Key Definitions
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1) Define basic terminology for the semester.
2) Describe different kinds of statistics and provide a
brief overview of how they are used.
3) Identify the most common methods researchers use to
collect data along with the most common pitfalls that
experimenters must avoid.
4) Define various types of data.
Key Definitions
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STATISTIC - an estimate of some characteristic (variable)
of a population based on a sample of available data
STATISTICS - a set of rules, and procedures for organizing,
summarizing, and interpreting data
POPULATION - the entire set of people or objects that we
are interested in studying
CENSUS - an exhaustive collection of data from every
member of the population of interest
SAMPLE - a group of observations drawn from a given
population; individual elements of the sample are
called units
VARIABLE - some characteristic of a population that we
are interested in measuring. By definition, variables
are free to VARY; that is, every member (unit) of the
population can generate different values.
More Key Definitions
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PARAMETER - the value of a variable for the population
(derived by a census). Does not vary.
STATISTIC - the value of a variable for a sample drawn
from the population. Varies depending upon which
members of the population are sampled.
Two Different Kinds of Statistics
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DESCRIPTIVE STATISTICS - numerical and graphical
methods for analyzing patterns within a data set; used
to summarize information contained within a data set
and present it to an audience.
INFERENTIAL STATISTICS - the use of sample information
(i.e., descriptive statistics) to make estimates,
decisions, predictions and/or other generalizations
about a larger set of data (i.e., the population of
interest).
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DSs allow you to
a) SUMMARIZE an unwieldy set of numbers.
 24% of the students in the survey smoked
ISs allow you to
a) draw inferences about a population
b) compare two populations
 24%  5% of AC students smoke
 More students smoke at UMass than AC
How do they relate to one another?
 DSs are used as the basis to calculate ISs
Combining DS and IS: an Overly Brief Intro
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You got a 70 on the first exam:
Did you do better than average?
Step 1 - Determine an average for the class.
a) Take a census and calculate a parameter
Problems?
b) Take a sample and calculate a statistic
You and your four friends got:
70, 80, 80, 60, 50
Mean = 68 (that's a DS)
Compare 70 and 68.
 You did better than the average of the SAMPLE.
 To know if you did better than the average of the
population, you need to calculate an IS.
IS takes into account not only the magnitude of the
statistic, but its variability as well.
 What if everyone in the class scored 68, except for
one person who scored a 66?
 What if everyone in the class scored in the 80s
except for a few people who scored in the 20s?
Statistics ain’t perfect
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The Mozart effect – college students who listened to
Mozart performed better than those who did not on a
complex mental paper-folding task.
Problem #1:
People have kind of run wild with these results
 Municipal governments used tax money to
purchase CDs for at-risk kids
 Other capitalists entered the fray
http://www.mozarteffect.com/
http://www.howtolearn.com/Mozart.html
Problem #2:
Even the original result has not replicated
http://skepdic.com/mozart.html
Problem #3:
Casts doubt on legitimate research findings
http://www.psychologicalscience.org/pdf/ps/musiciq.pdf
Data Collection Methods
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Observational Methods
 Look out into the world and see if two variables
tend to co-exist.
Methods:
a) Questionnaires/self-report
b) Case Studies
c) Naturalistic Observations
Experimental Method (Quasi-Experimental)
 Isolate the effects of one variable by holding all
other variables constant.
Methods:
a) Designed studies
Differences:
 Observational method: key variables are all
measured
 Experimental method: some variables are
measured, some are set by the experimenter
(nature).
As a result, the experimental method allows the
researcher to draw cause and effect relationships.
Comparing the Observational and
Experimental Methods
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Does eating oat bran reduce heart disease?
Observational method:
 Find 20 people that eat oat bran and 20 people that
don't eat oat bran. See how many in each group
die within some time period.
Experimental Method:
 Find 40 people matched for age, health, etc.
RANDOMLY assign people to two groups. One
group eats lots of oat bran, the other does not. See
how many people in each group die within some
period.
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Questions:
1. Why can we not draw a cause-and-effect inference
based on the observational study?
2. Can we ever be sure that two groups are exactly the
same except for a single variable?
Keys to the Experimental Method
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Random assignment
 It's the only way to ensure that all other variables
are as equal as possible. Remember, with quasiexperimental at least one key IV is out of the
experimenter's control.
Elimination of CONFOUNDING variables
 What if non-oat-bran eaters smoke, but oat-braneaters do not?
 Comparing HC and AC students: you measure HC
students coming out of Intro Psych, and AC
students leaving Organic Chem?
o Real world Example: TOT
Setting up an Experiment: Key Terms
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Independent Variable (IV)
 the quality of interest that is more or less fixed by
either the researcher or nature. Free to vary across
groups but not within groups.
EX:
Gender
college affiliation
drug dosage
Dependent Variable (DV)
 the experimental variable of interest that is believed
to depend on the magnitude of the associated
independent variable. Not assigned by the
experimenter.
EX:
intelligence
post-graduation success
remission of illness
Operational Definition - the way a researcher chooses to
define the key constructs (variables) in an
experiment.
EX:
IQ test score
Salary 5 years post-graduation
patient report
Designing an Experiment
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Design an experiment to answer the following question:
does exercise reduce stress?
Questions:
 Is your experiment observational or
experimental?
 What is/are your independent variable(s)?
 What is are your dependent variable(s)?
 What was the operational definition for each
IV/DV?
 What are some potential confounding variables?
Important Sampling Issues
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Randomness
 in a perfectly random sample, every unit in the
population has the same probability of being
selected. An ideal that is rarely obtained.
Reliability
 the degree of uncertainty about some measurement;
not the same as accuracy
Representativeness
 the degree to which the sample captures important
characteristics of the population; representativeness
affects reliability
Size
 in general, the larger the sample, the more
representative it will be and the more reliable it will
be.
Sampling Errors
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Response Bias
 wording of the question affects the response
Selection Bias
 although a quasi-random sampling method is
undertaken, some important segment of the
population is not represented
Non-response Bias
 some people refuse or are unavailable to respond
Types of Data
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a) Discrete vs. Continuous
b) Qualitative vs. Quantitative
Scales of Measurement
Nominal
 a set of measurement labels that fall into different
categories with no numerical relations
EX: Political Party, Gender, Jersey #, Class
Ordinal
 a set of categories that can be ordered along some
dimension of size or magnitude
EX: Preference Ratings
Interval
 ordinal + the intervals between categories are
identical; allows for addition and subtraction
EX: Temperature (C, F)
Ratio
 interval + an absolute 0 point which corresponds to
the absence of the measured quantity; allows for
multiplication and division
EX: Height, Weight, Temperature (K)
Who are you gonna call…a Statistician?
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1) What team won the most games in the NFL last year?
2) Who hit the most home runs in a single baseball
season?
3) How many people watched the last episode of
Survivor?
4) How much does a senior citizen have to pay to see a
movie in Amherst, MA?
5) What is the per capita income in Hampden County?
6) How does the per capita income in Hampden County
compare with that in Aspen, CO?
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When do you need a statistician?