Relationship between Number of Enrollees and Number of Graduates of US Medical Schools - Term Paper Example

? Relationship between Number of Enrollees and Number of Graduates of US Medical Schools [Type the [Pick the There has been a noted consistent trend in the number of enrollees and the number of graduates in US medical schools. This observation is investigated using data gathered from 30 US medical schools. Using descriptive statistics, correlation and regression analysis, it was found that there is a low positive relationship between number of first year enrollees and the number of graduates from medical schools four years later. Thus, although higher graduates are produced by schools with higher first year enrollees, this may not be a crucial factor and other affecting elements may have to be considered. Table of Contents Page Number Abstract 2 Introduction 4 Presentation and Discussion of Results 5 Conclusion 19 Critique 21 Bibliography 22 Introduction There are a number of factors that influence the volume of graduates from medical schools in the US. The Association of American Medical Colleges (AAMC) reports that for the past decade, there has been a fluctuation in the number of applicants to US medical schools (AAMC Website). However, the number of enrollees and the number of graduates have both seen a constant rate over the past years. This study is interested in finding out if there is a significant relationship between the number of enrollees in US medical schools with the number of graduates four years later. That is, the research asks the following question: RQ: Is there a significant relationship between the number of enrollees in US medical schools with the number of graduates four years later? To correspond with this research question, this investigation has the following hypotheses: Ho: There is no relationship between the number of enrollees in US medical schools with the number of graduates four years later (r = 0). Ha: There is a significant and positive relationship between the number of enrollees in US medical schools with the number of graduates four years later (r > 0). The independent variable for this study is “Number of enrollees,” corresponding to the number of first year enrollees in each medical school for the year 2006. The dependent variable for this study is “Number of graduates,” corresponding to the number of students who graduated four years later from the same schools, or those labeled as “Class of 2010.” This topic is of particular interest to me because I have always wondered about the performance of medical school programs in terms of how many people make it past the MCATS and how many actually graduate the university. I personally have the desire to attend medical school and eventually become a doctor. As such, this research will make an impact in my decision to pursue Medicine. I am an ambitious girl, but I do know that ambition is not the only way to get through medical school. Rather, one needs courage as well. This research will determine at the end of the day if I will have the courage to try out this field or to close the doors to medical school behind me. Presentation and Discussion of Results In order to answer the research question, descriptive statistics was first taken from the data in order to have a picture of how the data behave. Then, a scatter plot of number of graduates against number of enrollees was produced to find if there is an existing relationship between the two variables. Finally, the data were subjected to regression analysis in order to find out if Number of Enrollees is a significant predictor of Number of Graduates. The regression analysis conducted also produced the coefficients for the desired regression equation. Table 1. Presentation of Raw Data By Alphabetical Order 30 Selected Medical Schools First Yr Enrollment (2006) vs. Graduates (2010) Name of School First Yr Enrollment (2006) Graduates (Class of 2010) Boston University School of Medicine 179 153 Brown Medical School 91 79 Drexel University College of Medicine 255 233 Florida State University College of Medicine 109 94 Joan C. Edwards School of Medicine at Marshall University 64 61 Louisiana State University School of Medicine in Shreveport 118 112 Medical College of Georgia School of Medicine 190 179 Medical University of Ohio 155 110 Medical University of South Carolina College of Medicine 150 138 Meharry Medical College School of Medicine 93 85 Michigan State University 460 117 Oregon Health and Science University School of Medicine 120 117 Pennsylvania State University College of Medicine 152 148 Rush Medical College of Rush University Medical Center 140 137 St. Louis University School of Medicine 176 163 Stony Brook University Health Sciences Center 108 103 Tulane University School of Medicine 165 164 University of Alabama School of Medicine 176 164 University