Intro to Stats

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Intro to Stats

• Lecture Notes
• November 13, 2008
• R. Sinn

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Example 1

• You are working for a carbohydrate-happy weight
  loss group that hates the Atkins diet. You
  compare a group of 10 female Atkins dieters to a
  behavioral modification approach used with 10
  females. The data is given on the next slide.
• Select an appropriate statistical test.
• Test the hypothesis that behavioral modification
  works better than Atkins at an appropriate level
  of significance.

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Example 1 Data
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Example 2

• A study about child safety restraints found that
  the average days spent in intensive care for 135
  children involved in auto accidents while wearing
  seat belts on average was .83 days (s.d. 1.16).
  In general, children involved in auto accidents
  spent 1.39 days in intensive care.
• Run an appropriate statistical test.
• Test the hypothesis that seat belts use improves
  child safety in auto accidents at an appropriate
  level of significance.

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Example 3

• Mental measurements of children are often made by
  giving them blocks and telling them to make
  towers as tall as possible. A timed experiment
  of block building towers of certain heights was
  repeated two months later after the children had
  spent an hour each week having stories read to
  them. The data is given below.
• Run an appropriate statistical test.
• Test the hypothesis that reading affects block
  building capability at an appropriate level of
  significance.

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Example 4

• The nighttime cold medicine Dozenol bears a label
  indicating the presence of 600 mg of
  acetaminophen in each fluid ounce of the drug.
  The FDA randomly selects 65 bottles to verify
  their claim. The average acetaminophen content
  is 589 mg (s.d. 21).
• Run an appropriate statistical test.
• Test the hypothesis that Dozenol has falsely
  advertised their cold remedy at an appropriate
  level of significance.

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Example 5

• Stress Interrogation. A group of 80 police
  trainees viewed a videotaped crime. Two weeks
  later they were split into two interrogation
  groups stress vs. non-stressful. The number of
  correct details (out of 75) are given below for
  both groups.
• Run an appropriate statistical test.
• Test the hypothesis that there is a significant
  difference in the effectiveness of these two
  types of interrogation.

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Example 6

• MMs weigh approximately 920 mg. Joe weighs 82
  MMs and finds an average of 912 mg and a
  standard deviation of 43 mg. He is concerned he
  is being ripped off and is considering writing
  a letter of protest.
• Run an appropriate statistical test.
• Test the hypothesis that Joe is being ripped off.

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Solutions Example 1

• Treatment vs. Treatment Design Independent
  Samples
• H0 µB µA Group 1 is behavior or B Ha
  µB µA
• Verify normality (all 4 graphs check out).
• Type I Error Falsely claim behavior diet is
  better.Type II Error Falsely claim no
  difference in diets (group would minimize Type II
  set a high, a 0.1)
• Run test (t 1.9002, p 0.038)
• Since p 0.038
• Evidence suggests behavior diet is better than
  Atkins.

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Graphics Example 1

• Enter data into List1 and List2
• Run an independent samples t-test

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Solutions Example 2

• Sample vs. Population
• H0 µ 1.83Ha µ 1.83
• Verify normality (Law of Large Numbers).
• Type I Error Falsely claim seat belts
  work.Type II Error Falsely claim they dont
  (minimize Type II set a high, a 0.1)
• Run test (t -5.6091, p 0)
• Since p 0
• Evidence suggests child safety seats improve
  safety.

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Graphics Example 2

• Run a one sample t-test

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Solutions Example 3

• Dependent Samples T-Test (Pretest-Posttest)
• H0 µ 0Ha µ 0
• Verify normality Box Plot show outliers (see
  graphics, next slide).
• Cannot run test.

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Graphics Example 3

• Make difference list
• Check Graphics stop since outliers are detected