Theoretical Models and Accuracy

• As we discussed previously, one of the most useful ways of evaluating a theoretical model is to compare the predictions of the model against empirical data

• Unfortunately, many industries do not provide you with information on the accuracy of their predictions– how many people improve after taking a drug– how many people actually lose weight by eating Subway

sandwiches– how many horoscopes accurately predict the future

• As a consequence, it is almost impossible for you, as a consumer, to evaluate the quality of the product

• In general, weather forecasters make their predictions based on either mathematical models/simulations of weather systems, past weather conditions, intuitive judgments based on the movement of current weather systems, or “all of the above”

• Unfortunately, weather forecasters do not tell us—the consumers—how accurate their forecasts are. We don’t know what the “track record” is for any weather/news team. (Moreover, they don’t keep records of past forecasts on their websites, thereby preventing consumers from investigating the matter themselves.)

A scientific analysis of the accuracy of weather forecasting

• Students recorded the 5-day forecasts (on Sunday nights) for 3 weeks for the following sources

– WGNTV

– NBC

– CH. 7

– Fox News

– Intellicast

– Chicago Tribune

• Dr Fraley recorded the actual, end-of-the-day weather from an unrelated source: Weather Underground.

• This allows us to compare the predictions made by the different teams with the actual weather.

Average temperature observed, as recorded by Weather Underground, Chicago

Days

Ave

rag

e t

em

pe

ratu

re

2 4 6 8 10 12 14

40

45

50

55

60

65

70

April 5th – April 23rd, 2004

Date Predicted Observed Discrepancy

4/5 46.00 41.00 5.0

4/6 48.50 58.00 -9.5

4/7 43.50 54.00 -10.5

4/8 38.00 50.00 -12.0

4/9 38.00 46.00 -8.0

4/12 35.50 38.00 -2.5

4/13 43.00 40.00 3.0

4/14 47.00 50.00 -3.0

4/15 53.50 62.00 -8.5

4/16 55.00 70.00 -15.0

Average absolute discrepancy: 7.7 degrees~ not too bad, eh? ~

Predictions made by WGN, Channel 9, on Sunday nights

Errors tended to get larger as more days passed between when the prediction was made (Sunday evenings) and the day in question.

Five days later, the average prediction was off by about 10 degrees.

(These numbers are based on WGN TV)

Number of days since prediction

Dis

crep

ancy

be

twee

n pr

edic

ted

and

act

ual t

emp

erat

ure

Predicted Temperature

Act

ua

l Te

mp

era

ture

30 40 50 60 70 80

30

40

50

60

70

80

Predicted TemperatureA

ctu

al T

em

pe

ratu

re

30 40 50 60 70 80

30

40

50

60

70

80

Predicted Temperature

Act

ua

l Te

mp

era

ture

30 40 50 60 70 80

30

40

50

60

70

80

Predicted Temperature

Act

ua

l Te

mp

era

ture

30 40 50 60 70 80

30

40

50

60

70

80

Predicted Temperature

Act

ua

l Te

mp

era

ture

30 40 50 60 70 80

30

40

50

60

70

80

Predicted Temperature

Act

ua

l Te

mp

era

ture

30 40 50 60 70 803

04

05

06

07

08

0

WGNTV | Mean Discrepancy = 6.3

NBC | Mean Discrepancy = 4.2 CH. 7 | Mean Discrepancy = 7

Fox | Mean Discrepancy = 3.9 Intellicast | Mean Discrepancy = 8.9

Chicago Tribune| Mean Discrepancy = 6.2

Date Observed Predicted

4/5 41.00

4/6 58.00 41.00

4/7 54.00 58.00

4/8 50.00 54.00

4/9 46.00 50.00

4/12 38.00 46.00

4/13 40.00 38.00

4/14 50.00 40.00

4/15 62.00 50.00

4/16 70.00 62.00

As an additional comparison, we can generate predictions in another way: based on “day before” temperature

In this case, we’re assuming that the best bet for tomorrow’s temperature is today’s.

Average discrepancy: 7.35

What about broader weather conditions?

• Broader weather conditions– (a) sunny/clear– (b) partly cloudy/mostly cloudy– (c) thunderstorm– (d) rain/showers

• Accuracy in prediction– NBC 73%– Intellicast 80%– Chi. Trib 40%– Day before 71%

Summary

• It appears that the various weather teams do a pretty good job in predicting the temperature– They were only off by approximately 4 – 9 degrees, on average.

– Their ability to make accurate forecasts was lower for extended forecasts.

• In predicting weather conditions (e.g., rain, shine), the various stations were right 40 (Chi. Tribune) – 80% (Intellicast) of the time.

• Nonetheless, you wouldn’t know how good they are without doing the research yourself.

Quiz1. True/False: According to the graphs last week. You can predict a

persons level of Extroversion based on their Astrological Sign.

2. In our in-class exercise on horoscopes, which group felt that their horoscopes were most valid?a) the group with the true horoscopesb) the group with the true and false horoscopes provided fairly

comparable responsesc) the group with the Sun Times horoscopes

3. Why should we care about the pseudosciences in health care?a) People will use them in stead of scientifically supported health

care.b) They take money away from psycologists.c) They might harm people’s souls.