Introduction
The Role of Statistics in Science
• Research can be qualitative or quantitative
• Where the research results are numbers,
this information is called data
• Statistics are mathematical techniques
used to manipulate and analyze data
– Allow us to answer research questions or test
theories
– Example of fertility rates
Fertility Rate Example
• What causes overpopulation
– Things found to correlate with high fertility
rates
• Low levels of education—particularly for women
• Absence of social security system
• Low incomes
• Absence of birth control and fertility clinics
• The wealthiest people in the world make money
from overpopulation, so they do what they can to
encourage it
What the wealthy gain from
overpopulation
• When there are too many people looking
for jobs, wages go down
– So, profits go up dramatically
• When there are too many people buying
products, especially with shortages of
resources, prices go up
– So, profits go up dramatically
Ways the Wealthy Encourage
Growth
• Republicans speak for the wealthy, so
listen to what they say
– They have a Club for Growth
– They oppose abortion globally
– They oppose birth control, particularly funding
for it in family planning clinics
– They talk endlessly about “family values”
hoping that will translate to larger families
Statistics
• They are summary numbers
• Needed because our minds can only
remember and make sense out of small
sets of numbers
Why Do Quantitative Research
• Some of the most important works in the social
sciences do not use any stats
– Example of study of med school students
• Your audience will be persuaded if you use
statistics
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They are powerful
They make a stronger case in favor of a position
It’s easier to get quantitative research published
Your expertise with stats helps you to evaluate the
research of others
Descriptive and Inferential
Statistics
Descriptive Statistics
• Used to describe the distribution of a single
variable in a sample (the first four chapters in
your book)
– Example, the ages of all the people in a community
• So, use data reduction
– Allows a few meaningful numbers to
summarize large masses of data
• Can’t list all the ages
– Use percentages, averages, graphs, and charts
– Called univariate statistics
Explanatory Statistics
• Sometimes also classified as descriptive
– Bivariate if two variables
– Multivariate if more than two (last two
chapters in your book)
• Explanatory statistics are used to
understand the relationship between two
or more variables in a sample
– Use measures of association
Measures of Association
• Will tell you three things
– Existence of a relationship
– Direction of a relationship
• E.g., the older you get, the higher your income
– As one goes up, the other goes up (a positive association or a
direct relationship
• E.g., the higher your level of education, the less prejudiced
you tend to be
– A negative association
– Strength of a relationship
• Is it true for all people, most people, or just a slight tendency
Depending on Strength and
Direction
• We can find evidence for causation
– Correlation is not causation—just evidence for
it
• You have to use your own logic to decide if
the association is causal
– We want to know if there is a cause and
effect relationship
• The cause is the independent variable,
represented by the letter “X”
• The effect is the dependent variable,
represented by the letter “Y”
Hypothesis
•
– An hypothesis is a statement about the
predicted relationship between the variables
• It comes from theory
• Example: the more education you receive,
the higher your income will be
–Which is the independent variable and
which is the dependent
We can also find evidence for prediction
– Can predict your score on one variable from
your score on another
Inferential Statistics
• We want to generalize the findings from the
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sample to a larger population
We don’t have the money or time to survey
every person
So we draw a small random sample from the
larger population
Inferential statistics involve using information
from samples to make inferences about
populations
Discrete and Continuous Variables
• Discrete
– A variable is discrete if it has a basic unit of measurement that
cannot be subdivided
• Example, number of people per household
– The basic unit is people
– The fewest you can have is one
• Continuous
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– It can be subdivided infinitely, at least theoretically
• Example, time, which can be subdivided into
seconds or nanoseconds (one billionth of a
second)
• Do actually report these scores as discrete
Mostly, this information is needed to decide between a
bar graph and a histogram
Level of Measurement
Nominal Level of Measurement
• Very important, in that it decides which statistics to use
• Nominal Level of Measurement
– The word “nominal” means naming
– With nominal variables, you classify people into
categories, and look at how many people are in each
category
– The categories are not thought of as “higher” or
“lower” than the others, or “greater than” or “lesser
than”
– Examples: religion, sex, race, political party, marital
status, and variables with only two choices—like
“Yes” or “No”
Ordinal Level of Measurement
• Also classifies cases into categories
• Additionally, it allows the categories to be ranked
– Ordinal categories can be ranked from “low” to “high”, “more”
or “less”
• Examples of ordinal level variables
– Occupation, social class, grade point average, education
measured by degrees, degree of religiosity
– Also SES, measured as upper class, middle class, working class,
or lower class
– Also, all attitude and opinion scales, like prejudice, alienation, or
political conservatism
• Usually measures in a Likert Scale
• The limitation of ordinal level variables is that you cannot describe
the distance between the scores or categories in precise terms
Interval/Ratio Level of
Measurement
• Variables measured at the interval-ratio level permit classification
like nominal ones
• Permit ranking like ordinal
• But also exactly define the distance from category to category
• Examples of interval-ratio level of measurement
– Age
• The unit of measurement (years) has equal intervals
• Also, income, number of children, and number of years
married
• All math operations are permitted for data measured at this
level
Levels of Measurement
• A single variable can be measured in any
of the three levels
– Example of education
• Nominal, if asking “do you have a college
degree?” with a yes or no response
• Ordinal, if asking “what educational degrees do
you have?”
• Interval/ratio if asking “how many years have you
been in school?”