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1. 1
Interpreting Data

2. •Empirical research usually uses some type of
statistical analysis
•Mathematics – Language for accomplishing
logical operations inherent in good data analysis
•Statistics – Branch of math appropriate to
research
•Descriptive statistics – Method for describing data
in manageable forms
•Inferential statistics – Assist in forming conclusions
from our observations
•About a population, based on studying the sample
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3. •Univariate Analysis: Only one variable at a time
•Bivariate Analysis: Two variables
•Multivariate Analysis: Three or more variables
•Distributions – Reporting all individual cases
•Marginals – Frequency distributions of grouped data
(age of students)
•Frequency Distribution: (2, 7, 11, 14, 16)
Class Frequency
1-9 2
10-19 3
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4. •“Summary Averages”
•Mode: Most frequent attribute
•Mean: Sum of all values divided by # of total
values
•Median: Middle attribute of ranked data
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5. •Range: Distance separating the highest value
from the lowest value
•Standard Deviation: The average amount of
variation about the mean
•Variance: Sum of squared standard deviations
from mean divided by total number of cases
•Percentile: What percentage of cases fall at or
below some value; can be grouped into quartiles
•Rates: Used to standardize some measure for
comparative purposes
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6. •We are interested how variables are related
(explanation)
•Contingency table: Used to compare subgroups;
“percentage down” column, read across row
•Values of the dependent variable are contingent
on values of the independent variable
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Own a Gun? Men Women
Yes 49% 24%
No 51 76
100% = (1,270) (633)

7. •Instead of explaining the dependent variable
on the basis of a single independent variable -
seek an explanation through the use of more
than one independent variable
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Assault Rates, Poverty, & Mobility in 60 Boston
Neighborhoods
_______________Mobility_______________
_
Poverty Low High Total
Low 12.2 (22) 19.5 (21) 15.8 (43)
High 43.8 (4) 25.0 (13) 29.4 (17)

8. •Indicates strength of relationship (01)
•Based on Proportionate Reduction of Error
(PRE):
•How much variation in y can be predicted by x;
how much you can reduce your error in
predicting y by knowing x
•The greater the relationship between two
variables, the greater the reduction of error
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9. •Nominal Variables: Gender, marital status, or
race
•Lambda (λ) : Based on your ability to guess values
on one of the variables
•Ordinal Variables: Occupational status,
education
•Gamma (γ) : Same as lambda, except based on the
ordinal arrangement of values
•Interval or Ratio Variables: Age, income
•Pearson’s product-moment correlation (r )
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10. • Variables are linearly related:
• The mean of Y increases linearly with X
• Check scatterplot for general linear trend
• Watch out for non-linear relationships
(e.g., U-shaped)
• Y is normally distributed for every outcome of
X in the population; “Conditional normality”
Ex: Income = X, Happiness = Y
• Is a histogram of Income approximately
normal? For those with X = $25K? $50K?
$100K?
• If all are roughly normal, the assumption is met
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11. • Association between two variables: Y = f (x)
• Regression Line: All four points lie on a
straight line, we can superimpose that line
over the points; Y' = a + b(x)
• “Unexplained Variation”: The sum of squared
differences between actual and estimated
values of Y
• Represents errors that exist even when estimates
are based on known values of X
• “Explained Variation”: The difference between
the total variation and the unexplained
variation
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12. • When we generalize from samples to larger
populations, we use inferential statistics to
test the significance of an observed
relationship
• Data analysis & sampling
• Most research projects involve samples
• Ultimate purpose is to make inferences about that
larger (target) population
• Both univariate and multivariate findings can be
interpreted as a basis for inference
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13. • Univariate Measures: Percentages & Means
• “Standard Error”: p x q
s=√ n
• Any statement of sampling error must contain
two essential components:
• Confidence Level
• Confidence Interval
• Inferential statistics apply to sampling error
only; they do not take account of nonsampling
errors
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14. • So, two variables are related? Is the
relationship a significant one?
• Parametric tests of significance can tell us
• We report probability that a parameter falls
within a certain range (confidence interval) &
that degree of uncertainty is due to normal
sampling error
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15. •Statistical significance is expressed with
probabilities
•What does P < .05 or .01 or .001 mean?
•Significance at .05 level means that probability
of achieving result by chance alone is 5 out of
100 (or 1 at the .01 level)
•If it’s not by chance, it represents a real finding
between the variables!
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16. • Based on the Null Hypothesis: the assumption
that there is no relationship between two
variables in a population
• Compares what you get (empirical) with what
you expect given a null hypothesis of no
relationship
•Computing: For each cell in the tables, we
•Subtract the expected frequency for that cell
from the observed frequency
•Square this quantity, and
•Divide the squared difference by the expected
frequency
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17. • Significance tests are guideline, not ultimate
standard
•Dangers due to sampling error, sample size,
etc
•Check and compare to other tests
•"Empirical research is, first and foremost, a
logical rather than a mathematical operation."
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18. • What is a statistically discernable difference?
• Results from tests on a non-random sample
would be considered statistically significant if
found in a random sample
• Findings should be viewed as important but not
statistically significant
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