Articles

Presented By: Yaa Tawiah Wonkye

MATH 6820 Reading Assignment

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1) Looking at Blood Sugar

Author: Howard Wainer and Paul Velleman

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2) Giving the Finger to Dating Services

Author: Grace Lee, Paul Velleman and Howard Wainer

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Looking at Blood Sugar

• Diabetes is dangerous and it is spreading at a faster rate

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• It is estimated that 14.6 million children and adults in the USA have been diagnosed with diabetes while 6.2 million are unaware they have diabetes

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• Some of the causes include;
• Increased obesity
• Decreased physical activity
• Consumption of more processed food
• Aging population

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• Diabetes in the US over the past 70 years is growing at an exponential rate

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Looking at Blood Sugar

• If diabetes is left untreated, it may lead to serious consequences such as
• Liver and kidney damage
• Circulatory problems leading to blindness, neuropathy and loss of limbs

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• One requires close cooperation between the physician and the patient in order to effectively treat diabetes

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• Although it is the duty of the physician to prescribe drugs and routine diet and exercise, it is the responsibility of the patient to follow them

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• The patients need to control their cholesterol, blood pressure, glucose as well as their weight through regular exercise

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Looking at Blood Sugar

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• When a patient is diagnosed with diabetes, the patient needs to
• keep the blood sugar under control
• maintain a health meal plan
• exercise regularly
• Usually, patients are given a small remarkable device that helps to control the blood sugar level by;
• reading a small blood sample and indicating its glucose content
• recording the time and date the reading was taken
• calculating the mean blood sugar levels, among other functions
• From the readings obtained from the small instrument, we can compute and display summaries of the blood sugar data

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• Instead of listing of numbers or the averages, one can use graphical and resistant statistical methods to convey answers to the patient

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Looking at Blood Sugar

• The median is much more resistant to unusual points compared to the mean, although both numerical values are summaries of the middle

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• We can also graph the blood sugar levels over a period of time and find a smooth trace through the scatterplot of the data

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• The smooth trace can show the overall pattern, free of the ‘noise’ of point-to-point variation and facilitate identifying exceptions

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• One way of finding a smooth trace is to take local averages of values in the sequence which is called the running mean or moving average

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• But again, running mean is sensitive to outlying values hence it is advisable to use resistant smoothing methods such as the running medians or the running trimmed means which give a less smooth trace

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Looking at Blood Sugar

• Howard explained his ideas using an example

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• Subject: 63-year-old male in generally good health

Height - 6’4’’ and weighed 230 pounds

Exercises robustly five days a week

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• The patient’s fasting blood sugar taken over the past 15 years is shown on the right

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• From the plot, the patient’s blood sugar level was less than 140 mg/dl until after 2005 where we see an upward trend portending a prediabetic condition

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• In 2006, the annual result increased to 183 and after 6 months his fasting blood sugar had risen to 249. The patient was diagnosed as a Type 2 diabetic patient

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Looking at Blood Sugar

• The four possible ways to efficiently decrease the blood sugar level was through
• Medication
• Change in diet
• Change in exercise
• Loss of weight of more than 25 pounds

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• The summary of the efficacy of the four measures is shown in the upper right plot

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• Also, the residual plot allowed the patient to see which actions on his part were helpful

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• I like this article because it is very educative and uses simple graphical displays

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Giving the Finger to Dating Services

• The next article was quite interesting and talked about dating services and the pieces of information requested to help find a better match

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• Many users of these dating services tend to lie about some of the information they give out

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• For example, tall women complained that some of the men lied about their height.

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• One dating service decided to ask the length of the index finger of their members as
• A proxy for height
• A question with no bearing on anything at all but included to distract attention from other, more meaningful questions

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Giving the Finger to Dating Services

• Howard investigated the relationship between the heights and finger lengths from 121 students from University of Pennsylvania

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• There was a modest of correlation (r= 0.52)
• The mean height was 172 cm with standard deviation 9.7cm

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• Knowing the person’s finger, one can predict the height with greater accuracy; the standard deviation was only 8 cm (3.15 inches)

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• Thus 98% of the people would be within six inches of the predictions (plus or minus) which seem hardly likely to help in correcting fraudulent heights

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Giving the Finger to Dating Services

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• Although this was better than the unconditional standard deviation, they concluded that the inclusion of the length of the index finger on the dating serve questionnaire was not likely to be of any help in predicting the height

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Giving the Finger to Dating Services

• 147 Cornell students reported the heights and their ideal height for their ideal spouse

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• The overall correlation was -0.30 which was quite surprising since we expect tall people to want tall mate and short people wanting short people

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• But assessing the variation by gender, we see that each with each gender, there is a fairly strong positive association

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• Thus the difference between the means of the two distributions gave rise to the negative relationship, showing the existence of Simpson’s Paradox

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Comments

• I enjoyed reading both articles mainly because both articles were clear and used graphical displays to explore and understand the data.

Article 1: Looking at Blood Sugar

• The use of scatterplot as well as residual plot was extremely helpful to understand the changes in blood sugar levels
• It explained the use of resistant methods and made use of both statistical and graphical methods
• Unfortunately, some of the horizontal axes of the graphs were not labeled

Article 2: Giving the finger to Dating Services

• This article focused on whether to draw inference for each group (gender) or to draw inference on the entire data sample
• The plot also showed separate regression lines for each sex and the overall regression in both scenarios, which was very good

Overall, everything was good

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