09 CHI-SQUARE TEST FOR PROPORTIONS

09 CHI-SQUARE TEST FOR PROPORTIONS
In the 9th Minitab tutorial, we are in the injection molding production of Smartboard Company for the production of skateboard wheels. Skateboard wheels are manufactured by using the injection molding process, for which the technical plastic, polyurethane is used. In the first step, the starting material in the form of polyurethane granulate is thermally liquefied in the injection molding system. In the second step, the liquid polyurethane is then injected into the corresponding mold at high pressure until the mold is completely filled. In the third step, the liquid polyurethane is cooled by high-pressure water cooling. After cooling and solidification, the finished skateboard wheels are automatically ejected from the injection mold in the fourth step, and the mold is released for the next wheel production. Large-scale injection molding production at Smartboard Company is carried out in three shifts, so that the required high quantities can be produced in early late and night shifts, and delivered to customers on time. For some time now however, an increasing number of skateboard wheels have had to be scrapped due to various surface defects. It was therefore decided to launch a quality improvement project, to identify the causes of the increased defect rates. Our central task in this Minitab tutorial will be, to answer the following two key questions on the basis of a sample: 1. Is there a fundamental correlation between the high defect rate, and the respective production shift. 2. are there certain defect types in the respective production shifts, that are generated significantly more frequently than other defect types. The special feature of this task is that we are dealing with more than two categories in which the laws of the so-called chi-square distribution apply. In this training unit, we will learn how to properly perform and interpret the corresponding hypothesis test for chi-square distributed data.

MAIN TOPICS MINITAB TUTORIAL 09

• Preparing the data using the „Recode to text“ function
• Counting variables using the „tally individual variables“ function
• Use of bar charts in the chi-square test
• Identify interaction effects using grouped bar charts
• User-specific bar charts as part of the chi-square test
• Hypothesis definition in the chi-square test
• Derivation of the chi-square distribution from a standard normal distribution
• Number of degrees of freedom in the chi-square test
• Interpretation of the “cross tabulation” function in the context of the chi-square test
• Pearson’s chi-square value and the likelihood ratio