Reference no: EM133501859

Discussion Post: Inferences Based on Two Samples- The Analysis of Variance

Select and post to one of the following options. Alternatively, you can post on a topic of your own creation, related to these chapters (following similar guidelines).

I. Anticipating Your Career

Mason (2010) describes a collection of statistical skills that are typically required of engineers today, sorting them into lists based on whether they might be learned in a single introductory statistics course versus requiring slightly more advanced learning. This class covers almost all of this material, although we don't go as deeply into the more advanced topics. We finished his first basic list, and we introduced his most advanced topic (e.g., SPC) very early in this class. We will introduce many of these topics in the remaining weeks of the class.

Discuss Mason's notion that you are to be an engineer first and a statistician second. What does that mean to you in terms of how you think about the career you are studying to begin, and how do you think this class might impact a job interview you might ultimately go on later in your studies?

II. Variances and Freedom

We learned at the outset of the semester some differences between Variance and Standard Deviation. One important difference is that variances (of independent variables) can be effectively added together to yield new information about the combination, while standard deviations cannot. We're used to taking the square root of the Variance to get the Standard Deviation, although in ANOVA we don't do that. Instead, we apply a Degree of Freedom to find a Mean Squared.

Discuss how and where the adding of Variance concept is being used in the ANOVA technique, and then discuss what is being described by the Mean Squares being calculated.

III. Sampling New RVs

In earlier class units, we saw that a dataset that included the mean values derived from sampling from a dataset with an unknown distribution could be treated as a new random variable, and that this new variable had several important properties.

Explain how collecting mean values (X-bar) from samples drawn from a dataset, regardless of the statistical distribution of the dataset, results in a distribution of those values that is centered on the mean value of the original dataset and is approximately normally distributed depending upon the sample size used. Include the name the theorem that describes this phenomenon, and discuss what it means to treat the X-bar data points derived from sampling as a new random variable. Why is this important in engineering?