Evaluation Research and Problem Analysis

1. 1
Chapter 11:
Field Observation
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Learning Objectives
• Understand that descriptive statistics are used to
summarize data under study
• Describe a frequency distribution in terms of cases,
attributes, and variables
• Recognize that measures of central tendency summarize
data, but they do not convey the detail of the original
data
• Understand that measures of dispersion give a summary
indication of the distribution of cases around an average
value
• Provide examples of rates as descriptive statistics that
standardize some measure for comparative purposes

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Learning Objectives, cont.
• Describe how bivariate analysis and subgroup comparisons
examine relationships between two variables
• Compute and interpret percentages in contingency tables
• Understand that multivariate analysis examines the
relationships among several variables
• Explain the logic underlying the proportionate reduction of
error (PRE) model
• Describe the use of lambda (λ) and gamma (γ), and
Pearson’s product-moment correlation (r) as PRE-based
measures of association for nominal, ordinal, and
interval/ration variables, respectively
• Summarize how regression equations and regression lines
are used in data analysis

4. 4
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Learning Objectives, slide 3
• Understand how inferential statistics are used to
estimate the generalizability of findings arrived at in the
analysis of a sample to a larger population
• Describe the meaning of confidence intervals and
confidence levels in inferential statistics
• Explain what tests of statistical significance indicate, and
how to interpret them
• Recognize the difference between statistical significance
and substantive significance
• Understand that tests of statistical significance make
assumptions about data and methods that are rarely
satisfied completely in social science research

5. 5
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Introduction
• 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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Univariate Description
• 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)

7. 7
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Measures of Central Tendency
• “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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Measures of Dispersion & Computing Rates
• 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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Discussion Question 1
Which variables would you prefer to use in
your research: continuous, discreet, or both?

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Discussion Question 2
What if you had to read a large number of
studies as a part of your research? Do you
think you would be more concerned about
having enough detail or being able to
manage the data easily?

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Bivariate Analysis
• 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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Multivariate Analysis
• 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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Measures of Association
• 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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Levels of Measurement
• 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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Regression Analysis
• Variables are linearly related:
• The mean of Y increases linearly with X
• Check scatterplot for general linear trend
• Watch out for nonlinear relationships
• 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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Regression Analysis, cont.
• 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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Inferential Statistics
• 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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Univariate Inferences
• Univariate Measures: Percentages &
Means
• 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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Tests of Statistical Significance
• 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) and that degree of
uncertainty is due to normal sampling error

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Tests of Statistical Significance, cont.
• Statistical significance is expressed with
probabilities
• What does the p-value 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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Discussion Question 3
What if someone insisted that they
were 100 percent certain about their
survey results? Could you challenge
that statement? How?

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Chi Square
• 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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Interpreting Statistical Significance
• 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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Visualizing Discernible Differences
• What is a statistically discernible
difference?
• Results from tests on a nonrandom sample
would be considered statistically significant if
found in a random sample
• Findings should be viewed as important but
not statistically significant