# When to Use Which Statistical Test

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1 When to Use Which Statistical Test Rachel Lovell, Ph.D., Senior Research Associate Begun Center for Violence Prevention Research and Education Jack, Joseph, and Morton Mandel School of Applied Social Sciences 98 Years of Leadership in Social Justice 1

2 Importance of Using the Appropriate Test Lies, Damned Lies, and Statistics Examples when this goes wrong Task made difficult by breadth of statistics 2

3 Which Type of Test Is Based on: Level of measurement of dependent variable (DV) including number of DVs Level of measurement of the independent variable (IV) - including number of IVs Research question(s) Statistical assumptions Random sample Normal distribution of the sampling distribution 3

4 Levels of Measurement Nominal, Ordinal, Interval Often organized into categorical (discrete) or continuous (interval) Fuzzy levels of measurement Ordinal Ex: using Likert scales as interval variable (scales vs. items) Nominal Yes/No or Presence/Absence must be 0,1 Can treat as interval 4

5 Research Question(s): Degree of Relationship Correlation: how much variables co-vary (bivariate and partial) Regression: prediction of DV based on IV(s) (bivariate and multivariate) Path Analysis (AKA structural equation modeling): extension of regression causal what are the direct and indirect effects 5

6 Research Question(s):Significance of Group Differences T-test: group mean differences (interval DV) 2 groups (IV) Gender impact SAT scores? (Males and females have different SAT scores?) One-way analysis of variable (ANOVA): group mean differences (interval DV) 2+ groups (IV) Race/ethnicity (2+ grps) impact SAT scores? (Do their scores significantly differ?) One-way analysis of covariance (ANCOVA): like ANOVA except controlling for third variable (covariate) Race/ethnicity impact SAT scores controlling for family income? One-way multivariate analysis of variance (MANOVA): >1 DV, controlling for correlations among DVs (assuming correlation among DVs) Race/ethnicity impact reading, math, and overall achievement (DVs) among 6 th grade students? 6

7 Research Question(s): Significance of Group Differences (con d) One-Way MANCOVA: >1 DV while controlling for covariate Race/ethnicity (IV) impact reading, math, and overall achievement (DVs) among 6 th grade students after adjusting for family income? Factorial MANOVA like MANOVA but with 2+ IVs Race/ethnicity and learning preference (IVs) impact reading, math, and overall achievement (DVs) among 6 th grade students? Factorial MANCOVA like factorial MANOVA but with >1 covariate Race/ethnicity and learning preference (IVs) impact reading, math, and overall achievement (DVs) among 6 th grade students after controlling for family income? 7

8 Research Question(s): Prediction of Group Membership Goal: identify specific IVs that best predict group membership as defined by categorical DV Discriminant Analysis: combination of interval IVs that best distinguish categorical DV Which risk-taking behaviors (amt of alcohol use, drug use, sexual activity, and violence - IVs) distinguish suicide attempters from nonattempters - DV? Logistic Regression: categorical or interval IVs that predict odds of Y (categorical DV) Which risk-taking behaviors (amt of alcohol use, drug use, sexual activity, and presence of violence, y/n) increase the odds of a suicide attempt occurring (DV)? DV can be binary or multinomial 8

9 Research Questions: Structure Goal: reduce the number of IVs (no DVs) Factor analysis: explores the underlying structures of scale or instrument (aka latent factors) Exploratory Factor Analysis (EFA) exploratory stage not testing theory, let data tell you the factor structure Confirmatory Factor Analysis (CFA) confirmatory stage testing theory, theory guides structure, often done after EFA Principal Components Analysis (PCA): similar to factor analysis, same goal (variable reduction) Usually first exploratory procedure conducted In practice very similar to EFA Preferred method of factor extraction 9

10 Level of Measurement: Bivariate Categorical IV and DV: Chi-square Interval DV and categorical IV (2 grps): independent sample t-test Interval DV and categorical IV (2+ grps): ANOVA Categorical DV and Interval IV: discriminant (if applicable) or can categorize IV and do Chi-square or logistic regression Interval DV and IV: correlation (covariance) and regression (prediction) 10

11 Level of Measurement: Multivariate Categorical IV and DV + categorical covariate: Chisquare Interval DV and categorical IV + covariate: ANCOVA Interval DVs and categorical IVs: MANOVA Other OVAS previously discussed Interval IVs and DV: partial correlation 11

12 Level of Measurement: Multivariate Regression Interval IVs and DV DV: DV = interval: multivariate regression (AKA OLS regression) DV = binary (0,1): logistic regression DV = ordinal (ex: 0, 1, 2, 3): multinomial regression DV = count (ex: # of children, # visits to doctor in last 6 mths): negative binomial or Poisson regression IVs: supposed to be interval, if not. Dichotomous (dummy) variable (0,1) Polychotomous (2+ groups): white, black, other put two in regression, leave one out, coefficients are in reference to the group left out 12

