This document outlines learning objectives and concepts for descriptive and inferential statistics. It discusses univariate, bivariate, and multivariate analysis methods for summarizing and examining relationships between variables. These include frequency distributions, measures of central tendency and dispersion, contingency tables, measures of association, regression analysis, confidence intervals, and tests of statistical significance. The goal is to describe data concisely and make generalizations from samples to populations.

1. 1
Chapter 11:
Field Observation
© 2018 Cengage Learning. All Rights Reserved.

2. 2
© 2018 Cengage Learning. All Rights Reserved.
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

3. 3
© 2018 Cengage Learning. All Rights Reserved.
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
© 2018 Cengage Learning. All Rights Reserved.
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
© 2018 Cengage Learning. All Rights Reserved.
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

6. 6
© 2018 Cengage Learning. All Rights Reserved.
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
© 2018 Cengage Learning. All Rights Reserved.
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

8. 8
© 2018 Cengage Learning. All Rights Reserved.
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

9. 9
© 2018 Cengage Learning. All Rights Reserved.
Discussion Question 1
Which variables would you prefer to use in
your research: continuous, discreet, or both?

10. 10
© 2018 Cengage Learning. All Rights Reserved.
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?

11. 11
© 2018 Cengage Learning. All Rights Reserved.
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

12. 12
© 2018 Cengage Learning. All Rights Reserved.
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

13. 13
© 2018 Cengage Learning. All Rights Reserved.
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

14. 14
© 2018 Cengage Learning. All Rights Reserved.
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)

15. 15
© 2018 Cengage Learning. All Rights Reserved.
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

16. 16
© 2018 Cengage Learning. All Rights Reserved.
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

17. 17
© 2018 Cengage Learning. All Rights Reserved.
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

18. 18
© 2018 Cengage Learning. All Rights Reserved.
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

19. 19
© 2018 Cengage Learning. All Rights Reserved.
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

20. 20
© 2018 Cengage Learning. All Rights Reserved.
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!

21. 21
© 2018 Cengage Learning. All Rights Reserved.
Discussion Question 3
What if someone insisted that they
were 100 percent certain about their
survey results? Could you challenge
that statement? How?

22. 22
© 2018 Cengage Learning. All Rights Reserved.
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

23. 23
© 2018 Cengage Learning. All Rights Reserved.
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."

24. 24
© 2018 Cengage Learning. All Rights Reserved.
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