The document provides information about data analysis and presentation. It discusses various steps in data preparation including editing, coding, data entry, and handling missing data. It also covers hypothesis testing, which involves forming the null and alternative hypotheses, calculating a test statistic such as the z-statistic, determining the p-value, and making conclusions based on the significance level. An example is provided to illustrate a hypothesis test about population mean body weight. The document emphasizes that data preparation is crucial for ensuring accurate analysis. Hypothesis testing allows researchers to systematically evaluate claims about population parameters.

1. Course: MBA
Subject: Research Methodology
Unit-4.1
DATA ANALYSIS & PRESENTATION

2. Data Preparation
Hypothesis Testing
Introduction to bivariate and
multivariate analysis

3. Data Preparation: Introduction
• Once the data begin to flow, a
researcher’s attention turns to data
analysis.
• Data preparation includes editing, coding,
and data entry;
– It is the activity that ensures the accuracy of
the data and their conversion from raw form to
reduced and classified forms that are more
appropriate for analysis.

4. Data Preparation: Introduction
• Preparing a descriptive statistical
summary is another preliminary step
leading to an understanding of the
collected data;
– It is during this step that data entry errors may
be revealed and corrected.

5. Data Preparation: Editing
• The customary first step in analysis is to
edit the raw data.
• Editing detects errors and omissions,
corrects them when possible, and certifies
that maximum data quality standards are
achieved.

6. Data Preparation: Editing
• The editor’s purpose is to guarantee that
data are:
– Accurate;
– Consistent with the intent of the question and
their information in the survey;
– Uniformly entered;
– Complete; and
– Arranged to simplify coding and tabulation.

7. Data Preparation: Editing
• In the following question asked of adults aged 18
or older, one respondent checked two
categories, indicating that he was a retired
officer and currently serving on active duty.
– Please indicate your current military status:
• Active duty
• Reserve
• Retired
• National Guard
• Separated
• Never served in the army

8. Data Preparation: Editing
• The editor’s responsibility is to decide
which of the responses is both
– consistent with the intent of the question or
other information in the survey, and
– most accurate for this individual participant.

9. Data Preparation: Editing
Two types of editing are field editing and central
editing.
• Field Editing: In large projects, field editing
review is the responsibility of the field
supervisor;
– When entry gaps are present from interviews, a
callback should be made rather than guessing what
the respondent “probably would have said”.
– Self-interviewing has no place in quality research.
– Validating the field research is the control function of
the supervisor.
• It means he or she will reinterview some percentage of the
respondents to make sure they have participated.
• Many research firms will recontact about 10 percent of the
respondents in this process of data validation.

10. Data Preparation: Editing
• Central Editing: For a small study, the use of a
single editor produces maximum consistency. In
large studies, editing tasks should be allocated
so that each editor deals with one entire section.
– When replies are inappropriate or missing, the editor can sometimes
detect the proper answer by reviewing the other information in the data
set.
• It may be better to contact the respondent for correct information, if time and
budget allow.
• Another alternative is for the editor to strike out the answer if it is
inappropriate. Here an editing entry of “no answer” is called for.
– Another problem that editing can detect concerns faking an interview
that never took place.
• This “armchair interviewing” is difficult to spot, but the editor is in the best
position to do so.
• One approach is to check responses to open-ended questions. These are
most difficult to fake. Distinctive response patterns in other questions will
often emerge if data falsification is occurring. To uncover this, the editor
must analyze the set of instruments used by each interviewer.

11. Data Preparation: Coding
• Coding involves assigning numbers or other
symbols to answers so that the responses can
be grouped into a limited number of categories.
• In coding, categories are the partitions of a data
set of a given variable. For example, if the
variable is gender, the partitions are male and
female.
• Categorization is the process of using rules to
partition a body of data.
• Both closed and free-response questions must
be coded.

12. Data Preparation: Coding
• The categorization of data sacrifices some data
detail but is necessary for efficient analysis.
• Most software programs work more efficiently in
the numeric mode;
– Instead of entering the word male or female in
response to a question that asks for the identification
of one’s gender, we would use numeric codes, e.g., 0
for male and 1 for female
• Numeric coding simplifies the researcher’s task
in converting a nominal variable, like gender, to
a “dummy variable”

13. Data Preparation: Missing Data
• In survey studies, missing data typically occur
when participants accidentally skip, refuse to
answer, or do not know the answer to an item on
the questionnaire.
• In longitudinal studies, missing data may result
from participants dropping out of the study, or
being absent for one or more data collection
periods.
• Missing data also occur due to researcher error,
corrupted data files, and changes in the
research or instrument design after data were
collected from some participants, such as when
variables are dropped or added.

