Grade Curve

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• Grade Curve
• A 85 D 50-62
• B 77-84 F 49 and below
• C 63-76

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Sampling Distributions Hypothesis Testing
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Sampling Distributions

• What we know, so far
• Why Statistics is important
• Basic means to describe a set of data
• (i.e. Descriptive Statistics)
• Measures of Central Tendency
• Measures of Variability
• Graphs
• Z-Scores

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Sampling Distributions

• Where were going
• Statistics designed to help us infer
  characteristics of a population from the
  characteristics of our sample (i.e. Inferential
  Statistics) OR comparing two samples
• How do these statistics relate to the research
  questions that were asking?
• How can we phrase these questions so that our
  statistics will answer them?

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Sampling Distributions

• In our experiment, we want to say that change due
  to our IV exceeds variability naturally occurring
  in the sample, or that effect of IV was due to
  chance
• Every sample contains variability due to
  individual differences on whatever is being
  measured
• I.e. in a sample of people with AIDS, some will
  be healthier than others based on their T-cell
  count, degree of overall health before
  contracting AIDS, and how theyve taken care of
  themselves after contracting it

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Sampling Distributions
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Sampling Distributions

• We are conducting an experimental treatment for
  people suffering from AIDS to try to improve
  their quality of life (QOL)
• What is the Independent Variable? The Dependent
  Variable?
• We compare the QOL of our subjects for those
  receiving the Tx to those not receiving it

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Sampling Distributions

• Our Tx is successful to the extent that our
  treated Ss QOL exceeds the healthiest of our
  untreated Ss
• I.e. We want to say our subjects went from being
  sick, to being well, not just from being more
  sick to less sick
• We want to say that the subjects in our two
  groups are qualitatively, not merely
  quantitatively, different

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Sampling Distributions

• Sampling Error variability of a statistic from
  sample to sample due to chance
• Can potentially bias our results if it isnt
  equivalent across treatment and control groups
• I.e. if only the subjects in the Tx group for our
  hypothetical study were convinced as to the
  benefits of our Tx (sampling error), because they
  knew the PI personally beforehand, they may be
  more motivated than most other people and do
  better (the effect of sampling error)
• Random Assignment reduces sampling error by
  equating groups on these chance factors

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Sampling Distributions

• The essential question in any experiment is
• Are the changes in subject performance due to the
  effect of our independent variable, or to
  sampling error?
• I.e. Are the improvement in the treated group in
  our AIDS intervention due to our intervention, or
  to unequal sampling error across our groups?
• All statistics for the rest of this course (i.e.
  t-tests, ANOVA, etc.) are essentially proportions
  of variance due to the effect of our IV versus
  variance due to some kind of sampling error

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Sampling Distributions

• You can obtain many possible samples of any given
  population
• Those sample will tend to differ due to chance
• Therefore you can create a distribution of these
  samples in the same way you create a distribution
  of individuals that differ on a given variable
• This distribution of every possible sample from a
  population is called the sampling distribution
• Like the population of samples

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Sampling Distributions

• Just as you can determine the probability of
  obtaining a given score from a distribution of
  scores, you can find the p(sample) from its
  sampling distribution
• sample of individual scoresstandard
  deviationsampling distributionstandard error

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Sampling Distributions

• There are many ways to characterize a sample in a
  sampling distribution (i.e. mean, median, mode,
  z-scores), but the mean is the most common
• Sampling Distribution of the Mean
• Sampling Distribution of the Median
• Sampling Distribution of the Mode

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Sampling Distributions

• Population 1, 2, 3

Sample Mean
1, 1 1.0
1, 2 1.5
1, 3 2.0
2, 1 1.5
2, 2 2.0
2, 3 2.5
3, 1 2.0
3, 2 2.0
3, 3 3.0
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Sampling Distributions

• Sampling Distribution of the Mean