Transcript Sampling Distributions

Sampling Distributions &
Hypothesis Testing
Sampling Distributions
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What we know, so far/Where we’ve been
Why Statistics is important
 Basic means to describe a set of data
(i.e. Descriptive Statistics):
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Measures of Central Tendency
 Measures of Variability
 Graphs
 Z-Scores
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Sampling Distributions
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Where we’re going
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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 we’re asking?
How can we phrase these questions so that
our statistics will answer them?
Sampling Distributions
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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
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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 they’ve taken care of themselves after
contracting it
Sampling Distributions
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0
1.00
2.00
1.50
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2.50
4.00
3.50
5.00
4.50
6.00
5.50
6.50
Sampling Distributions
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We are conducting an experimental
treatment for people suffering from AIDS
to try to improve their quality of life (QOL)
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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
Sampling Distributions
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Our Tx is successful to the extent that our
treated S’s QOL exceeds the healthiest of
our untreated S’s
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I.e. We want to say our subjects went from
being “sick”, to being “well”, not just from
being more “sick” to less “sick”
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We want to say that the subjects in our two
groups are qualitatively, not merely quantitatively,
different
Sampling Distributions
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Sampling Error – variability of a statistic from
sample to sample due to chance
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Can potentially bias our results if it isn’t equivalent
across treatment and control groups
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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
Sampling Distributions
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The essential question in any experiment is:
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Are the changes in subject performance due to the
effect of our independent variable, or to sampling
error?
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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. ttests, ANOVA, etc.) are essentially proportions of
variance due to the effect of our IV versus
variance due to some kind of sampling error
Sampling Distributions
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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
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Like the population of samples
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 scores:standard
deviation::sampling
distribution:standard error
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Sampling Distributions
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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
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Sampling Distribution of the Mean
Sampling Distribution of the Median
Sampling Distribution of the Mode
Sampling Distributions
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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
Sampling Distributions
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Sampling Distribution of the Mean
3.5
3.0
2.5
2.0
1.5
1.0
.5
0.0
1.00
1.50
2.00
2.50
3.00