Transcript Data Analysis: Descriptive Statistics

Data Analysis: Descriptive
Statistics
Introduction
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After data are collected, analysis of the
findings is required
Analysis entails the application of both
investigative curiosity and a detective’s
instinct to make sense of the evidence
before you
Starting Point
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The exploration should start with
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Refamiliarizing oneself with the research
questions or hypotheses
Refreshing one’s memory on the
specification of needs important to the
study
Next, chart the course
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A mental (if not written) outline of the basic
information that will be important to writing
the story is a helpful guide
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Who: The research sample
What: The variables & operationalization criteria
used for each; relationships between variables
How: Research method and design
When
Where
Reporting Data
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The means by which data is reported is
partially driven by the choice of measurement
Nominal, ordinal = Lower levels of
measurement
Interval, ratio = Higher levels of
measurement
Reporting Data
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Fewer data analyses are appropriate for
lower levels of measurement
Higher levels of measurement can be
analyzed using all statistical techniques
Reporting Frequency Distributions
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Present the initial frequency distribution
(one-to-one match)
Re-categorize data as necessary to
present different ‘angles’ of the data
Category Data Descriptives
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Frequency distributions are most
commonly used by researchers to
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Get a sense of the raw number of
responses to each category
As a visual check of response codes
As a baseline to more commonly reported
proportions and percentages
Category Data Descriptives
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Proportions
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The frequency of responses relative to the total
Total response proportion = 1.0
Percentages (and adjusted percentages)
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Proportion multiplied by a quotient of 100
Utility: Presents data relative to
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The whole
Other categories within the response set
Other categories across response segments (cross tabs)
To the same question relative to other points of
measurement
Descriptive Techniques
Ratios
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Used when the relationship between
objects is important
X ‘in relation to’ Y
Example:
“The representation of males to female
respondents was 3 to 1….”
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Continuous Data Descriptives
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Continuous data utilize higher levels of
measurement
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Interval level of measurement
Ratio level of measurement
Researchers have the opportunity to
apply a wider range of statistics to their
description of the research results.
Important Information for
Continuous Data
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Average – Measure of Central Tendency
Spread – Dispersion or variance (around
the central point)
Shape (of the distribution) – skewness,
kurtosis
Data Descriptives for the
Average
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Mode
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The most frequently-observed value in a data set
‘The most typical case’
Median
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The middle value of a data set
Assumes an equal distribution of scores above and
below the mid-point
Measures of Central Tendency
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Mean
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Provides a summary of the data average
Assumes a normal (representative)
distribution of the scores
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Limited in its sensitivity to outliers, which can
result in an atypical reflection of the average
Data Descriptives for the
Spread
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Gives the researcher a sense of how
spread out the responses are around
the mean
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Maximum and minimum
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Reflect the extreme upper and lower points in
the data set
Range of distribution
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Maximum – minimum = range
Data Descriptives for the
Spread
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Standard deviation
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Allows for estimation of the proportion of
respondents/cases within certain ranges in the
center part of the distribution, assuming a
normal distribution of scores
*Limited in its applicability if the distribution of
scores does not reflect normalcy.
(see p. 291 Guidelist 10-3)
Data Descriptives for the
Spread
Skewness
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The degree and direction of asymmetry from a
normal distribution.
Indicates the presence of ‘leaning’ in responses
Can be a reflection of question bias, sample bias,
or some other form or bias (including deliberate
manipulation)
Data Descriptives for the
Spread
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Kurtosis
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An indication of how peaked or flat the
distribution is relative to a normal
distribution.
Indicates how tightly or loosely responses
are distributed around the mean
Issues that May Arise In
Descriptive Statistics
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Floor effects
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Responses grouped at or near the lower
boundary of a scale
Ceiling effects
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Responses groups at or near the upper
boundary of the scale
Issues that May Arise In
Descriptive Statistics
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Bimodality
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The presence of two ‘typical’ averages
Indicates segmentation differences within
the sample