of Colorado School of Medicine 155 146 University of Maryland School of Medicine 160 160 University of Medicine and Dentistry of New Jersey 165 163 University of Nevada School of Medicine 57 55 University of South Alabama College of Medicine 74 67 University of Texas Medical School at Galveston 229 221 University of Texas Medical School at Houston 226 222 University of Texas Medical School at San Antonio 220 211 University of Vermont College of Medicine 107 97 Wayne State University School of Medicine 288 273 West Virginia University School of Medicine 109 103 Yale University School of Medicine 500 110 First Year Enrollment The figures for first year enrollment were taken from the records at the AAMC website. This is defined as the number of first year students who were officially enrolled for the first semester of Academic Year 2006 – 2007 in the indicated medical school. Moreover, these figures only include those who enrolled in the indicated medical school for the first time. Based on figures from Table 1, the University of Nevada School of Medicine has the least number of enrollees, with only 57 enrollees, while the Yale University School of Medicine has the most number of first year enrollees, with 500. Graduates The figures for number of graduates were also taken from the AAMC website. This is defined as the number of those who graduated as Class of 2010, based on records collected from the indicated schools. The data indicate that University of Nevada School of Medicine also has the least number of graduates, with only 55, while Wayne State University School of Medicine has the most number of graduates with a total of 273. Table 2. Presentation of 30 Selected Medical Schools First Year Enrollment On data array Name of School First Yr Enrollment (2006) Graduates (Class of 2010) University of Nevada School of Medicine 57 55 Joan C. Edwards School of Medicine at Marshall University 64 61 University of South Alabama College of Medicine 74 67 Brown Medical School 91 79 Meharry Medical College School of Medicine 93 85 University of Vermont College of Medicine 107 97 Stony Brook University Health Sciences Center 108 103 Florida State University College of Medicine 109 94 West Virginia University School of Medicine 109 103 Louisiana State University School of Medicine in Shreveport 118 112 Oregon Health and Science University School of Medicine 120 117 Rush Medical College of Rush University Medical Center 140 137 Medical University of South Carolina College of Medicine 150 138 Pennsylvania State University College of Medicine 152 148 Medical University of Ohio 155 110 University of Colorado School of Medicine 155 146 University of Maryland School of Medicine 160 160 Tulane University School of Medicine 165 164 University of Medicine and Dentistry of New Jersey 165 163 St. Louis University School of Medicine 176 163 University of Alabama School of Medicine 176 164 Boston University School of Medicine 179 153 Medical College of Georgia School of Medicine 190 179 University of Texas Medical School at San Antonio 220 211 University of Texas Medical School at Houston 226 222 University of Texas Medical School at Galveston 229 221 Drexel University College of Medicine 255 233 Wayne State University School of Medicine 288 273 Michigan State University 460 117 Yale University School of Medicine 500 110 Total 5191   Table 2 shows that among the sampled medical schools, the University of Nevada School of Medicine has the lowest number of enrollees for 2006, with only 57 enrollees. As such, it was also the medical school with the least number of graduates in 2010. On the other hand, Yale University School of Medicine had the highest number of enrollees for 2006, having 500 enrollees. However, they were not the ones with the highest number of graduates in 2010 as that distinction goes to Wayne State University School of Medicine with 273 graduates. These figures suggest that while many applicants go to Yale, barely 25% of this first year medical students graduate four years later. This suggests that while a lot of students enroll at Yale, Yale Medical School is a tough place to study Medicine in, hence a low graduate count compared to initial enrollees. On the other hand, the low first year enrollment at the University of Nevada seems to translate to a low number of graduates as well. This could mean that not many students are interested in taking their Medicine studies at the University of Nevada. However, it does seem that those who do enroll at the University of Nevada have a high chance of graduating since only two did not make it four years later. Number of 1st year enrollees (2006) Mean: 5191 / 30 = 173.03 Median: 155 Mode: 109 Range: 500 – 57 = 443 Standard Deviation: 100.28 Data from the table and from the calculated descriptive statistics show that a great number of the figures fall below the Mean. While