Transcript Basic Statistics for the Behavioral Sciences

Chapter 9
Probability
More Statistical Notation
 Chance is expressed as a percentage
 Probability is expressed as a decimal
 The symbol for probability is p
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Probability
The probability of an event is equal to
the event’s relative frequency in the
population of possible events that can
occur.
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Obtaining Probability from the
Standard Normal Curve
Probability of Individual Scores
The proportion of the total area under
the normal curve for scores in any part
of the distribution equals the probability
of those scores.
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Obtaining Probability
To compute probability, use the same
techniques you learned for finding the
area under the normal curve using z
scores and the z-tables.
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Z-distribution Showing the Area for Scores Below
the Mean, and Between the Mean and Z = +1
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Making Decisions Based
on Probability
Representativeness
 Any sample may poorly represent one
population, or it may accurately
represent a different population
 The essence of inferential statistics is
to decide whether a sample of scores
is likely or unlikely to occur in a
particular population of scores
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Region of Rejection
 At some point, a sample mean is so far above or
below the population mean that it is unbelievable that
chance produced such an unrepresentative sample
 The areas beyond these points is called the region of
rejection
 The region of rejection is the part of a sampling
distribution containing values that are so unlikely that
we “reject” that they represent the underlying raw
score population
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Means in the Region of Rejection Are So
Unrepresentative of This Population That It’s a
Better Bet They Represent Some Other Population.
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Criterion
The criterion is the probability that
defines samples as too unlikely for us to
accept as representing a particular
population.
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Rejection Rule
 When a sample’s z-score lies beyond the
critical value, reject that the sample
represents the underlying raw score
population reflected by the sampling
distribution
 When the z-score does not lie beyond the
critical value, retain the idea that the
sample may represent the underlying raw
score population
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Sampling Error
 When the sample statistic is not
identical to the population parameter
 Amount of error between a sample
statistic & its corresponding
population parameter
- Different samples from same population
Distribution of Sample Means
 Collection of sample means for all the
possible random samples of a
particular size (n) that can be obtain
from a population
 To predict characteristics of
distribution
 Sample means should pile up around pop
mean
 Pile should form normal distribution
 Larger sample sizecloser sample
means to pop mean
Central Limit Theorem
 Distribution of sample means approach a
normal dist. as N approaches infinitiy n
 Dist. Of sample means tends to be normal
if:
 Pop from which samples selected is normal
 Number of scores is relatively large, n=30
Standard Error of the Mean
 Standard deviation of the distribution
of sample means
 SE measures the standard amount of
difference between sample mean and
the pop mean

estimate!!