Statistics is about decisionmaking

1
Statistics is about decision-making

• Why do we need statistical help in
  decision-making?
• Three possible worlds
• Completely systematic
• Completely random
• Partially systematic partially random
• Signal-to-noise problem

2
What would life be like if

• Every day, the weather was predictable?
• Predators were equally distributed in every
  direction?
• Volcanoes erupted on a schedule?
• That would be a completely systematic world.

3
What would life be like if

• The weather one day was unrelated to weather the
  day before?
• Animals attacked or fled unpredictably?
• Mating displays changed from year to year?
• That would be a completely random world.

4
What would life be like if

• Weather was predictable, but not perfectly
• Tigers were few in N. America (but there were
  some)
• Most people believed that Elvis is dead (but
  some just couldnt let go).
• In fact, that is how the world actually is.

5
Consider human height

• Known influences
• genetic influence (including in womb)
• nutrition effects
• sex effects testosterone? estrogen?
• Unknown influences
• ???

6
Consider human height

• The known influences have systematic effects
• On average, men are taller than women.
• The unknown influences have random effects
• Some women are taller than their brothers.

7
Consider human height

• In the long run, the unknown (random) influences
  are equally likely to increase and decrease human
  heights so when we look at the averages for the
  whole population, the average man is taller than
  the average woman.
• the and random effects cancel each other
  out, in the long run.

8
Decision-making

• We want our decisions to be informed.
• How can we make the health care system work
  better?
• How can we make the education system better?
• How can we make our factory run more efficiently?

9
Decision-making

• How can we make the health care system work
  better?
• Discover the systematic influences on health
  care.
• These may be obscured by random influences
  (e.g., surgeon killed in plane crash at Pelee
  Island three years ago).
• But they are all we can work with

10
Decision-making

• Systematic influences are seen in what is true
  in general.
• How do we find out what is true in general?
• One way would be to measure a whole population
  but that is not practical.
• too expensive
• too time-consuming

11
Decision making

• How do we find out what is true in general?
• Since we usually cant work with populations, we
• (a) find out what is true in representative
  samples
• (b) make an inference to what is true in general
• Problem what is true in samples is only
  approximately (more or less) true in the
  sampled population

12
Decision making

• Samples may not give us the long run picture
  random effects may not exactly cancel each other
  out.
• And thats why we need statistics to extract
  the long-run picture from sample data. Statistics
  is an aid to decision making. It pulls the signal
  (systematic influences) out of the noise (random
  influences).

13
Probabilistic statements

• Contrast this view with that held 200 years ago
• Knowledge assumed to be absolute
• Human nature though to be constant, true of all
  humans
• Rise of measurement for insurance, military, and
  political purposes
• led to concept of what is normal
• Normal implies that variability is expected.

14
Probabilistic statements

• We now know that many systems and behaviors we
  are interested in can be understood
  probabilistically.
• That is, our predictions of future system states
  or behaviors do not have to be 100 correct to be
  useful.
• Information that is likely to be true is the
  best we can do and it is good enough.

15
Probabilistic statements

• Scientists make probabilistic statements about
  the phenomena they study.
• Evaluating such statements requires an
  understanding of statistics.
• Thats why youre taking this course.