there is a mode for this set of figures, this mode occurs only twice in a data set with 30 values. This indicates that the mode is not a very reliable measure of central tendency for this set of data. Moreover, the extremely high range and standard deviation indicates that the best measure of central tendency for this set of data is the median because it is able to compensate for the extreme values of the data set. Furthermore, the figures for Michigan State and Yale University are very much higher than the other figures. Therefore, it may be concluded that figures for Michigan State and Yale University may be considered as outliers as they tend to pull the mean to a much higher value than the actual middle value. Table 3. Presentation of 30 Selected Medical Schools Graduates (2010) On data array Name of School Graduates (Class of 2010) First Yr Enrollment (2006) University of Nevada School of Medicine 55 57 Joan C. Edwards School of Medicine at Marshall University 61 64 University of South Alabama College of Medicine 67 74 Brown Medical School 79 91 Meharry Medical College School of Medicine 85 93 Florida State University College of Medicine 94 109 University of Vermont College of Medicine 97 107 Stony Brook University Health Sciences Center 103 108 West Virginia University School of Medicine 103 109 Medical University of Ohio 110 155 Yale University School of Medicine 110 500 Louisiana State University School of Medicine in Shreveport 112 118 Oregon Health and Science University School of Medicine 117 120 Michigan State University 117 460 Rush Medical College of Rush University Medical Center 137 140 Medical University of South Carolina College of Medicine 138 150 University of Colorado School of Medicine 146 155 Pennsylvania State University College of Medicine 148 152 Boston University School of Medicine 153 179 University of Maryland School of Medicine 160 160 University of Medicine and Dentistry of New Jersey 163 165 St. Louis University School of Medicine 163 176 Tulane University School of Medicine 164 165 University of Alabama School of Medicine 164 176 Medical College of Georgia School of Medicine 179 190 University of Texas Medical School at San Antonio 211 220 University of Texas Medical School at Galveston 221 229 University of Texas Medical School at Houston 222 226 Drexel University College of Medicine 233 255 Wayne State University School of Medicine 273 288 Total 4185   The University of Nevada School of Medicine has the least number of graduates for Class 2010 in the given set of data. This is to be expected as they also have the least number of enrollees in 2006. On the other hand, Wayne State University School of Medicine has the highest number of graduates even though it is not the school with the highest number of enrollees as Michigan State and Yale University have much higher enrollees than Wayne State. However, when I removed these two schools from the data, the figures showed that Wayne State does have the highest number of enrollees among the remaining schools, which seems to validate the initial hypothesized connection between the number of first year enrollees and the number of graduates four years later. Number of Graduates (Class of 2010) Mean: 4185 / 30 = 139.5 Median: 137.5 Mode: 110 Range: 273 – 55 = 218 Standard Deviation: 54.12 Figures from Table 3 and the calculated descriptive statistics show that the data for the number of graduates are quite evenly spaced as they have a narrower range, a smaller standard deviation, and a small difference between the mean and the median. Again. the mode for this set of data is quite irrelevant as there are only two data points with the same value. Moreover, the data points are clustered towards the middle values with only a few low and a few high points. Therefore, either the mean or median can accurately represent the best measure of central tendency for this group of data. Descriptive Statistics There were a total of 30 US medical schools chosen at random from the list of medical schools found at the AAMC website. The number of first year enrollees in 2006 and the number of graduates of Class 2010 were also taken from the website (AAMC Website). The descriptive statistics of the two variables provide a picture of how the data behave. Table 4 shows a summary of these descriptive statistics. The average number of enrollees for the 30 schools is 173.03 (SD = 100.28) while the average number of graduates is 139.50 (SD = 54.12). The kurtosis and skewness values for number of enrollees indicate that the data are concentrated around the mean (Kurtosis = 4.65) and have more low values than high values (Skewness = 2.00). On the other hand, the kurtosis and skewness values for number of graduates indicate that the data are concentrated around not highly concentrated around the mean (Kurtosis = - .04) and have more middle values than