Transcript Psychological Statistics PSYC 2330

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Understanding the scores from Test 2
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In-class exercise
Chapter 7
Probability and Samples: The
Distribution of Sample Means
Samples and sampling error
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Probability of randomly selecting certain
scores from a population
Probability of randomly selecting certain
samples from a population
Consider the probability of randomly
selecting Test #1 scores from our class
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Sampling error
Sample size and sampling error
Constructing a distribution of sample means
Distribution of sample means
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Distribution of sample means = sampling
distribution of the mean = all possible
random sample means (of a given size)
from a given population
In-class exercise (watching sampling
distributions develop)
Distribution of sample means
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Characteristics
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Central limit theorem
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Mean of sampling distribution = mean of
population (M = )
Shape of sampling distribution is normal if n>30
Variability of sampling distribution < variability of
population
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Standard error of M = M = /n
What does M tell you?
Amount of sampling error depends on SD of population
and size of sample
Probability and distribution of
sample means
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Sampling distribution of mean
approximates normal distribution
Can use concept of z-scores and apply to
sample means
Compare z-score formula for x-score to zscore formula for sample mean (M)
Now we can play with the probabilities of
sample means
More about standard error
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Standard error of the mean (SE) is a
measure of sampling error
Average error between a known sample
mean and the unknown population mean
it represents
SE often reported in research literature
and often depicted on graphs
More about standard error
Compare these two graphs:
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Mean +- 1 SE dv2
Mean +- 1 SE dv1
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Looking ahead to inferential
statistics
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Can determine the probability (or percent
chance) that a treated sample comes from
a known untreated population
If the probability is relatively high, then
we conclude no effect of treatment
If the probability is relatively low (<.05),
then we conclude effect of treatment