Math 145

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Math 145

• September 20, 2006

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Review

• Methods of Acquiring Data
• Census obtaining information from each
  individual in the population.
• Sampling obtaining information from a part of
  the population (sample) in order to gain
  information about the whole population.
• Observational Study observes individuals and
  measures variables of interest but does not
  attempt to influence the responses.
• Experiments deliberately imposes some treatment
  on individuals in order to observe their
  responses.

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Example of Designed Experiment

• Example 1 Consider the problem of comparing the
  effectiveness of 3 kinds of diets (A, B, C).
  Forty males and 80 females were included in the
  study and were randomly divided into 3 groups of
  40 people each. Then a different diet is assigned
  to each group. The body weights of these 120
  people were measured before and after the study
  period of 8 weeks and the differences were
  computed.
• Example 2 In a classic study, described by F.
  Yates in the The Design and Analysis of Factorial
  Experiments, the effect on oat yield was compared
  for three different varieties of oats (A, B, C)
  and four different concentrations of manure (0,
  0.2, 0.4, and 0.6 cwt per acre).

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Terminologies in Experiments

• Experimental Units These are the individuals on
  which the experiment is done.
• Subjects human beings.
• Response variables Measurement of interest.
• Factors Things that might affect the response
  variable (explanatory variables). new drug
• Levels of a factor different concentration of
  the new drug no drug, 10 mg, 25 mg, etc.
• Treatment A combination of levels of factors.
• Repetition putting more than 1 experimental
  units in a treatment.

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Example 1 Diet Study

• Example 1 Consider the problem of comparing the
  effectiveness of 3 kinds of diets (A, B, C).
  Forty males and 80 females were included in the
  study and were randomly divided into 3 groups of
  40 people each. Then a different diet is assigned
  to each group. The body weights of these 120
  people were measured before and after the study
  period of 8 weeks and the differences were
  computed.
• Experimental units People
• Response variable Weight lost
• Factor(s) Diet
• Levels diet A, diet B, diet C
• Treatments diet A, diet B, diet C

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Example 2 Oat Yield Study

• Example 2 In a classic study, described by F.
  Yates in the The Design and Analysis of Factorial
  Experiments, the effect on oat yield was compared
  for three different varieties of oats (A, B, C)
  and four different concentrations of manure (0,
  0.2, 0.4, and 0.6 cwt per acre).
• Experimental units Fields
• Response variable Oat yield
• Factor(s) Oat variety, Manure concentration
• Levels Oat A, B, C Concentration 0, .2, .4,
  .6
• Treatments (A, 0), (A, .2), , (C, .6)

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Designs of Experiments

• Completely Randomized Experimental units are
  allocated at random among all treatments.
• Double-Blind Study Neither the subjects nor the
  medical personnel know which treatment is being
  giving to the subject.
• Matched Pair Used for studies with 2 treatment
  arms, where an individual from one group is
  matched to another in the other group.
• Block Design The random assignment of units to
  treatments is carried out separately within each
  block.
• Block is a group of experimental units that are
  known to be similar in some way that is expected
  to affect the response to the treatment.

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Example 1 Diet Study

• Example 1 Consider the problem of comparing the
  effectiveness of 3 kinds of diets (A, B, C).
  Forty males and 80 females were included in the
  study and were randomly divided into 3 groups of
  40 people each. Then a different diet is assigned
  to each group. The body weights of these 120
  people were measured before and after the study
  period of 8 weeks and the differences were
  computed.
• Block - Gender

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Section 3.3 Sampling Designs

• Simple Random Sampling.
• Systematic Sampling.
• Cluster Sampling.
• Stratified Sampling (with proportional
  Allocation).

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Section 3.4 Sampling Distributions

• Parameters vs. Statistics.
• Parameter a number that describes the
  population. A parameter is a fixed number, but in
  practice we do not know its value.
• Statistic a number that describes a sample. We
  often use a statistic to estimate the value of an
  unknown parameter. Its value changes from sample
  to sample.
• Sampling Distribution
• A Statistic used to estimate a parameter is
  unbiased if the mean of its sampling distribution
  is equal to the parameter value.

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Homework
Exercises Sec 3.1 3.2 1, 2, 3, 5, 9, 11,
12, 20, 21, 23. Sec 3.3 3.4 36, 37, 38, 52,
56, 57, 63, 64, 66, 76.
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Thank you!