extreme values (Skewness = .60). Table 4. Summary of Descriptive Statistics (N = 30). Descriptive Statistics First Yr Enrollment (2006) Graduates (Class of 2010) Mean 173.03 139.50 Standard Error 18.31 9.88 Median 155 137.5 Mode 109 110 Standard Deviation 100.28 54.12 Sample Variance 10055.76 2929.50 Kurtosis 4.65 -0.04 Skewness 2.00 0.60 Range 443 218 Minimum 57 55 Maximum 500 273 Sum 5191 4185 Count 30 30 Confidence Level (95.0%) 37.44 20.21 Observations from Grouped Data Initial observations are further justified by the histograms of the data found in Figure 1 for number of enrollees and Figure 2 for the number of graduates. Figure 1 shows that the number of enrollees is more highly concentrated toward the low data points, with few data point concentration in the higher values. On the other hand, Figure 2 shows that number of graduates is more concentrated towards the middle value and thus, the histogram assumes an almost bell shape. Moreover, these figures point to the fact that more enrollees in a medical school would translate to more graduates as well. Thus, those schools that have higher enrollment rates do translate to higher graduation rates too, based on the given data. Table 5. Grouped data observations for Number of Enrollees (X). Number of enrollees Frequency Percentage Cumulative % Less than 155 14 46.67% 46.67% 155 – 204 9 30.00% 76.67% 205 – 304 5 16.67% 93.33% 305 – 404 0 0.00% 93.33% More than 404 2 6.67% 100.00% Total 30 100.00%   Range: 500 – 57 = 443 Class Width: 443 / 5 = 88.6 or 89 Figure 1. Histogram for Number of Enrollees (X). Table 6. Grouped Data Observations for Number of Graduates (Y). Number of enrollees Frequency Percentage Cumulative % Less than 95 6 20.00% 20.00% 95 - 144 10 33.33% 53.33% 145 - 194 9 30.00% 83.33% 195 - 244 4 13.33% 96.67% More than 244 1 3.33% 100.00% Total 30 100.00%   Range: 273 – 55 = 218 Class width: 218 / 5 = 43.6 or 44 Figure 2. Histogram for Number of Graduates (Y). Relationship between Variables After viewing the behavior of the dependent and independent variables separately, it is of the study’s interest to find out if there is an existing relationship between the two variables. Using the graphing utility of Microsoft Excel, a scatter plot was constructed and this is shown in Figure 3. The figure shows that there is a strong linear relationship between the dependent and independent variables as the points behave in such a way that a fitted line would have a positive slope. Figure 3. Scatter plot of Number of Graduates (Y) vs Number of Enrollees (X). Calculations indicate that the Pearson’s correlation coefficient for the two variables is r = .431, r2 = .186, Percentage ? 19%. This indicates a low positive relationship between the two variables. Specifically, this figure means that 19% of the variances in the number of graduates may be accounted for by the number of enrollees. Moreover, this observation indicates that higher number of enrollees correspond to higher number of graduates in US medical schools. This low correlation may be attributed to two outliers that are present in the given data. These findings provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis and conclude that there is a significant and positive relationship between the number of enrollees and the number of graduates of US medical schools. These results support the earlier observation of AAMC, which noted that there seemed to be a similar trend in the number of enrollees and number of graduates of US Medical Schools. With this result, it will be helpful to see if the relationship between the two variables is causative in nature, that is, does number of enrollees predict number of graduates? Regression Analysis Table 7 shows the results of the Analysis of Variance (ANOVA) conducted as part of the regression analysis performed on the two variables. The findings from the ANOVA indicate that there is a high causative relationship between the dependent and independent variables, F(1, 28) = 6.38, p = .02. This means that there is sufficient reason to conclude that the number of graduates of a US medical school may be predicted by the number of enrollees that it has. Table 7. Analysis of Variance of Regression Analysis.   df SS MS F Sig. Regression 1 15762.58 15762.58 6.38 0.02 Residual 28 69192.92 2471.18 Total 29 84955.50       With the causative relationship established between the dependent and independent variables, it is now necessary to find out how much does the number of first year enrollment affect the number of graduates of US medical schools. Table 8 provides the coefficients for the regression equation that will predict the number of graduates, when the number of first year enrollment of a particular school is provided. Table 8. Coefficients for Regression Equation.   