Chapter 1 by 39r8181

VIEWS: 5 PAGES: 17

									Introduction to Making
  Decisions with Data
       The Scientific Method
•   Formulate a theory
•   Collect data to test theory
•   Analyze the results
•   Interpret results and make a decision
•   Re-evaluate theory
      What is Statistics?
• Most basic: A way to summarize
  information.
• Real Purpose: A method for making
  decisions based upon data.
       What is a Theory?
• Write down the definition of “theory.”
• Share it with the persons next to you.
   Fundamental Idea of
 Decision Making with Data
• A theory is rejected if it can be shown
  statistically that the data observed
  would be very unlikely to occur if the
  theory were in fact true. A theory is
  accepted if it is not rejected by the
  data.
              Example
• Theory: There are 4 blue balls and 1
  yellow ball in the bag.
• Collect Data: Pull a ball from bag, note
  color and replace it.
• Analyze the Results: How many blue?
  How many yellow?
• Interpret and make Decision
  My Daughters Guinea Pig
• My daughters guinea pig started to get
  real fat. We were concerned that we
  had been over feeding her or that she
  had perhaps grown a tumor.
• Out popped three baby guinea pigs.
  The pet shop owner had assured us
  that the other pig in the pen with her
  was a female.
     The Decision to Make
• Competing Theories: The other guinea pig
  was female vs. the other guinea pig was male
• Collect Data: Three baby guinea pigs
• Analyze Results: The probability of the
  bunkmate being female is very small.
• Interpret and Make Decision: Don’t call the
  Vatican just yet.
   Example of Hypotheses
• Theory: A study suggests the taking
  Glucosamine and Chondroitin will reduce joint
  pain for the majority of users.
• To test this theory we need to form competing
  hypotheses about the statement.
• The Null Hypothesis is the status quo, or
  prevailing view.
• The Alternate Hypothesis is the opposite of
  the null, the research hypothesis.
State the Null and Alternate
• The null hypothesis is denoted H0 and the
  alternate is given by H1
• H0: Taking Glucosamine and Chondroitin will
  not reduce joint pain for the majority of users
  (more than 50% of users).
• H1:Taking Glucosamine and Chondroitin will
  reduce joint pain in the majority of users
  (more than 50% of users).
• (We’ll let Glucosamine and Chondroitin be
  abbreviated as G/C from here)
          Based on Data,
          Make a Decision
• If the proportion of subjects that report less
  joint pain is the same as with a placebo?
• If 75% of the subjects taking G/C report
  significantly less joint pain and only 35%
  reported less pain that were taking the
  placebo?
• If the difference between G/C and the
  placebo was 2%?
• How large of a difference in proportion is
  needed for you to feel confident in rejecting
  the null hypothesis?
  Recall: Fundamental Idea
• A theory is rejected if it can be shown
  statistically that the data observed
  would be very unlikely to occur if the
  theory were in fact true. A theory is
  accepted if it is not rejected by the
  data.
       Could’ve We Been
          Mistaken?
• Is it possible that if we concluded from
  our data that G/C worked that we could
  be wrong?
• Is it possible that if we concluded from
  our data that G/C didn’t work that we
  could be wrong?
          Types of Errors
• If we reject H0 when it was true we’ve
  made a Type I error
• If we fail to reject H0 when it is false,
  then we’ve made a Type II error
• For example,
   H0: Person is innocent
   H1: Person is guilty
  Explain what a type I and type II error
  would be in this case.
                   The Truth
                   Null True Alternate
                             True
Your     Null      No Error Type II
Decision Accepted            Error
Based
Upon     Alternate Type I    No Error
the Data Accepted Error
     Which Error is Worse?
• H0: The water is contaminated.
  H1: The water is not contaminated.
• H0: The parachute works.
  H1: The parachute does not work.
• H0: A hostile country has weapons of mass
  destruction.
  H1: A hostile country does not have weapons of mass
  destruction.
• H0: The infant pain reliever has the stated amount of
  acetaminophen.
  H1: The infant pain reliever has more than the stated
  amount of acetaminophen.

								
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