## STAT-3001 Statistical Methods and Applications

x² Calculation Workbook | |

File Size: | 50 kb |

File Type: | xlsx |

I created this Excel workbook as a means to work out Chi Square statistical calculations

Population Studies and Bias Introduction“Can a War be described with a graph” (Jeffrey o. Bennett, 2009, pp. 137-138)? This study focuses on a graph “created by Charles Joseph Minard in 1869” (Jeffrey o. Bennett, 2009). It describes the movement of Napoleon’s forces during the 1812 French campaign to invade Russia. The graph itself uses the width of the bars to describe population growth and losses, and the peaks and valleys to describe movement.As the graph moves from left to right, it shows Napoleon’s forces moving into Russia, and at the same time, the utter destruction of his Army by drastically becoming thinner and thinner. Upon arriving in Russia, Napoleon was forced to retreat. This is depicted on the graph by showing a very thin blue line heading back towards the left representing the temperature the soldiers faced, and a purple line, branching from the original blue line, showing in width the population of the French army. The population being studied for this analysis is the whole population of the French military during the French-Russian campaign between 1812 and 1813. It displays in vivid detail exactly how many soldiers were lost, but not only that, where they were lost. The only Bias that I can see from the graph would be the actual figure of Napoleon’s army. An army consists of more than soldiers; it has cooks, cleaners, workers, stablemen, and should have an extensive supply train (although the lack of such could be the reason for such horrendous losses). These people do not seem to be represented by the loss figures, and as such, the losses could in turn be much higher than those depicted. Nevertheless, the figures depicted in the graphical analysis are valid in showing the mistake of Napoleon’s decision to invade another country, without proper resources and planning. Fielding an Army of 422,000 men only to return, via retreat, with 10,000 marks a special kind of foolishness, especially considering his army never actually engaged the enemy. “Are we Smarter than our Parents” (Jeffrey o. Bennett, 2009, pp. 229-231)?“In the early 1980s, a political science professor named Dr. James Flynn began to look at the raw, unadjusted scores on unchanged [I.Q.] tests and questions. The results were astounding” (Jeffrey o. Bennett, 2009, p. 229). Dr. Flynn found children in 1997, on average, scored 20 points higher than children of 1932. These scores were unadjusted for the overall mean of children during the time, but instead used the raw scores of 1997 compared to the raw scores of the 1932 children. In essence, this means half the children today would fall in the intellectually superior area of the IQ test with very few falling in the intellectually deficient area of the 1932 scores. The population being studied is all children in 1932 compared to all children in 1997. However, the sample population is only those children which actually took an IQ exam during those time periods. The bias which I would like addressed would be the actual percentage of boys tested and girls tested throughout the two exams. My personal feeling, without actually seeing any data, would be tests today would have a much larger percentage of female participation due to an increased understanding between the sexes, which was not relevant at the time of the 1932 tests. Also, today’s tests would most likely contain an increased number of ethnic groups to those of the 1932 tests. Without having the two biased points mentioned above addressed fully, the IQ test increased results may or may not be relevant due to both the population size of 1932 tests, and the diversity of the population from which the test was taken. The article even states “There is some evidence that the rise in scores may have begun to slow or halt in recent years” (Jeffrey o. Bennett, 2009). This could very well be due to the alignment of sexes and the equal rights movements for all races. In my opinion, the statistical analysis of Napoleon’s army moving into Russia was represented in a clearer fashion not only for the simplicity of its data set, but the depiction in both width and length of the population loss over time. The labeling of the IQ graph is based on a fifteen point number line, without any numerical representation given to the y-axis, essentially leading the reader to believe whatever they would like about the graph itself. Proper labeling, strong data, and checking for unintentional bias are what make a statistical graph valid and worthwhile. Although the Napoleon dataset could have incorporated the support army for the population, it does not. However, it also does not bias itself based on these numbers, stating clearly the numbers are only those of the military itself. ReferenceJeffrey o. Bennett, W. L. (2009). Focus on History: Can War Be Described with a Graph? In W. L. Jeffrey o. Bennett, Statistical Reasoning for Everyday Life (3rd ed., pp. 137-138 and pp. 239-231). Boston: Addison-Wesley. |
Statistical Methods and Applications: Reflection In the first week of this statistics course, I came across the definition for statistics which on first inspection was both simple and profound, “Statistics is the science of collecting, organizing, and interpreting data” (Jeffrey O. Bennett, 2009, p. 2). It is simple in that it outlines such an incredibly robust focus of work into ten words, and it is profound in that it highlights something which I never understood about statistics, it is a science. This is an important acknowledgement about statistics; without this understanding, one can become lost, as I did at first. Prior to taking this course, I did not realize how much my life is surrounded by statistics. From the numbers on the back of my cereal box, to the way street lights operate to keep traffic jams from piling up. I even deal with statistics at work on a daily basis, but only perceived of them in terms of “reports.” Statistics, to me, always remained firmly in the grounds of mathematics. However, seeing the definition for statistics, and subsequently “doing” statistics, opened my eyes to the idea it is a science, it is everywhere in everything we do. Statistics is a way to describe the world. I take away from this course further insight into how to define the world around me. Statistics shoved in my face from the media can now be better analyzed and understood. No longer will I remain oblivious to improper statistical methodology, when viewing material which is touted to be “conclusive.” This is especially true in this day and age when all around us is media, news agencies, scientific analysis, and religious rules about how and why I should live my life and the “statistics” given for any number of things. This knowledge allows me to make up my own mind, and in turn, give sound advice when stating statistical reasons for doing anything. ReferenceJeffrey O. Bennett, W. L. (2009). Statistical Reasoning for Everday Life (3rd ed.). Boston: Pearson Education, Inc. |

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