14. Data Preparation: Missing Data
• The strategy for handling missing data consists
of two-step process:
– the researcher first explores the pattern of missing
data to determine the mechanism for missingness
(the probability that a value is missing rather than
observed), and
– then selects a missing-data technique. The three
basic types of techniques which can be used to
salvage data sets with missing values are:
• Listwise deletion
• Pairwise deletion
• Replacement of missing values with estimated scores

15. Data Preparation: Data Entry
• Data entry converts information gathered by
secondary or primary methods to a medium for
reviewing and manipulation.
• Keyboarding remains a mainstay for researchers
who need to create a data file immediately and
store it in a minimal space on a variety of media.
• However, researchers have profited from more
efficient ways of speeding up the research
process, especially from bar coding and optical
character and mark recognition.

16. Data Preparation: Data Entry
• Keyboarding: A full screen editor, where an
entire data file can be edited or browsed, is a
viable means of data entry for statistical
packages like SPSS or SAS.
– SPSS offers several data entry products, including
Data Entry Builder which enables the development of
forms and surveys, and Data Entry Station which
gives centralized entry staff, such as telephone
interviews or online participants, access to the survey.
– Both SAS and SPSS offer software that effortless
accesses data from databases, spreadsheets, data
warehouses, or data marts.

17. Data Preparation: Data Entry
• Bar-code technology is used to simplify
the interviewer’s role as a data recorder.
When an interviewer passes a bar-code
over the appropriate codes, the data are
recorded in a small, lightweight unit for
translation later
• Researchers studying magazine
readership can scan bar codes to denote
a magazine cover that is recognized by an
interview participant.

18. Data Preparation: Data Entry
• Optical Character Recognition (OCR):
– Users of a PC image scanner are familiar with OCR
programs which transfer printed text into computer
files in order to edit and use it without retyping.
• Optical scanning of instruments is efficient for
researchers.
– Optical scanners process the marked-sensed
questionnaires and store the answers in a file.
– This method has been adopted by researchers for
data entry and preprocessing due to its faster speed,
cost savings on data entry, convenience in charting
and reporting data, and improved accuracy.
– It reduces the number of times data are handed,
thereby reducing the number of errors that are
introduced.

19. Hypothesis Testing
• Is also called significance testing
• Tests a claim about a parameter using
evidence (data in a sample
• The technique is introduced by
considering a one-sample z test
• The procedure is broken into four steps
• Each element of the procedure must be
understood

20. Hypothesis Testing Steps
A. Null and alternative hypotheses
B. Test statistic
C. P-value and interpretation
D. Significance level (optional)

21. §9.1 Null and Alternative
Hypotheses
• Convert the research question to null and
alternative hypotheses
• The null hypothesis (H0) is a claim of “no
difference in the population”
• The alternative hypothesis (Ha) claims
“H0 is false”
• Collect data and seek evidence against H0
as a way of bolstering Ha (deduction)

22. Illustrative Example: “Body Weight”
• The problem: In the 1970s, 20–29 year
old men in the U.S. had a mean μ body
weight of 170 pounds. Standard deviation
σ was 40 pounds. We test whether mean
body weight in the population now differs.
• Null hypothesis H0: μ = 170 (“no difference”)
• The alternative hypothesis can be either
Ha: μ > 170 (one-sided test) or
Ha: μ ≠ 170 (two-sided test)

23. §9.2 Test Statistic
n
SE
H
SE
x
x
x
σ
µ
µ
=
≡
−
=
and
trueisassumingmeanpopulationwhere
z
00
0
stat
This is an example of a one-sample test of a
mean when σ is known. Use this statistic to
test the problem:

24. Illustrative Example: z statistic
• For the illustrative example, μ0 = 170
• We know σ = 40
• Take an SRS of n = 64. Therefore
• If we found a sample mean of 173, then
5
64
40
===
n
SEx
σ
60.0
5
1701730
stat =
−
=
−
=
xSE
x
z
µ

25. Illustrative Example: z statistic
If we found a sample mean of 185, then
00.3
5
1701850
stat =
−
=
−
=
xSE
x
z
µ

26. Reasoning Behinµzstat
( )5,170~ Nx
Sampling distribution of xbar
under H0: µ = 170 for n = 64 ⇒

27. §9.3 P-value
• The P-value answer the question: What is the
probability of the observed test statistic or one
more extreme when H0 is true?
• This corresponds to the AUC in the tail of the
Standard Normal distribution beyond the zstat.
• Convert z statistics to P-value :
For Ha: μ > μ0 ⇒ P = Pr(Z > zstat) = right-tail beyond zstat
For Ha: μ < μ0 ⇒ P = Pr(Z < zstat) = left tail beyond zstat
For Ha: μ ≠ μ0 ⇒ P = 2 × one-tailed P-value
• Use Table B or software to find these
probabilities (next two slides).

