of Variance test for difference in standard deviations.
>Fourth, you run the test
>Finally, you interpret the results.
Instructor : The hypothesis test will provide the statistical basis for rejecting or accepting the Alternative Hypothesis.
Instructor : The test statistic (called a P Value) indicates the probability of making a Type One error. You will use it to decide whether to reject or not reject the Null Hypothesis.
Instructor : The Null Hypothesis is assumed true unless otherwise shown. This is the "innocent until proven guilty" statement.
Instructor : The value that answers this question critical item in this case is the p value.
Instructor : The p value in this case is less than zero point zero five, indicating a less than five percent chance of making a type one error.
Instructor : This means that the Null Hypothesis is rejected and we accept the alternative hypothesis. Our next task is to identify potential variations, including differences between our process and that of our competitor.
Instructor : In order to identify the source of variation, we must look at all of the possible areas that may provide differences between the two processes and be the cause of the variation. A Fishbone diagram is often a good starting point.
Instructor : We place the title Removal time too long in the title box of the fishbone diagram. Let's see what categories we can define for potential causes of variation that lead to this result.
Instructor : Some areas we can look into include the tools used in the process,
Instructor : The various factors associated with the people doing the work
> The environment in which the work is done
> The methods used to remove the nuts, including heating them when they won't come off.
> And the type of nut used. There is one extra space, it we think of any other categories, but this seems to cover everything necessary for this process.
Instructor : First, let's look at the factors associated with the people. There are four items listed under this title.
Instructor : Here is our completed fishbone diagram. If we think about something that we can test easily and which may make a significant difference, what would you pick? You won't find out until the Improve phase.
Instructor : Other tools, such as the F M E A and the Q F D could have been used to potential causes as well. Different tools may be appropriate for different circumstances. However you do this brainstorming exercise, it will help your planning on either the experimentation or the data mining which will complete the search for potential Vital X's. Some variables may be discarded at this point if historical data exists to justify that action. If the effect of a variable is unknown, it should be added to the list of potential Vital X's
Instructor : However you discover them, some of these potential causes produce continuous data and some produce discrete data. There are different tools for handling the two data types.
Instructor : Besides the 2-sample T-Test, which we have recently used, there is also a 1-sample T-Test. There are a number of other tools for hypothesis testing with continuous data. These tools can be used to determine which X has what level of impact on Y.
Instructor : The Homogeneity of Variance test determines if the variances between two populations are the same.
Instructor : The Anova, or Analysis of Variance test allows you to compare the centering of multiple populations or samples.
Instructor : Scatter plots and simple regression allow you to assess the relationship between two variables.
Instructor : There are two primary tools used for discrete data. The Chi-Square analysis and Logistic Regression are both useful in dealing with discrete items. Logistic regression allows you to investigate the relationship between a categorical response variable (a discrete type of data) and one or more predictors. The resulted prediction functions are often used for optimizing the process. When both the response variables and predictors are discrete, the Chi-square test allows one to investigate their relationship. More information on these can be found in the Resources section.
Instructor : We have now identified many potential sources of variation, but we still have to discover the Vital Xs which will lead us to our solution.
Instructor : It's really easy to get caught up in the details of the process, so it's time to step back and look at what we've done in the this step.
Instructor : Well, here we are at the end of step six, and the end of the Analyze phase. Before I turn you back over to Master, let's recap what we accomplished here in step six.
Instructor : We examined the purpose of Hypothesis Testing,
Instructor : We identified and explained the tools used in this step,
Instructor : We performed a two-sample T-test
Instructor : and evaluated the results of the T test used to compare groups of data.
Instructor : Finally, we used a cause and effect, or fishbone, diagram to brainstorm possible sources of variation. This will be the starting point for the next phase.
Instructor : The statistical tools which we use allow us to analyze historical data in order to reduce the number of variables to investigate in the Improve Phase. You'll get to see them at work in the next section of this course.
Instructor : You've done a great job with the Analyze phase and it's been a pleasure being your instructor. However my job is done and I'm going to turn things back over to Master so he can take you to Improve
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