As part of my recent efforts to end hunger in young adults, I have been delving into the homeless issue in our city. Here is a mathematical analysis of the city of Portland’s homeless issue using data I have collected at one homeless shelter in the city

Portland:


When looking at Portland, we can look a the data that I collected at Clay Street Table and see if there is a connection between temperature and number of meals served.

Date Temp

(Degrees Fahrenheit)

Conditions Number of people served Expected number of people served
9/6 72 Clear sky, humid 318 274
9/10 64 Sun out, blue sky, dry 312 274
9/13 55 Drizzled mid day, cool breeze 360 274
9/15 59 Clear 323 274
9/20 54 Drizzled mid day 362 274
9/24 55 Cloudy 312 274
9/27 66 Clear, cold wind 415 274
10/1 54 Drizzled during serving 327 274
10/4 48 Rain Showers 212 274
10/8 53 Cloudy 276 274
10/11 54 Cloudy 271 274
10/14 52 Rain showers 285 274
10/18 52 Storm warning, torrential rains, cloudy, thunder 212 274
10/21 51 Cloudy, drizzles 302 274
10/25 47 Cloudy, cold breeze 251 274
10/29 52 Drizzled before cooking, wet 216 274
11/1 49 Clear, crisp and cold 277 274
11/6 46 Finished raining at about 2, cool and clear after 226 274
11/13 44 Showers midday, cloudy during serving 212 274
11/15 42 Rain midday 217 274

 

I found the temperature (in fahrenheit) by recording it each time I volunteered using the Weather application on my phone. I collected a few descriptive words as well to aid in the recollection of the weather. While I only attend every week, I had one of my colleagues, jot down the temperature at 6 pm every tuesday or Friday night as well as how many meals were served using either dashes on a piece of paper or a clicker-counter that I left at the site for them to use.

 

The expected data I got from some simple math. Expected data is how many meals are expected to be served each night regardless of any outside characteristics. By finding the expected number of meals served and comparing it to the number of meals served I can calculate the Chi Squared calculation and see if there is connection between temperature and whether or not more or less people come to a shelter due to a drop in temperature.

 

I found the expected value by finding the total number of meals served per year. This number is around 97,000. I found this number because the total number of meals and groceries used is around 145,000 and groceries account for ⅓ of this data, meaning that the hot dinners are ⅔ times 145,000 which is around 97,000 hot meals. Since CST serves dinner, 354 days a year (on a non-leap year) we can divide 97,000 by 354. This gives us an expected number of meals served to be 274 meals.

In the following table are my chi squared tests. The equation is

Residual

(Observation – Expected)

(Residual)2 (Residual)2/Expected Σ
44 1936 7.07
38 1444 5.27
86 7396 27.0
49 2401 8.76
88 7744 28.3
38 1444 5.27
141 19881 72.6
53 2809 10.3
-63 3969 14.5
2 4 .015
-3 9 .033
11 121 .442
-62 3844 14.0
28 784 2.86
-23 529 1.93
-58 3364 12.3
3 9 .033
-48 2304 8.41
-62 3844 14.0
-57 3249 11.9 244.993

Residual: (Residual)2/Expected: Σ

318 – 274 = 44 1936 ÷ 274 7.07

312 – 274 = 38 1444 ÷ 274 12.34

360 – 274 = 86 7396 ÷ 274 39.34

323 – 274 = 49 2401 ÷ 274 48.1

362 – 274 = 88 7744 ÷ 274 76.4

312 – 274 = 38 1444 ÷ 274 81.67

415 – 274 = 141 19881 ÷ 274 154.27

327 – 274 = 53 2809 ÷ 274 164.57

212 – 274 =  -63 3969 ÷ 274 179.07

276 – 274 = 2 4 ÷ 274 179.085

271 – 274 = -3 9 ÷ 274 179.118

285 – 274 = 11 121 ÷ 274 179.56

212 – 274 = -62 3844 ÷ 274 193.56

302 – 274 = 28 784 ÷ 274 196.42

251 – 274 = – 23 529 ÷ 274 198.35

216 – 274 = -58 3364 ÷ 274 210.65

277 – 274 = 3 9 ÷ 274 210.683

226 – 274 = -48 2304 ÷ 274 219.093

212 – 274 = -62 3844 ÷ 274 233.093

217 – 274 = -57 3249 ÷ 274 244.993

 

My chi squared sum is lower than my expected value by about 30 people. This means that the decreasing temperature decreases the overall value of the attendance. The chi squared data shows us that the temperature does in fact alter the data and since the temperature has been decreasing in the recent data sets, the decrease in temperature has caused the chi squared value to drop below the expected rate. This means there is in fact a relationship between the two variables: temperature and attendance.

The lower the temperature, the lower the attendance compared to the expected.

 

In addition to chi squared analysis, I also performed a graphical analysis on my data.

 

The data line of best fit worked best in cubic form. The equation for this cubic was:

Attendance = 3153 + (-180 (Degrees Fahrenheit)) + 3.6 (Degrees Fahrenheit 2) + (-.023 (Degrees Fahrenheit3))

This equation worked for for every temperature test I ran.

Example:

At 44 degrees: 3153 + (-180 (44)) + 3.6 (442) + (-.023 (443)) = 223 people

Actual average attendance at this temperature: 212

At 55 degrees:  3153 + (-180 (55)) + 3.6 (552) + (-.023 (553)) = 316 people

Actual average attendance at this temperature: 336

At 51 degrees: 3153 + (-180 (55)) + 3.6 (552) + (-.023 (553)) = 285 people

Actual average attendance: 302

At 49 degrees: 3153 + (-180 (49)) + 3.6 (492) + (-.023 (493)) = 271 people

Actual average attendance: 277

There are some flaws in this equation. For example, at 90 degrees, it says that there would be a negative attendance at at 10 degrees it says that the attendance would be over a thousand people. However, there are several things that this equation does well:

  1. Adequately evaluates the attendance for temperatures of between 40 degrees and 70 degrees
  2. Shows prime attendance temperatures (the graph should not be linear because at a certain point for temperatures very low and very high the attendance will decrease sharply)

 

Advertisements

2 thoughts on “

  1. You lost your old granny.
    Thank God for the last line or two.
    Does it seem that clients have a place to stay out of inclement weather?

    Like

  2. I love the analysis! Now, when students say, “Where can I apply chi shared???” Now there’s an answer. You are so smart! Thanks for looking out for our most vulnerable.

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

w

Connecting to %s