28. One-sided P-value for zstat of 0.6

29. One-sided P-value for zstat of 3.0

30. Two-Sided P-Value
• One-sided Ha ⇒
AUC in tail
beyond zstat
• Two-sided Ha ⇒
consider potential
deviations in both
directions ⇒
double the one-
sided P-value
Examples: If one-sided P
= 0.0010, then two-sided
P = 2 × 0.0010 = 0.0020.
If one-sided P = 0.2743,
then two-sided P = 2 ×
0.2743 = 0.5486.

31. Interpretation
• P-value answer the question: What is the
probability of the observed test statistic …
when H0 is true?
• Thus, smaller and smaller P-values
provide stronger and stronger evidence
against H0
• Small P-value ⇒ strong evidence

32. Interpretation
Conventions*
P > 0.10 ⇒ non-significant evidence against H0
0.05 < P ≤ 0.10 ⇒ marginally significant evidence
0.01 < P ≤ 0.05 ⇒ significant evidence against H0
P ≤ 0.01 ⇒ highly significant evidence against H0
Examples
P =.27 ⇒ non-significant evidence against H0
P =.01 ⇒ highly significant evidence against H0
* It is unwise to draw firm borders for “significance”

33. α-Level (Used in some situations)
• Let α ≡ probability of erroneously rejecting H0
• Set α threshold (e.g., let α = .10, .05, or
whatever)
• Reject H0 when P ≤ α
• Retain H0 when P > α
• Example: Set α = .10. Find P = 0.27 ⇒ retain H0
• Example: Set α = .01. Find P = .001 ⇒ reject H0

34. (Summary) One-Sample z Test
A. Hypothesis statements
H0: µ = µ0 vs.
Ha: µ ≠ µ0 (two-sided) or
Ha: µ < µ0 (left-sided) or
Ha: µ > µ0 (right-sided)
B. Test statistic
C. P-value: convert zstat to P value
D. Significance statement (usually not necessary)
n
SE
SE
x
x
x
σµ
=
−
= wherez 0
stat

35. §9.5 Conditions for z test
• σ known (not from data)
• Population approximately Normal or
large sample (central limit theorem)
• SRS (or facsimile)
• Data valid

36. The Lake Wobegon Example
“where all the children are above average”
• Let X represent Weschler Adult Intelligence
scores (WAIS)
• Typically, X ~ N(100, 15)
• Take SRS of n = 9 from Lake Wobegon
population
• Data ⇒ {116, 128, 125, 119, 89, 99, 105,
116, 118}
• Calculate: x-bar = 112.8
• Does sample mean provide strong evidence
that population mean μ > 100?

37. Example: “Lake Wobegon”
A. Hypotheses:
H0: µ = 100 versus
Ha: µ > 100 (one-sided)
Ha: µ ≠ 100 (two-sided)
B. Test statistic:
56.2
5
1008.112
5
9
15
0
stat =
−
=
−
=
===
x
x
SE
x
z
n
SE
µ
σ

38. C. P-value: P = Pr(Z ≥ 2.56) = 0.0052
P =.0052 ⇒ it is unlikely the sample came from this
null distribution ⇒ strong evidence against H0

39. • Ha: µ ≠100
• Considers random
deviations “up” and
“down” from μ0 ⇒tails
above and below ±zstat
• Thus, two-sided P
= 2 × 0.0052
= 0.0104
Two-Sided P-value: Lake Wobegon

40. §9.6 Power and Sample Size
Truth
Decision H0 true H0 false
Retain H0 Correct retention Type II error
Reject H0 Type I error Correct rejection
α ≡ probability of a Type I error
β ≡ Probability of a Type II error
Two types of decision errors:
Type I error = erroneous rejection of true H0
Type II error = erroneous retention of false H0

41. Power
• β ≡ probability of a Type II error
β = Pr(retain H0 | H0 false)
(the “|” is read as “given”)
• 1 – β = “Power” ≡ probability of avoiding a
Type II error
1– β = Pr(reject H0 | H0 false)

42. Power of a z test
where
• Φ(z) represent the cumulative probability
of Standard Normal Z
• μ0 represent the population mean under
the null hypothesis
• μa represents the population mean under
the alternative hypothesis







 −
+−Φ=− −
σ
µµ
β α
n
z a ||
1 0
1 2

43. Calculating Power: Example
A study of n = 16 retains H0: μ = 170 at α = 0.05
(two-sided); σ is 40. What was the power of test’s
conditions to identify a population mean of 190?
( )
5160.0
04.0
40
16|190170|
96.1
||
1 0
1 2
=
Φ=







