This document provides an overview of key concepts in research methods for public administration, including: 1. Levels of measurement for variables, including nominal, ordinal, interval, and ratio levels. Examples are provided for each level. 2. Common research designs such as experimental, quasi-experimental, cross-sectional, and longitudinal designs. 3. Quantitative data analysis techniques including descriptive statistics, inferential statistics like ANOVA and regression, and correlation analysis. Frequency distributions, measures of central tendency and variability are covered. 4. Confidence intervals and how they are used to estimate population parameters more accurately than point estimates, by providing a probability assessment through setting a confidence level. Common confidence levels like 90%, 95%,

1. PUBA 601 Research Methods for Public Administration
Section 01
2021 Summer II Express Session
April Heyward, MRA
Adjunct Faculty
College of Charleston
Master of Public Administration (MPA) Program
Thursday, August 5, 2021

2. Levels of Measurement

3. Level of Measurements
 Level of Measurement is the mathematical
precision with which the values of a variable can
be expressed.
 Levels of Measurements are expressed as either a
Qualitative level of measurement or a
Quantitative level of measurement.
 It is a good idea to measure variables at the
highest level of measurement possible.
 There are more possibilities for statistical
analysis with quantitative variables than with
qualitative variables.

4. Level of Measurements
 Qualitative variables can be coded with dummy
coding for statistical analysis. For example, Life
Sciences = 1 and Physical Sciences = 2.
 Other considerations may preclude measurement
at a high level.

5. Levels of Measurements
1. Nominal – Qualitative Level of Measurement
2. Ordinal – Quantitative Leve of Measurement
3. Interval – Quantitative Level of Measurement
4. Ratio – Quantitative Level of Measurement
Note: Sometimes Statisticians and Researchers combine interval level
of measurement and ratio level of measurement into one level of
measurement in literature and practice.

6. Nominal Level of Measurement
 Nominal level of measurement are variables
whose values have no mathematical
interpretation.
 Nominal variables vary in kind or quality but
not in amount.
 Nominal variables are not rank ordered.
 Nominal variables can be characterized
categorically.
 Categories must be mutually exclusive and
exhaustive.
 Dummy code can be applied if there is a
desire to do quantitative analysis.

7. Nominal Level of Measurement
Nominal Variables and Value Categories Examples
Variable Categories Dummy Code
Gender Male
Female
1
2
Religion Protestant
Christian
Jewish
Muslim
1
2
3
4
Marital Status Married
Single
Widowed
Other
1
2
3
4

8. Nominal Level of Measurement
Nominal Variables and Value Categories Examples
Variable Categories Dummy Code
Social Class Lower
Working
Middle
Upper
1
2
3
4
Education Less than High School
High School
Some College
College
1
2
3
4

9. Question
Are there other categories that can be added to
exhaust all possibilities for:
 Gender
 Religion
 Marital Status
 Social Class
 Education?

10. Ordinal Level of Measurement
 Ordinal level of measurement is a measurement
of a variable in which the numbers indicate a
variable’s value to specify the order of cases.
 Ordinal level of measurement is expressed
mathematically.
 Ordinal level of measurement is rank order.
 Facilitates greater than (>) and less than (<)
distinction.
 Must be mutually exclusive and exhaustive.

11. Ordinal Level of Measurement
Ordinal Ranking Scale Example
Rank Value/Categories
1 Strongly Agree
2 Agree
3 Neither Agree nor Disagree
4 Disagree
5 Strongly Disagree

12. Question
Are there other categories that can be added to
exhaust all possibilities?

13. Interval and Ratio
Level of Measurements
 Interval level of measurement is a measurement of a
variable in which numbers indicates a variable’s value
representing fixed measurement units but not
absolute zero point (e.g., zero degrees).
 Ratio level of measurement is a measurement of a
variable in which the numbers indicates the variable’s
value representing fixed measurements and absolute
zero point.
 Ratio numbers can be added, subtracted, multiplied,
and divided.
 Ratio can be used in more complex data analyses.

