Transcript Statistics Supplement

Intro to Psychology
Statistics Supplement
Statistics Supplement
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Descriptive Statistics: used to describe different aspects
of numerical data; used only to describe the sample.
Includes measures of central tendency, variability, and
correlation
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Inferential Statistics: uses probability theory to allow
researchers to generalize and predict results of the
population outside of the sample; used to determine
whether or not a hypothesis is supported or rejected
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Can make inferences about a population from a sample
Can compare multiple groups to each other (i.e. experimental
and control)
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Measures of central tendency
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Mean
Median
Mode
Variability
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Range
Standard Deviation
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Normal Distribution – the “bell curve”
Statistics Supplement
Statistics Supplement
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Many things are normally distributed:
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Intelligence Scores
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[(Mental Age) / (Chronological Age)] x 100 = IQ
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Mean IQ = 100
Std. dev = 15
IQ over 130 is exceptionally smart
IQ under 70 is one criteria for Intellectual Disability
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We use assumptions about the normal distribution in
order to determine if data collected comply with a known
distribution or are significantly different
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You can also compare a single score to a population
distribution to see how rare it is
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Percentiles and standardized tests
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SAT v. ACT
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SAT
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ACT
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Mean = 1026
SD = 209
Mean = 20.8
SD = 4.8
Which is better, getting a 1277 on the SAT or
a 28 on the ACT?
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Correlation & Regression
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Correlation coefficient R describes the strength and direction of the relationship
between two observed variables
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-1≤ r ≤ 1
 -1 being a perfect negative correlation
 +1 being a perfect positive correlation
 0 represents no relationship
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Linear Regression equations draw an imaginary line through the data cluster;
the slope and intercept of the line is used to predict future values based on
previous data
 Expressed as y = mx + b
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Statistics Supplement
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Just because something has a strong
correlation doesn’t mean there is a
cause/effect relationship
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Many statistics can be misleading if you don’t
pay close attention
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Inferential statistics
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Determine whether a sample of data is due to chance
responding or due to a meaningful trend
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Can compare two or more groups
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Can compare a group to a known norm
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Can compare longitudinal data from the same group
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Statistical Significance
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Statistical Significance is achieved when the probability of getting
a specific set of data by chance is extremely slim
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Typically, this probability is less than .05 or 5%
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IF the groups were the same, THEN the probability of getting that sample
by chance would be very unlikely. Therefore, the researcher concludes
that the groups are (probably) not the same.
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Because of the way statistics tests work, a researcher can never “prove”
anything. They can only demonstrate how probable or improbable a
certain event is.
 If someone claims they have “proven” anything, don’t trust them.
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Power
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Statistical power is the ability to correctly detect
an effect if one exists
Power is effected by:
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Sample size
Reliability and validity of measures
Within vs. between participants designs
Effect size of the treatment
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Type I Error: False Positive
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The researcher incorrectly determines that there is an effect
when in reality none exists
The probability of a Type I error is α
α is determined by the researcher based on how bad implications
for a false positive would be
Type II Error: False Negative
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The researcher incorrectly determines that there is not effect
when in reality there is an effect
The probability of a Type II error is β
β can be reduced by increasing Power
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While researchers want to find statistically
significant differences between their groups,
just because something is “statistically
significant” doesn’t mean that it is practically
significant.
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Studies with very large sample sizes can
detect tiny differences that may not be
meaningful
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Be a thoughtful consumer of science
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Ask:
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How big was the sample?
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What was the effect size?
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Was the sample representative of the
population?
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Did they use random assignment?
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Did they have an appropriate control group?
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Were the measures reliable and valid?
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Was the study blind/double-blind?