Data Analysis as a Decision Making Process

Transcription

1 Data Analysis as a Decision Making Process

2 I. Levels of Measurement A. NOIR - Nominal Categories with names - Ordinal Categories with names and a logical order - Intervals Numerical Scale with logically ordered and equidistant units. - Ratio Numerical Scales with logically ordered and equidistant units and contains a true Zero.

3 I. Levels of Measurement B. vs. Variables = Observations are counted in whole units (Quantitative or Qualitative Categories) and sub-dividing units does not add new information. - How many times have you smoked Crack? Variables = Observations that are ordered across a continuum, with an infinite number of meaningful points between each whole unit. Sub-dividing units adds new information. - How many grams of Crack have you smoked?

4 None Goodness of Fit Chi Square (χ 2 ) O = E O E -Pearson s Chi Square (χ 2 ), Test of Independence O = E O E - Φ (2x2) Effect Size Φ = 0 Φ 0 - Φ cramer (3x3+) Effect Size Φ = 0 Φ 0

5 (Ordinal) (Ordinal) Spearman s Rho ρ = 0 ρ 0 ρ or r s (Ordinal) (Ordinal) Kendall s Tau τ τ = 0 τ 0

6 (2 Groups) Z-Test: One Sample Mean (M 1 ) vs. Population Mean (μ); σ known M 1 = μ M 1 μ (2 Groups) Single Sample t-test: One Sample Mean (M 1 ) vs. Population Mean (μ); σ unknown M 1 = μ M 1 μ (2 Groups) Independent Sample t- Test: Compares two Sample Means M 1 = M 2 M 1 M 2 (1-2 Groups) Repeated Measures / Matched Sample / Difference t-test: Compares a single group at Time 1 and Time 2, or Matched Groups M t1 = M t2 M t1 M t1

7 (2 Groups) Point Biserial Correlation: is naturally dichotomous r pb = 0 r pb 0 (2 Groups) Biserial Correlation: Dichotomize a Variable r b = 0 r b 0 (2 or more Groups) One-Way ANOVA: Compares 2 or more group means. Significant ANOVA does not indicate which means are different. M 1 = M 2 = M j At least 1 Mean diff from at least 1 other Mean Planned Comparisons or Post Hoc tests are needed

8 Multiple Factorial ANOVA: Tests Main effects for each variable and Interaction Effect Main Effects 1: M.1. = M.2. = M.j. 2: M..1 = M..2 = M..k Interaction 1: M.11 = M.12 = M.jk Main Effects 1: 2 groups differ 2: 2 groups differ Interaction Groups differentially differ across levels of other variable At least 1 ANCOVA - Analysis of Covariance: -Includes a Covariate

9 Pearson s Product Moment Correlation Coefficient (r): r = 0 r 0 -Assesses Strength and Direction of Association -r 2 : % variance accounted for Regression (simple linear/least squares): b = 0 b 0 b = Slope = Strength and Direction - Used for Prediction

10 Multiple Multiple Regression: Flexible Design and Research Questions R = 0 R 0 -Single Step -Hierarchical -Mediation -Moderation -R: Multiple Correlation Coefficient strength but not direction -R 2 : % variance in accounted for by all s -b for each indicates strength and direction

11 (at least 1) Multiple MANOVA: Multivariate Analysis of Variance: Controls inflation of Type I Error F = 0 Other effects may be tested depending on design F 0 (at least 1) Multiple MANCOVA: Multivariate Analysis of Covariance: Includes a Covariate F = 0 F 0 Multiple Multiple - Canonical/Set Correlation -Path Analysis/Causal Modeling -Structural Equation Modeling (Uses Latent Variables)

12 (at least 1) (2+ groups) Logistic Regression