April 20, 2006
Douglas Houseworth
6493 S US Highway 31
Alanson, MI 49706
Dear Mr. Houseworth
Attached is an analysis of the Alanson Cemetery data that you had provided several months ago. You were interested in knowing whether the longevity of people from this locale was significantly different from national trends. I can state conclusively that the data provided from the Alanson Cemetery records indicate that these individuals, taken as a group, lived significantly longer than the norm for the United States for the same time periods. Details are in the attached document.
Statistical tests were conducted using the Alanson Cemetery Data compared with Government longevity statistics provided by the U.S. Statistical Abstracts from the Census Bureau. This comparison yielded that with almost certain probability (>99.99%), individuals from the Alanson area lived significantly longer than U.S. norms. Computing the difference between these individual ages and the national norms, the data indicate that the these people from the Alanson area live an average of 8.6 years longer than those from the U.S. as a whole with a margin of error of ± 1.66 years.
If you need any other information or have questions concerning the analysis, please feel free to contact me at the address below.
Sincerely,
Gary S. Kersting
Professor of Mathematics and Statistics
North Central Michigan College
1515 Howard Street
Petoskey, MI 49770
(231) 348-6646
gkers@ncmich.edu
Statistical Analysis
The following is a statistical analysis comparing the age of death of individuals from the Alanson area to national (U.S. trends). The analysis was performed using the MINITAB software program and information obtained from the Alanson Cemetery and the U.S. Census Bureau.
Data for the following analysis was provided by Douglas Houseworth and was presented as an Excel file titled "Burial Report" consisting of 1,368 records. The records included name, age, date of birth (day, month and year) and date of death (day, month and year). Other information was also presented, but not used in the subsequent analysis.
Many of the records were incomplete, but enough information was available to fill in the appropriate fields. For example, the date of birth and death may have been included, but age was not. This could be calculated with the given information. A total of 126 records, or 9.2%, were deleted from the file for lack of information A total of 1,242 records were analyzed. It is not believed that the deleted records would cause a significant difference in the final analysis.
Data included was for individuals born between 1814 and 2002 and those who died between 1814 and 2004. Data for last year was not available, but once again it is the belief that this would not change the results of the statistical analysis.
Mortality statistics for the United States were obtained from the Unites States Statistical Abstract of the Census Bureau. This abstract included mortality records from the year 1900 to the present and gave life expectancy as a function of birth year. Since the abstract did not go back as far as the Alanson Cemetery data, regression analysis was used to compute a predicted life expectancy for those years prior to 1900. A fitted line plot shown below as Figure 1 shows the mortality data with the fitted line superimposed.
This data shows a strong linear correlation with a correlation coefficient of r = 0.958 and a p -value of 0.0000 indicating a significant positive relationship between year born and life expectancy. The regression equation was computed to be Age = –514.5 + 0.2971 Year and this equation was used to calculate the life expectancy for those years prior to 1900 not included in the abstract.
Following the data gathering a Two-Sample t-test was conducted using MINITAB comparing the actual mean age of death with the predicted mean age of death using the tables from the abstract and it was found that a significant difference was present between these two means. MINITAB results are shown below:
Two-Sample T-Test and CI: actual age of death, pred age of death Two-sample T for actual age vs pred age
Difference = mu (actual age) - mu (pred age)
N Mean StDev SE Mean
actual age 1233 58.5 28.0 0.80
pred age 1242 49.92 9.64 0.27
Estimate for difference: 8.60397
95% CI for difference: (6.95173, 10.25621)
T-Test of difference = 0 (vs not =): T-Value = 10.21 P-Value = 0.000 DF = 1518
The p-value of 0.000 from the test indicates a significant difference exists between the actual mean age of death for the Alanson sample and the predicted mean age of death from the U.S. national standards.
The confidence interval included with the hypothesis test states with 95% confidence that individuals from the Alanson area lived an average of 8.6 years longer than U.S. national trends. The margin of error for this interval is ± 1.65 years.
Conclusion : People from the Alanson almost certainly live longer than the U.S. norm as reported by the census bureau by an average of 8.6 years. What causes this increased longevity is not known and is not the subject of this study. Copies of the data file and the MINITAB output are included for review.
MINITAB STATISTICS
Results for: ALANSON CEMETARY DATA1.MTW
Correlations: Year, Age
Pearson correlation of Year and Age = 0.958
P-Value = 0.000
Regression Analysis: Age versus Year
The regression equation is
Age = - 514 + 0.297 Year
Predictor Coef SE Coef T P
Constant -514.46 17.19 -29.93 0.000
Year 0.297104 0.008808 33.73 0.000
S = 2.65777 R-Sq = 91.8% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 8037.2 8037.2 1137.81 0.000
Residual Error 101 713.4 7.1
Total 102 8750.7
Unusual Observations
Obs Year Age Fit SE Fit Residual St Resid
85 1918 39.100 55.387 0.391 -16.287 -6.20R
R denotes an observation with a large standardized residual.
Two-Sample T-Test and CI: Actual Age, Pred Age
Two-sample T for Actual Age vs Pred Age
N Mean StDev SE Mean
Actual Age 1233 58.5 28.0 0.80
Pred Age 1242 49.92 9.64 0.27
Difference = mu (Actual Age) - mu (Pred Age)
Estimate for difference: 8.60397
95% CI for difference: (6.95173, 10.25621)
T-Test of difference = 0 (vs not =): T-Value = 10.21 P-Value = 0.000 DF = 1518