14. SAT Scores and Percentiles
SAT Composite Score Percentile Score
1550-1600 99 to 99+
1500-1550 98 to 99
1450-1500 96 to 98
1400-1450 94 to 96
1350-1400 90 to 94
1300-1350 86 to 90
1250-1300 81 to 86
1200-1250 74 to 81
1150-1200 67 to 74
1100-1150 59 to 67
1050-1100 50 to 59

15. SAT Scores and Percentiles
SAT Composite Score Percentile Score
1000-1050 41 to 50
950-1000 33 to 41
900-950 25 to 33
850-900 18 to 25
800-850 11 to 18
750-800 6 to 11
700-750 3 to 6
650-700 1 to 3
600-650 -1 to 1
550-600 -1
500-550 -1

16. Research Designs

17. Sample Research Designs:
Experimental Design
 Experimental Design- Ability to assign
human subjects to different groups,
manipulate the independent variable, and
control most environmental influences.
 For instance, a segment of human subjects
can be assigned to a group that receives an
intervention or treatment which is known
as the experimental group and a segment
of human subjects can be assigned to a
group that does not receive an intervention
or treatment which is known as the control
group.

18. Sample Research Designs:
Quasi-Experimental Design
 Quasi-Experimental Design – This design
does not have the full control of the
environment and does not have the ability
to randomly assign human subjects to
groups as compared to the experimental
design.
 This is characterized as “Quasi” because
there are aspects of experimental design
that can be employed.

19. Sample Research Designs:
Cross-Sectional Design
 Cross-Sectional Designs collects data on all
relevant variables at one time.
 Designed for studies that involve collecting
data:
 On many variables
 From a large group of human subjects
 From human subjects who are dispersed
geographically.

20. Sample Research Designs:
Longitudinal Designs
 Longitudinal designs collects information
on the same cases or comparable cases for
two or more distinct time periods.
 Trend design employs a longitudinal
approach as data is drawn from at least two
different samples at two different times.
 Panel design employs a longitudinal
approach as data is drawn from one sample
at least two different times.

21. Quantitative Data Analysis

22. Quantitative Data Analysis
 Quantitative data analysis is statistical techniques used to describe and analyze
variation in quantitative measures.
 Quantitative data can be analyzed with descriptive statistics and inferential
statistics.
 Descriptive statistics describes and summarizes data. Also describes the
distribution of and relationship among variables.
 Inferential statistics estimates how likely it is that a statistical result based on data
from a random sample is representative of the population from which the sample is
assumed to have been selected.

23. Quantitative Data Analysis
 Quantitative data must be cleaned, process referred to as data cleaning, prior to data
analysis.
 Data cleaning is the process of checking data for errors after the data have been
entered in a computer file. Data cleaning also prepares data in a format that is
acceptable of the data analysis software (e.g., Excel, SPSS Statistics, STATA, SAS, R).

24. Descriptive Statistics
 Frequency Distribution – Table the depicts the number of observations that fall into
each category of the variable being analyzed.
 Measures of Central Tendency – Numbers that describe the average or typical
distribution (e.g., Mode, Median, and Mean).
 Measures of Variability – Numbers that describe the diversity or variation (e.g.,
index of qualitative variation, range, interquartile range, variance, standard deviation)
and sometimes captured in concert with measures of central tendency.

25. Types of Frequency Distributions
Source: Frankfort-Nachmias and Leon-Guerrero, 2018

26. Frequency Distribution for Categories of Region of Birth for Foreign-Born
Population, 2016
Source: Frankfort-Nachmias and Leon-Guerrero, 2018

27. How to Choose a Measure of Central Tendency
Source: Frankfort-Nachmias and Leon-Guerrero, 2018

28. How to Choose a Measure of Variation
Source: Frankfort-Nachmias and Leon-Guerrero, 2018

29. Inferential Statistics
 There are many inferential statistic techniques but
will focus on ANOVA and Regression.
 ANOVA – Analysis of Variance
 ANOVA examines the variation among means
(averages) among two or more groups.
 ANOVA can examine whether the variance between
samples is larger than the variance within samples.