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 99.27 18.33 5.41 0.00 61.72 136.82 First Yr Enrollment (2006) 0.23 0.09 2.53 0.02 0.04 0.42 Slope: .23 Intercept: 99.27 Using the information from Table 8, it is now possible to derive the regression equation that will predict the number of graduates, when the number of first year enrollment of a particular school is provided. This equation is given below: (Eqn 1) Y = 99.27 + .23X where Y = number of graduates four years from enrollment year X = number of first year enrollees. This equation suggests that every additional student enrolled in a medical school translates to a .23 unit increase in enrollment. This may also be translated to mean that for every 5 additional students enrolled in a medical school, there corresponds an additional one graduate four years later. To test this equation, let us use the value for number of first year enrollees for Medical University of Ohio, X = 155, which is the median for this data set. Y = mx + b = .23(155) + 99.27 Y = 135 graduates This result indicates that Medical University of Ohio should have 135 graduates but it only has 110. This seems to indicate that the school is not producing as many graduates as it should, and may not be a good medical school choice. On the other hand, let us consider Boston University School of Medicine with X = 179, a value closer to the mean. Y = mx + b = .23(179) + 99.27 Y = 140 graduates Although the regression equation shows that Boston University School of Medicine is predicted to have only 140 graduates, it was actually able to produce 153 graduates, which is much higher than the projected number of graduates. This could indicate that Boston University has a good rate when it comes to producing medical school graduates. Conclusion Findings from this investigation indicate that there is a significant and positive, but low relationship between the number of enrollees in a US medical schools and the number of graduates four years later. These results support the earlier hypothesis established in this study. This means that as more first year students enroll in medical schools, more graduates are to be expected four years later. This suggests that medical schools are quite successful in producing graduates as more students enroll in their respective institutions. Thus, medical schools should be more aggressive in acquiring more first year enrollees in order to come up with more graduates in the future. However, the low relationship between the two variables also points to the fact that number of first year enrollees is not a very serious consideration when producing a high number of graduates four years later. Therefore, students looking for a medical school must not focus so much on these values as they do not necessarily accurately guarantee higher rates of enrollment. The conducted investigation gave me additional insights in the process of conducting a research, especially one that is quantitative in nature. Moreover, I have found myself more familiar with the concepts of descriptive statistics, correlation and regression. It is hoped that further studies investigating the factors affecting the number of graduates from US medical schools will be helped by the investigation carried out in this paper. The results of this research indicate that there is sufficient motivation for me to join medical school since there is quite a high chance for me to get through the four years of medical school and graduate when the time comes. This is applicable to my life today since it speaks of the amount of output in terms of students graduating from medical school being directly proportional to the amount of input in terms of students who enter medical school. Thus, if I input enough amount of dedication and hard work to my goals and plans for the future, I will correspondingly reap its rewards. Critique and what’s next For an extension of this research, it may be helpful if the study were more area-specific. That is, better and more useful information may be produced if the schools sampled in the study were from a particular area only, such as those in the East or those in the West so that students who are searching for a good medical school may be provided with a better idea of which to choose. Moreover, the research may benefit from removing outliers in order to produce more reliable results. Overall, I believe that this research is able to provide useful information to medical students and other researchers as well. Bibliography 2011. AAMC Website. 10 December 2011 . 2011. AAMC Website. 9 December 2011 . Anderson, D. R., D. Sweeney and T. Williams. Statistics for Business and Economics. Mason, OH: Thomas Higher Education, 2009. Black, Ken. Business Statistics: Contemporary Decision Making. Hoboken, NJ: John Wiley & Sons, 2010. Creswell, John. Research design: qualitative, quantitative, and mixed method approaches. Thousand Oaks, CA: Sage Publications, Inc., 2003. Read More