Article Review of “Demonstration of Ranking Issues for Students: A case Study” Essay

Article Review of “Demonstration of Ranking Issues for Students: A case Study”


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            This article review aims to analyze the study shown by the authors - Article Review of “Demonstration of Ranking Issues for Students: A case Study” Essay introduction. The article that we will review here is published by the Journal of Statistical Education Volume 13 (Number 3) in 2005. The title of article is “Demonstration of Ranking Issues for Students: A Case Study” written by I. Elaine Allen and Norean Radke Sharpe from Babson College. The paper was initiated by the editor of the Boston magazines. This editor contacted the two authors to do the study. The article is about the demonstration of the issues in the ranking methods done by other statisticians which aims a better understanding of student in the matter.

Bias, Sources, and Sampling Method

            They listed the source the Boston Magazine researchers gathered and validated.The sources came from the public database like United States census, Executive Office o Environmental Affairs, Massachusetts Department of Revenue, Massachusetts Department of Revenue, Massachusetts Department of Education, Federal Bureau of Investigation, Environmental Protection Agency, Massachusetts Municipal Association, Massachusetts Beverage Business, Massachusetts Department of public Health, Registry of Motor Vehicles and the “Banker & Tradesman” (Allen & Sharpe, 2005).

These data from different institutions are in public libraries. The data were gathered by these different institutions are seemingly unbiased since the study aims to study the records of the whole population in Massachusetts. Additionally, the data collected is not collected for the purpose of this study so it is evident that the data is unbiased and selected on purpose to control the result.

The data for the study is the records of which came from different sources. The sample size is not given since the sample is the whole population of the towns in Massachusetts. The sampling methods are not given since the data were just obtained from records from different Institutions.

            If we analyze the data gathered the objectivity of the author’s is evident they just an obtained data from the public database that respectable institution gathered not just by the purpose of this study.  Even though there is no enough biological information of the authors from the article, the unbiased analysis of the authors is obvious as they explained every detail of the study and prove that they do not have control over the result of the study whatever method of analysis they chose to use.

            As the article reports, the author was contacted by the editor of the Boston Magazine to the study so the authors don’t have any interest in the result that would make them change the result of study. Moreover, the authors seemingly will not benefit in promoting such result.

            The authors laid their methods clearly and presented problems that might occur. These problem mentioned in the report is given proper advised to solve it. Moreover, the authors had presented the limitations of the study as it is not definitive and suggest that further studies is needed to established a good ranking method.

Statistics in the Article

The raw data in the study were standardized to create variables with the same measure. The resulting standardized data were then average to calculate the mean of the standardized scores per category which the author chose due to different reasons. The chosen categories are public safety, health and environment. In these categories, they ranked each town accordingly and then average the rankings to get the overall ranking (Allen & Sharpe, 2005).

The method use here makes use of variables of per capita which supposedly eliminate the effect of the population density to resulting rank. This is expected to yield better ranking since it will eliminate the effects of the population of overall ranking. However, the results seem to have a relationship on the population density.

To test this observation, the authors test the relationship between mean standardized indices and the log of population of township. They presented a scatter plot to get an overview and slightly prove their hypothesis. They also test the relationship of the population to the each of the three categories. However, the correlation analysis shows that they do not have a strong positive which leads to the conclusion that the ranking model is good enough for statistical analysis and found out that the health category is the most related of the three but is still strongly related. On the other hand, the authors continue to pursue a better method which will incorporate the population density into the ranking method.

The article presented a method in which they integrated the population in the first approach. The method showed that there are no significant changes to upper most and lowest ranks. However, they observed a significant difference in the ranks of the towns in the middle ranks. This method, on the other hand, help the author identify the towns that are over performing and under performing. This is not included in the initial goal of the study. However, the authors felt that it is necessary to include this statistic to determine which towns are more beneficial to live in.

Averages and Variation

The average is basically used to obtain the mean of data that they got from surveys done by other institutions. They make use of the average to get a more precise measure since the towns have different numbers in population. It is an appropriate measure to use to better rank the towns which have different population density. The authors chose to use the average with the aim of eliminating relationship of the results to the density of the towns’ population.

            The variation does not appear in the study. The authors does not feel that the study of variance to achieve the goal of the study. I also think that is so since the aim of the study is to obtain a better ranking method. The study of variance deals with the amount of variation an observed data to its mean. This is rather irrelevant to the study.

Graphs and/or Charts and/or Tables

            The article presented some tables and scatter plots for the readers to visually understand the things being discuss. Figure 1 is a scatter plot which compares the result for the mean-standardized rank and the log of population of every town. This clearly shows a relationship between the two variables. However, the correlation says otherwise.

            Figure 2, 3, and 4 are also scatter shows the relationship between each of the three categories, the public safety, the environment and health, respectively. The plots show that there are clearly no relationship between population and the categories of environment and public safety. Although the plot shows a relationship between the population and health category, the correlation analysis shows that the three categories fail to achieve strong relationship to the population density.

            The next figure, Figure 5, shows the relationship of the results of the two methods, the mean-standardized rank method and the population-adjusted rank method. The correlation analysis also agrees with the visual presentation. However, the text does not elaborate on it. It just proves that the two methods will most likely yield the same result.

            The Figure 6 shows the relationship between the difference of the two ranks and the average of the two ranks. The text explained that this plot shows that the towns in the middle of rankings in both ranks are the most greatly affected by the population adjustment. This claim is supported by table 2 and 3 as it shows the upper and bottom, respectively, rankings of both ranking method. The tables show that there are 9 towns common in the top 15 and 8 towns common the lower 15.

            Figure 7 shows a scatter plot that compares the difference of ranks in the mean-standardized rank method and population-adjusted rank method against the log of population of each town. This plot shows the towns which does rise or fall as expected by the authors. The article does not elaborate on what its importance to the study.

The Figure 8 is also a plot of which the author shows the towns that are over performing and under performing. The figure include lines that determines the under and over performance of every town. It is a more detailed plot of Figure 7.

            The Table 4 is a table of top fifteen over and under performers which shows the towns which are classified by figure 8.

            The Figure 8 and Table 4 is a report of result which is irrelevant to the study. The authors do not clearly explain the importance of this two in the study.

Descriptive and/or Inferential Statistics

The descriptive statistics is basis of this study for its analysis. The authors use statistical average to analyze the data in the study. The authors describe the results to definitive about some points of the study. However, the authors fail to establish a better method for ranking. In line with this, they only suggest that the ordinary ranking done today by many statisticians is inappropriate relative to the aim of the study. This because that many decision is based in this statistics and therefore needed more of the attention and deeper studies.

            There are no inferential statements made in this article as it tackles the ranking of populations. Additionally, the authors do not use of the samples in the study. They used the records of various institutions regardless of the method of how they achieved the data.

Modifications and/or Additional Statistics

The study as implied by the authors of this article is not enough to establish a better standard ranking method. The authors should collect their own data to ensure better the reliability of the results. The absence of data in some necessary variables may cause the result to be more imprecise. The authors must pursue the search for a better method in ranking to obtain their main goal.


            The article written by the Allen and Sharpe gave a better understanding on the fact that the conventional ranking methods many people use to be inappropriate and a more in depth study needed to achieve a more precise ranks. However, the article deviates the topic to the over and under performing towns without establishing their standard on better ranking method. The students may wonder what the best method there is for the authors did not show it clearly. The authors must pursue their goals of future studies give a definitive explanations on the standards of better ranking method.


Allen, I. A. and Sharpe, N. R. (2005). “Demonstration of Ranking Issues for Students: A Case Study”. Journal of Statistical Education, Volume 13Number (3)

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