Quantitative Analysis

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Quantitative Analysis

• Define Quantitative Analysis
• Describe the coding process
• Identify two functions of codebooks
• Practice doing a codebook format
• Describe ways to enter data
• Give examples of univariate analysis
• Explain central tendency and issues that surround
  it
• Distinguish discrete from continuous variables
• Differentiate the goals of univariate, bivariate,
  and multivariate analyses
• Identify the goal of subgroup comparisons
• Differentiate dependent from independent
  variables
• Show how bivariate data are presented and
  analyzed
• Show how multivariate data are presented and
  analyzed

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Assignment for 4/1

• Qualitative Article Review
• 2-3 page review describing the relevant
  components of the research
• Critique of whether or not the study has been
  done right
• What improvements, if any, are needed? If none
  needed, what are the strengths of the study?

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• Quantitative analysisNumerical representation
  and manipulation of observations for the purpose
  of describing and explaining the phenomena that
  those observations reflect.

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Sources of Quantitative Data

• Questionnaires
• Rating forms
• Measurements
• Open-ended questions
• Field observations

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Terminology

• Attribute A characteristic of a person or
  thing.
• Variable A logical grouping of attributes.

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Variables

• Independent
• Variable with values that are not problematical
  in an analysis , but are simply taken as givenit
  causes or determines a dependent variable
• Dependent
• Variable assumed to depend on or be caused by
  another (Dincome, Ieduc)
• (Intervening)

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• Continuous variableIncreases steadily in tiny
  fractions.
• Discrete variableJumps from category to category
  without intervening steps.

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Levels of Data

• Nominal
• Ordinal
• Interval
• Ratio
• Important when determining codes for independent
  and dependent variables

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What level of data are they?

• Age
• Sex
• Blood pressure
• IQ
• Income
• Job title
• Finish place in race
• Ethnicity

• of work-outs per week
• Test score
• Job responsibility classification
• Temperature
• Height
• Satisfaction level (Likert scale)

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Developing Code Categories

• Two basic approaches
• Beginning with a coding scheme derived from the
  research purpose.
• Generate codes from the data.
• Coding
• Code categories should be exhaustive and mutually
  exclusive.
• Reliability

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Student Responses That Can Be Coded Financial
Concerns
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Codebook Construction

• Purposes
• Primary guide used in the coding process.
• Document that describes the locations of
  variables and lists the assignments of codes to
  the attributes composing those variables.

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Entering Data

• Data entry specialists enter the data into an
  SPSS data matrix or Excel spreadsheet.
• Optical scan sheets.
• PDAs.
• Part of the process of data collection.

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Transforming and Missing Data

• Transform A specific function in SPSS that can
  recode variables
• Age into age categories
• Missing or misrepresented responses?

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Types of Analyses

• Univariate
• Bivariate
• Multivariate

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• Univariate analysisDescribes a case in terms of
  a single variable - the distribution of
  attributes that comprise it.
• Frequency distribution (f )Description of the
  number of times that the various attributes of a
  variable are observed in a sample.

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Descriptive Statistics

• Frequencies
• Percentages
• Central tendency
• Mean
• Median
• Mode

• Dispersion measures
• Range
• Variance
• Standard deviation

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Graphical Representation - Frequencies

• Pie Charts
• Bar Graph
• Histogram

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SPSS Analysis GSS Attendance at Religious
Services, 2000
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• AverageMeasure of central tendency.
• Mean (x bar)Result of diving the sum of the
  values by the total number of cases.

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• ModeThe most frequently occurring attribute.
• MedianMiddle attribute in the ranked
  distribution of observed attributes.

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• DispersionRefers to the way values are
  distributed around some central value.
• Range X(max) X(min)
• Interquartile range
• Standard deviationIndex of the amount of
  variability in a set of data.

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Basketball Example

• Team 1
• 0
• 1
• 10
• 14
• 20

• Team 2
• 8
• 8
• 9
• 10
• 10

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Calculating Std. Deviation and Variance

• Calculate the mean
• Subtract the mean from each score (this is your
  deviation score)
• Square the deviation scores
• Add the squared deviation scores
• Divide this number by n-1
• Take the sq. root of this number
• Square the number

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What do the data look like?(Distribution Curves)

• Normal distribution
• 68/95 rule
• Skewness
• Positive
• Negative

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Univariate Analysis

• Describing a case in terms of the distribution of
  attributes that comprise it.
• Example
• Gender - number of women, number of men.

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Presenting Univariate Data

• Goals
• Provide reader with the fullest degree of detail
  regarding the data.
• Present data in a manageable from.

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Subgroup Comparisons

• Describe subsets of cases, subjects or
  respondents.
• Examples
• "Collapsing" response categories.
• Handling "don't knows."

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• Bivariate analysisAnalysis of two variables
  simultaneously. Focus is on the variables and the
  empirical relationships.
• Descriptive, univariate
• Inferential, bivariate multivariate

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Bivariate Analysis

• Describe a case in terms of two variables
  simultaneously.
• Example
• Gender
• Attitudes toward equality for men and women

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• Contingency tablesValues of the dependent
  variable are contingent on values of the
  independent variable.

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Constructing Bivariate Tables

• Divide cases into groups according to the
  attributes of the independent variable.
• Describe each subgroup in terms of attributes of
  the dependent variable.
• Read the table by comparing independent variable
  subgroups in terms of an attribute of the
  dependent variable.

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Construct a contingency Table

• 150 Fathers favor year-round schools and 50
  oppose it 100 Mothers favor year-round schools
  and 300 oppose it

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So whats the deal on significance?

• Statistical significance unlikeliness that
  relationships observed are due to chance
• Significance level .05 (based on probability)
• Type I Error
• Type II Error
• The key is how meaningful the results are- not
  necessarily if statistically significant.

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Tests of Associations

• Chi-square (nominal, ordinal data)
• Expected vs. observed
• Phi (2x2)
• Cramers V (larger tables)
• Correlations (Pearson, Spearman)
• Depends on level, sample size
• 1 and 1 (perfect correlations) 0 none
• Used to determine reliability
• Correlation does not equal to causation
• Gives p value but the corr statistic more useful

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Tests of Difference (Parametric)

• Parametric- compares means
• Non-parametric- compares ranks (median based)
• T-test (grouped data with 2 values)
• Indep usually nominal/ordinal dep usually
  interval/ratio
• Indep t-test (2 groups)
• matched pairs t-test (same group at 2 times)
• Reports as a t statistic (check Lavenes)
• Check means to determine differences

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Tests of difference cont

• Analysis of variance (2 groups on indep with
  nominal/ord and int/ratio dep)
• Post hoc to determine which groups differ
• F statistic (like the t statistic)
• Check for meaningfulness

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Test of Difference (non-parametric)

• Mann-Whitney U test (like indep t-test)
• Sign test (like matched t-test)
• Wilcoxin Signed Ranks test- like t-test when
  dependent has more than 2 ranked values
• Kruskal-Wallis (like oneway)
• Friedman Analysis of variance (repeated measures)

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Multivariate Analysis

• Analysis of more than two variables
  simultaneously.
• Can be used to understand the relationship
  between two variables more fully.

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Things to remember about stats

• Pay attention to levels of your data
• Identify independent and dependent variables
• Know when to choose parametrics/ non-parametrics
  and the appropriate test
• Plt .05
• Check for meaningfulness
• Sometimes not finding significance is more
  important

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Quantitative Analysis

• Univariate - simplest form,describe a case in
  terms of a single variable.
• Bivariate - subgroup comparisons, describe a case
  in terms of two variables simultaneously.
• Multivariate - analysis of two or more variables
  simultaneously.