13 Statistical Assumptions Random sample and normal sampling distribution Transformation of nonnormal DV: log, square root, z score Nonparametric tests: doesn t assume normal distribution Can use when small sample DV is extremely nonnormal (test for this) More conservative tests; not as statistical strong as parametric tests 13

14 Common Nonparametric Tests Chi-square = nonparametic test Pearson s correlation: Spearman s rho and Kendall s tau Paired sample t-test: Wilcoxon t test Independent sample t-test: Mann Whitney U test ANOVA: Kruskall-Wallis test There are many others. 14

15 Other considerations Are your data longitudinal? (more than one observation for same person/observation) Paired sample t-tests (pre and post) Repeated measures ANOVA Regression: fixed, random, and mixed models Are your data nested? Multi-level modeling (AKA hierarchical linear modeling) Do your data have tons of missing data? Multiple imputations Are you interested in survival how long one stays in a certain state before an event occurs (timing is important)? Survival analysis 15

16 Longitudinal Data Analysis (LDA) Use when modeling pattern(s) of change in DV over time and need to explore the effects of time-varying predictors and events on individual/unit outcomes A more robust model because have more information (more variability, less collinearity, more degrees of freedom, and more efficiency) 2 points=great; 3 points=awesome; 2 points: change score regression (Allison 1990) 16

17 Most Common Models in LDA Random Effects (RE) AKA Error Components Models Ability to control for individual heterogeneity (or variability) Example: Units are same industries observed at multiple time points, DV = racial earning inequality. Random effect of industry error assumes that there is some process that creates random variation across industries in the generation of inequality. Fixed Effects (FE) AKA Least Squares with Dummy Variables Ability to control for unobservables (omitted variable bias) Example: Budig, Michelle and Paula England The Wage Penalty for Motherhood. American Sociological Review Studying change in women s wages as a result of motherhood. Didn t matter what the unobserved variables impacts wages were because these are held stable (constant). Only interested in what happens to changes over time within the individual as a result of motherhood. Hybrid of FE and RE AKA Mixed modeling 17

18 Pros and Cons Pros: Listed above Cons: Complicated modeling (lagged variables, time-varying and invariant variables) Attrition and missing data Must account for and correctly model correlated errors (violation of independence) SPSS doesn t do Getting data in correct format! -- (one of the) most difficult part of LDA: getting data in correct format 18

19 Nesting: Hierarchical Linear Model (HLM) AKA: multilevel modeling, mixed linear models, random coefficient models Used when there is a natural nesting to the data Provides coefficients for each levels (parcel out the variance explained by each level) Example - DV: student achievement scores; Level 1: student, Level 2: classroom; Level 3: school Must have variables at all levels or can cluster Violate assumption of independence correlated errors, which you MUST correct! 19

20 Pros and Cons Pro: Con: Interpretation of the levels very useful Language and formulas are unnecessarily difficult Sample size drastically reduced (need any more cases and clusters) Can get complex very quickly, especially with the addition of predictors SPSS doesn t do 20

21 Missing Data Mostly concerned when it is on the DV Use when: Losing lots of cases Assume that missing cases bias your results Three main ways to deal with missing data Ignore: listwise deletion Using ML methods Multiple imputations (can be done in SPSS) 21

22 Survival Analysis Came from epidemiology, hence, the term survival -- AKA event history analysis Use when: Timing is important and must be modeled You have an event (death, job, election, etc.) Censoring of data can be a problem Difficult: Wrapping your brain about the terminology and logic Determining the correct distribution model (usually Cox models SPSS can do Cox models) 22

23 Structural Equation Modeling (SEM) Very good for certain questions: educ, pol sci, psy Use when theory of paths is important direct and indirect paths Difficult when: have more than a few (control) variables, data is nonnormal, exploring with lots of variables, have small samples 23

24 Steps for Determining Which Test Step 1: Identify variables in RQ Step 2: Identify variables as IV(s), DV(s), and covariates (aka control variables) Step 3: Determine the level of measurement (categorical or interval) for all variables Step 4: Determine purpose of the research question degree of relationship, group differences, etc. Step 5: Put all together to Use 24

25 Helpful sources of info Handout borrowed heavily from Mertler and Vannatta tm Tree/ https://play.google.com/apps?hl=en Recommend my favorite stats books 25

26 Questions? Contact info: Rachel Lovell

27 Social Work Leader for 98 Years Countdown to Centennial

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