30. Inferential Statistics
 ANOVA involves a 5-step hypothesis
testing model.
 Regression is a linear prediction model
using one or more independent
variable to predict the values of the
dependent variable.
 There are multiple ANOVA and
Regression techniques.

31. Correlation Analysis

32. Correlation Analysis
 Correlation analysis is one of the
techniques to examine the relationship
between interval-ratio variables.
 It assesses the existence and strength of
the relationship between independent
variables and dependent variables.
 It is recommended to depict the
relationship between the independent
variable and the dependent variable in a
scatterplot prior to executing correlation
analysis.

33. Correlation Analysis
 The independent variable is on the X-axis
and the dependent variable is on the Y-
axis.
 Scatterplots can present a positive
relationship, negative relationship,
moderate relationship, and no
relationship between the independent
variable and the dependent variable.
 Correlation does not indicate if two
variables are causally related.

34. Correlation Analysis
Relationship and Scores
Perfect Negative
Relationship –
-1.00
Very Strong
Negative
Relationship –
-0.80
Strong Negative
Relationship-
-0.60
Moderate Negative
Relationship –
-0.40
Weak Negative
Relationship –
-0.20
No Relationship at
All
– 0.00

35. Correlation Analysis
Relationship and Scores
Perfect Positive
Relationship –
+1.00
Very Strong
Positive
Relationship –
+0.80
Strong Positive
Relationship-
+0.60
Moderate Positive
Relationship –
+0.40
Weak Positive
Relationship –
+0.20

36. Correlation
Analysis
Depicted
Source: Frankfort-Nachmias and Leon-Guerrero, 2018

37. Correlation
Analysis
Source: Frankfort-Nachmias and Leon-Guerrero, 2018
Correlation Matrix for Internet Hours Per Week, Educational Attainment, and Age

38. Confidence Intervals and Confidence Levels

39. Confidence Intervals
and
Confidence Levels
 Confidence intervals is an estimate of
population parameters and a method of
increasing accuracy as compared to point
estimates.
 Point estimates provides a single value for
a population parament and confidence
interval projects the probability the
estimate will be accurate as a confidence
level which is expressed as a percentage.
 The most notable confidence levels include
90%, 95%, and 99%.
 Confidence levels indicates the number of
chances out of 100 the interval estimate
will be accurate.

40. Confidence Intervals
and
Confidence Levels
 The difference between the confidence level
and 100 is the margin of error.
 For instance, if the confidence level is 90%,
there is a 10% chance the interval estimate
will be inaccurate.
 If the confidence level is 95%, there is a 5%
chance the interval estimate will be
inaccurate.
 If the confidence level is 99%, there is a 1%
change the interval estimate will be
inaccurate.

41. Confidence Intervals
and
Confidence Levels
 The higher the confidence level, the lower
the margin of error.
 It is preferred the confidence level be 95%
or higher.

42. Confidence Interval
and
Z Scores
The confidence interval determines the Z
score. The Z score or the standard Z score is
the number of standard deviations that a raw
score is above or below the mean (average). Z
score can be found in the Standard Normal
Table.
 Confidence Level of 90% = Z Score of 1.65
(+1.65, -1.65)
 Confidence Level of 95% = Z Score of 1.96
(+1.96, -1.96)
 Confidence Level of 99% = Z Score of 2.58
(+2.58, -2.58)

45. Source: Frankfort-Nachmias and Leon-Guerrero, 2018

54. References
 Chambliss, D., Schutt, R. (2018). Making Sense of the Social World: Methods of
Investigation. SAGE.
 Creswell, J., Creswell, J. (2018). Research Design: Qualitative, Quantiative, and Mixed
Methods Approaches. SAGE.
 Frankfort-Nachmias, C., Leon-Guerrero, A. (2018). Social Statistics for a Diverse Society.
SAGE
 Rassel, G., Leland, S., Mohr, Z., O’Sullivan, Elizabethann. (2021). Research Methods for
Public Administrators. Routledge.