QSO 510 week 7 milestone

Module Six introduced hypotheses and hypothesis testing on a single population mean. Module Seven compares several population means through a statistical procedure called analysis of variance (ANOVA). One-way ANOVA, also referred to as one-factor ANOVA or completely randomized design, is a part of Design of Experiments, a larger subset of statistics used extensively in the automotive, chemical, and medicinal drug industries.How does the ANOVA test work? To determine whether the various sample means came from a single population or populations with different means, you actually compare these sample means through their variances. For example, a general manager of a chemical plant may wish to determine whether a difference exists in the annual salaries of his shift supervisors, assistant plant managers, and maintenance managers. Within-group variation exists among salaries in each of the three groups, and between-group variation is present across the three groups. ANOVA uses a ratio of between-group variation to within-group variation to form an F statistic. If the F statistic results in a p value that is less than or equal to a given significance level (typically 5%), then he may conclude that the salaries of shift supervisors, assistant plant managers, and maintenance managers are significantly different. If the p value exceeds the significance level, then the annual salaries of the three groups are not significantly different.Note that probability computation for an F statistic is based on an F distribution. There is not a single F distribution but a family of F distributions. A particular member of the family is determined by two parameters: the degrees of freedom in the numerator and the degrees of freedom in the denominator.

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