Homework 6
Math 114Q, Sections 9, ll

Due in class Tuesday, October 28.

  1. The article ``False positives, false negatives, and the validity of the diagnosis of major depression in primary care" appeared in the Archives of Family Medicine in September 1998 ( see archfami.ama-assn.org/cgi/reprint/7/5/451). The article reports a study of 372 patients who were screened by family physicians for clinical depression. Patients were also interviewed by psychiatrists and completed mental health surveys. The results of the study were 
    True positives:  31
False positives:  34
False negatives:  50
True negatives:  257

    1. Make a contingency table in Excel that displays this data. Be sure to label the spreadsheet and the rows and columns you use in it. The condition being tested here is major depression, so a positive result means that major depression is present.

    2. Use Excel formulas to compute the false positive probability and the false negative probability. (These are often the statistics that are reported.) Check your work by computing the same probabilities by hand.

    3. Write a brief explanation of what the false positive and false negative rates mean in this context. Discuss how the false positives and false negatives might matter to the doctor and to the patient.

    4. Suppose the authors of the paper suddenly realize that they misreported their results, accidentally interchanging the values for false positives and false negatives. Use Excel to compute the new probabilities. Note: this did not happen! We've asked the question only to give you practice at asking "what-if" questions in Excel.

    Turn in a printout of your spreadsheet (it should fit on one page) along with your homework.

  2. The following (made up) table shows the salary structure of two departments in a (hypothetical) university. 
    
	Physics				English
	# in dept	salary		# in dept	salary
Women	1		$100K		9		$50K
Men	9		$90K		1		$40K

    1. What is the probability that a professor in this sample is in the English department?

    2. What is the probability that a professor in this sample is a woman?

    3. What is the probability that a professor in this sample is a woman if you know he or she is in the English department?

    4. What is the average (mean) salary of a professor?

    5. What is the average (mean) salary of a professor you know to be a woman?

    6. What is the average (median) salary of the women professors? Of the men?

    7. What is the average (modal) salary of the women professors? Of the men?

    8. Use the given statistics to argue first that women are being discriminated against and then that they are not.

  3. Common Sense Exercise 9.3 (in the original version of the book).

    Add five Workers each earning $18K to the Wing Aero payroll by inserting some rows in the table. Comment on what has happened to the mean, median and modal incomes.

    Note that Excel automatically recomputes the averages, but not the histogram for which we created data by hand.

    You can start with your spreadsheet, or with ours, from WingAeroStudy.xls.

  4. Common Sense Exercise 10.3 (in the original version of the book).

    This histogram from en.wikipedia.org/wiki/Household_income_in_the_United_States shows the percentage of the population per income group in $10K increments, except for the furthest two right columns which are $50K increments.

    You can find the raw data at the US Census 2006 Economic Survey pubdb3.census.gov/macro/032007/hhinc/new06_000.htm

    Use the techniques we developed in class to estimate mean, median and modal household income. Then discuss how your answers compare to the corresponding figures in wikipedia.

    (You need to be careful with those last two categories.)