Demonstration of Ranking Issues for Students: A Case Study

Figures & data

Table 1. Variables included in Town rankings for the three categories.

Public Safety:

Violent crimes per capita in 2001

Structure fires per capita in 2001

Motor vehicle deaths per capita in 2001

Public spending per capita in 2001

Health:

Incidence per 100,000 of HIV in 2001

Incidence per 100,000 of Sexually Transmitted Diseases in 2001

SIR of Cancer (Leukemia, Breast, Lung, Bronchus, Prostate, Colon, and Rectal) in 2001

Environment:

Percent open space in 2001

Air pollution sources per square mile in 2001

Number of contaminated sites per square mile in 2001

Presence of Radon (low, medium, high)

Figure 1. Mean of standardized indices versus log of population of townships.

Figure 2. Standardized scores for the safety index versus log of population.

Figure 3. Standardized scores for the environmental index versus log of population.

Figure 4. Standardized scores for the health index versus log of population.

Figure 5. Relationship between the mean of standardized ranks and population-adjusted ranks.

Figure 6. Difference between population-adjusted ranks and mean-standardized ranks versus the average of the two ranks.

Table 2. Top fifteen towns using different ranking methods

Rank	Mean-Standardized Rank Town	Population-Adjusted Rank Town
1	Dover	Wayland
2	Wayland	Plymouth
3	Cohasset	Wellesley
4	Wenham	Quincy
5	Carlisle	Hingham
6	Hingham	Brookline
7	Lincoln	Needham
8	Boxford	Dover
9	Medfield	Franklin
10	Weston	Weston
11	Duxbury	Cohasset
12	Wellesley	Duxbury
13	Hanson	Sharon
14	Bolton	Bridgewater
15	Maynard	Medfield

Table 3. Bottom fifteen towns using different ranking methods

Rank	Mean-Standardized Rank Town	Population-Adjusted Rank Town
147	Chelsea	Chelsea
146	Lawrence	W. Bridgewater
145	Worcester	Avon
144	Boston	Lawrence
143	Lowell	W. Newbury
142	Brockton	Topsfield
141	Lynn	Worcester
140	New Bedford	Wilmington
139	W. Bridgewater	Brockton
138	Cambridge	Lynn
137	Avon	Rowley
136	Everett	Lowell
135	Somerville	Rockland
134	Wilmington	Everett
133	Haverhill	Littleton

Figure 7. Relationship between the difference between ranks and log of population.

Figure 8 Display of Under Performing and Over Performing Towns.

Table 4. The fifteen best over-performing towns and worst under-performing towns.

Under-performing Towns (Rose less, or fell more, than expected in rank)		Over-performing Towns (Rose more, or fell less, than expected in rank)
Actual Change in Rank (positive means they moved closer to the bottom of the rankings)	Town/City	Actual Change in Rank (negative means they moved closer to the top of the rankings)	Town/City
−27	Boston	−44	Billerica
−4	Worcester	8	Avon
−3	Brockton	−60	Newton
−3	Lynn	−51	Waltham
−7	Lowell	−40	Beverly
−8	New Bedford	13	W. Newbury
−2	Lawrence	−33	Lexington
54	Stow	7	Dover
62	Nahant	−36	Marlborough
46	Newbury	−40	Methuen
41	Hamilton	−31	Andover
39	Southborough	−38	Arlington
56	Sherborn	−47	Framingham
49	Manchester-by-the-Sea	7	W. Bridgewater
59	Essex	−25	N. Andover