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Review
Measure testosterone level in rats; test whether it predicts
aggressive behavior.
What would make this an experiment?
A.
B.
C.
D.
Randomly choose which rats to measure
Force some rats to get into fights
Manipulate testosterone levels
Make sure nothing differs across rats except
testosterone
Review
Measure testosterone level in rats; test whether it predicts
aggressive behavior.
Perhaps getting in fights increases testosterone. What kind
of problem is this?
A.
B.
C.
D.
Reverse causation
Confound
Self-selection
Third-variable problem
Review
Test people’s memory for lists of nouns or verbs,
to see if one is easier to recall.
Word type (noun/verb) is a(n)
A.
B.
C.
D.
Confound
Independent variable
Dependent variable
Data
Goals of Statistics
9/2
Overview
• Populations and samples
• Parameters vs. statistics
• Types of statistics
Populations and Samples
• Population
– Set of subjects, items, or events we want to learn about
– Generally very large or infinite
– All people, all men/women, all pigeons, all concrete or abstract
nouns
• Sample
–
–
–
–
Subset of population assessed in a given study
Much smaller
Randomly selected
Not perfectly representative of population (sampling variability)
• Sometimes population is hypothetical
– Experimental trials (repetitions)
• Your reaction time to a red square
– Imagine we could repeat infinite times
– Sample is finite times we actually do it
Random Selection
• Every member of population must have equal chance of
inclusion
• Property of data-gathering process
– Study design must take random selection into account
• Otherwise sample is biased
– Only testing students at library
• Selection variables may interact with outcome
– People/events in sample may differ from rest of population
– Undergrads
– Racial distribution
Parameter
• Characteristic of the population
• Usually theoretically meaningful
• Mean, variance, proportion, rate, correlation
– What's the average IQ of college students?
– How many attempts does it take a normal rat to learn
this maze?
– How many attempts if we cut out its hippocampus?
– What fraction of words can a subject remember?
– What's the correlation between height and
extraversion?
…
Statistic
• Mathematical function to be computed from data
• Difference between statistic and its value
– E.g., mean is a statistic (arithmetic average)
– Value for any dataset will be some number
• Usually serves one of three functions
– Descriptive statistic: Summarizes some aspect of the
sample data
– Estimator: Estimates some parameter of the
population
– Inferential statistic: Aids testing of some hypothesis
about the population
Descriptive Statistic
• Summarizes some aspect of the data
– Mean, median, maximum, quartiles, standard
deviation, etc.
• Used only for describing sample data
– Not for making inferences about population
– Can be first step of data analysis
– Also useful if sample is all you’re interested in
• E.g. average age of students in class
Estimator
• Estimates some parameter of the population
– Mathematical function applied to sample that usually
gives close to correct answer for population
• Usually also a descriptive statistic
– Sample mean is estimator for population mean
– Difference is just in what you use it for
• Sampling error
– Value of estimator almost never exactly correct
– Different samples give different results
Inferential Statistic
• Aids testing of some hypothesis about the
population
• Indicates how reliable an effect in the sample is
• Value generally has no physical meaning
– Not like inches, time, or even psychological variables
• Examples: t, F, c2, p
Effect Size * Sample Size  “t”
Variability
t > 2  difference probably real
t < 2  probably chance
Review
Which qualifies as random selection?
A. Measure 200 people, then randomly choose 100 to
base your analysis on
B. Randomly select what variables to measure
C. Randomly choose members of the population to be in
your study
D. For every subject, randomly decide which experimental
group they are in
Review
Which of these is NOT a population?
A. All women in Lithuania
B. All English prepositions
C. Your mom’s reaction times to a blue circle, if we
showed it to her an infinite number of times
D. All subjects in an experiment
Review
You want to know whether men or women can hold their
breath longer. You measure 10 of each and get averages
of 116 seconds for the men and 107 seconds for the
women. Then you compute a number that tells you whether
that difference is reliable. This number is a(n)
A.
B.
C.
D.
Descriptive statistic
Estimator
Inferential statistic
Parameter