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Quantitative Analysis
June 25th, 2014
By Dr. James Lani
Statistics Solutions
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Data Cleaning and Preparation
• Select the correct analysis
(RQ and level of measurement• Clean your data• Describe variables• Conduct the
analyses/assess assumptions• Present the findings• Summarize the findings
Putting the Pieces Together
Describe
Variables
Clean Data
Present &
Summarize
Findings
Conduct Analyses/
Assess Assumpti
ons
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Quantitative Results StrategyGarbage In, Garbage Out
Assess data for outliers (±3.29);
Multiple imputation for missing data;
Create composite score (with reverse coding if necessary);
Conduct Cronbach’s alpha (α);
Assess for normality
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Descriptive StatisticsMeans & Standard Deviations, Frequency & Percentages
Variable n %
Location
Urban 72 48.0
Rural 78 52.0
Ethnicity
White 36 24.0
Hispanic 13 28.7
Other 71 47.3
Table 1Frequencies and Percentages for Nominal Variables
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Chi-SquareGoodness of Fit & Test of Independence
Chi-square analysis answers what research questions?
Assumptions of analysis:• Each cell has count of
1;• 80% of cells have an
expected value of 5.
Conducting analysis;
Presenting findings;
Write up in narrative;
Tables and figures.Republican Democrat Green Independent Libertarian
X X X X X
Repub. Democrat Green Indep. Libert.
Male X X X X X
Female X X X X X
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Pearson Correlation
Examines the relationship between two or more scales level variables
Assumptions of the analysis:
• Linearity• Homoscedacit
y• Normality
AssumptionsLinear
Non-Linear
Homoscedasticity Met
Heteroscedasticity
Normal
Non-normal
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Independent Samples t-testLet’s look at differences in IQ by Gender
Examines mean differences on a scale level dependent variable by a dichotomous nominal level independent variable.
Assumptions of analysis:
• Homogeneity of variance
• Normality
Males Females
Part 1=1 Part 4=2
Part 2=2 Part 5=3
Part 3=3 Part 6=4
X=2 X=3
Males Females
Part 1=1.9 Part 4=2.9
Part 2=2.0 Part 5=3.0
Part 3=2.1 Part 6=3.1
X=2 X=3
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One-Way ANOVALet’s look at differences on Scores by Political Affiliation
Examines mean differences on a scale level dependent variable by a dichotomous nominal level independent variable.
Assumptions of analysis:
• Homogeneity of variance
• Normality
Males Females Independent
Part 1=1.9 Part 4=2.9 Part 7=3.9
Part 2=2.0 Part 5=3.0 Part 8=6.0
Part 3=2.1 Part 6=3.1 Part 9=8.1
X=2 X=3 X=6
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Dependent Samples t-testLet’s look at differences between science scores Pretest vs. Posttest
Examines the mean difference between two paired scale level variables.
Assumptions of analysis:• Normality
Science Pretest Science Posttest
Part 1=1 Part 1=2
Part 2=2 Part 2=3
Part 3=3 Part 3=4
X=2 X=3
Science Pretest Science Posttest
Part 1=1.9 Part 1=2.9
Part 2=2.0 Part 2=3.0
Part 3=2.1 Part 3=3.1
X=2 X=3
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Repeated-Measures ANOVALet’s look at differences among test scores Pretest vs. Posttest vs. Follow Up
Examines mean differences among two or more scale level variables
Assumptions of analyses:
• Sphericity• Homogeneity of
variance
Science Pretest
Science Posttest
Science Follow-Up
Part 1=1.9 Part 1=2.9 Part 1=
Part 2=2.0 Part 2=3.0 Part 2=
Part 3=2.1 Part 3=3.1 Part 3=
X=2 X=3 X=
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Linear RegressionDoes IQ predict Creativity?
Examines if one or more scale, ordinal, or nominal level independent variables predict a scale level dependent variable.
Assumptions of analysis:• Normality,
Multicollineality, Homoscedastcity
IV DV
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Regressions:Multiple, Logistic, Ordinal, Multinomial
It’s all about the level of measurement of the DV
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Mediation AnalysisDoes Education mediate the relationship between IQ and Creativity?
Examines if one scale level mediator variable explains the relationship between a scale level independent variable and a scale level dependent variable
Assumptions of analysis:• Assumptions of regression
3 Regression Equations
IV M; must be significantIV DV; must be significantM, IV M, IV DV; IV is no longer significant
Education (M)
IQ (IV) Creativity (DV)
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Moderation AnalysisDoes Age moderate the relationship between IQ and Creativity?
Examines if one scale level moderator variable strengthens or weakens the relationship between a scale level independent variable and a scale level dependent variable
Assumptions of analysis:• Assumptions of regression
Regression with 2 blocks
Step 1: IQ and Age enteredStep 2: Interaction term entered
Moderation is supported if interaction is significant.
Age (Mod)
IQ (IV)
IQ x Age Interaction
Creativity
Note. To avoid multicollinearity, center IV/Mod (subtract mean), then create the interaction term.
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Moderation Analysis (Continued)
Does Age moderate the relationship between IQ and Creativity?Variable namesName of independent variable: IVMeaning of moderator value “0” Men Intercept/Constant: 3Meaning of moderator value “1” Women
Unstandardised Regression CoefficientsIndependent variable: 0.6Moderator: 0.4Interaction: -0.8
Means/SD’s of variablesMean of independent variable:0SD of independent variable: 1
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I’m All Yours:Questions and Answers
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