 −
+−Φ=







 −
+−Φ=− −
σ
µµ
β α
n
z a

44. Reasoning Behind Power
• Competing sampling distributions
Top curve (next page) assumes H0 is true
Bottom curve assumes Ha is true
α is set to 0.05 (two-sided)
• We will reject H0 when a sample mean exceeds
189.6 (right tail, top curve)
• The probability of getting a value greater than
189.6 on the bottom curve is 0.5160,
corresponding to the power of the test

46. Sample Size Requirements
Sample size for one-sample z test:
where
1 – β ≡ desired power
α ≡ desired significance level (two-sided)
σ ≡ population standard deviation
Δ = μ0 – μa ≡ the difference worth detecting
( )
2
2
11
2
2
∆
+
=
−− αβσ zz
n

47. Example: Sample Size
Requirement
How large a sample is needed for a one-sample z
test with 90% power and α = 0.05 (two-tailed)
when σ = 40? Let H0: μ = 170 and Ha: μ = 190
(thus, Δ = μ0 − μa = 170 – 190 = −20)
Round up to 42 to ensure adequate power.
( ) 99.41
20
)96.128.1(40
2
22
2
2
11
2
2
=
−
+
=
∆
+
=
−− αβσ zz
n

48. Illustration: conditions
for 90% power.

49. Three types of analysis
• Univariate analysis
– the examination of the distribution of cases on only
one variable at a time (e.g., college graduation)
• Bivariate analysis
– the examination of two variables simultaneously (e.g.,
the relation between gender and college graduation)
• Multivariate analysis
– the examination of more than two variables
simultaneously (e.g., the relationship between
gender, race, and college graduation)

50. “Purpose”
• Univariate analysis
– Purpose: description
• Bivariate analysis
– Purpose: determining the empirical
relationship between the two variables
• Multivariate analysis
– Purpose: determining the empirical
relationship among the variables

51. Types of Statistics
• Techniques that summarize and describe
characteristics of a group or make comparisons
of characteristics between groups are knows as
descriptive statistics.
• Inferential statistics are used to make
generalizations or inferences about a population
based on findings from a sample.
• The choice of a type of analysis is based on the
evaluation questions, the type of data collected,
and the audience who will receive the results.

52. Univariate Analysis
• Involves examination of the distribution of
cases on only ONE variable at a time
• Frequency distributionsFrequency distributions are listings of the
number of cases in each attribute of a
variable
– Ungrouped frequency distribution
– Grouped frequency distribution
• ProportionsProportions express number of cases of
the criterion variable as part of the total
population; frequency of criterion variable
divided by N

53. Cont..
• PercentagesPercentages are simple 100 X
proportion
– Or [100 X (frequency of criterion
variable divided by N)]
• RatesRates make comparisons more
meaningful by controlling for
population differences

54. Measures of Central Tendency
• Measures of central tendencyMeasures of central tendency reflect the
central tendencies of a distribution
– ModeMode reflects the attribute with the
greatest frequency
– MedianMedian reflects the attribute that cuts
the distribution in half
– MeanMean reflects the average; sum of
attributes divided by # of cases

55. Measures of Dispersion
• Measures of dispersionMeasures of dispersion reflect the spread
or distribution of the distribution
– RangeRange is the difference between largest &
smallest scores; high – low
– VarianceVariance is the average of the squared
differences between each observation and the
mean
– Standard deviationStandard deviation is the square root of
variance

56. Types of Variables
• Continuous:Continuous: increase steadily in tiny
fractions
• Discrete:Discrete: jumps from category to
category

57. Subgroup Comparisons
• Somewhere between univariate &
bivariate, are Subgroup Comparisons
• Present descriptive univariate data for
each of several subgroups
– Ratios: compare the number of cases in one
category with the number in another

58. Bivariate Analysis
• Bivariate analysisBivariate analysis focus on the
relationship between two variables

59. Contingency Tables
• Format: attributes of independent variable
are used as column headings and attributes
of the dependent variable are used as row
headings
• Guidelines for presenting & interpreting
contingency tables
– Contents of table described in title
– Attributes of each variable clearly described
– Base on which percentages are computed should be
shown
– Norm is to percentage down & compare across
– Table should indicate # of cases omitted from analysis

60. Multivariate Analysis
• Multivariate AnalysisMultivariate Analysis allow the
separate and combined effects of the
independent variable to be examined

61. Reference
• www.uky.edu
• https://www.stat.auckland.ac
• www.polymtl.ca