Screening and Cleaning Data

1. Screening and Cleaning Data Have my data been entered correctly? Do I have missing data? If yes, now what? Are the assumptions of the statistical procedure met? Do I need to transform my variables? And how? Do I have pesky outliers? Is my data singular or multicollinear?

2. Specific Issues in Data Screening Accuracy of data file for continuous variables: means, standard deviations reasonable? all values �in range�? for discrete variables: splits reasonable? all values �in range�? Have you correctly programmed missing values?

3. Missing Data How missing data occurs overlooked questions missing scores not related to other measured variables missing values a function of other measured variables e.g., missing income scores for low education participants Pattern and amount of missing data are important

4. Missing Data Types of missing data Missing completely at random (MCAR) missingness on a variable does NOT depend on the variable itself or any other variable in the data set no patterns of missingness e.g., no differences between those with missing data and individuals with complete data on measured variables can be tested in SPSS the MVA procedure consult the MCAR test want it to be non-significant

5. Missing Data Missing at random (MAR) missingness on a variable is predictable from other variables missingness related to other variables, not DV Missing not at random (MNAR) missingness is related to the DV e.g., chronic smoker enrolled in a smoking cessation study misses an assessment problem with this approach, this can typically only be inferred

6. Missing Data continued Rule of thumb: < 5% of cases missing, any substitution method is generally OK Testing the missing data (how are they different?) i.e., look for differences as a function of missingness How do you do this? create a (or a number) of dummy-coded variables (missing/not missing) or create multiple variables if missing data patterns emerge run t-tests, regressions, and chi-square tests with other variables to determine if differences exist demographics, other target study variables differences exist...what do we do?

7. Missing Data continued What do we do with missing cases? deleting variables > 50% missing...yikes...delete variable create a dummy-coded missing data variable for analyses deleting cases listwise deletion delete cases with missing values altogether pairwise deletion keep cases with missing values not OK ever, never, ever

8. Missing Data continued Methods for estimating (imputing) missing values: �best guess� = prior knowledge mean substitution regression substitution (insert predicted value) problem: predicted score is �better� than actual score

9. Missing Data continued Hot-deck imputation missing value replaced by randomly chosen case that is similar Maximum Likelihood (ML) - Expectation maximization (EM algorithm) assumes a (normal) distribution estimates a correlation (covariance) matrix for missing values using existing & missing data uses maximum likelihood (ML) estimation �best� method and easily accessible in SPSS does NOT use random error

10. Missing Data continued Multiple imputation similar to EM method, however... create a missing data score for multiple data sets using EM or data augmentation (DA; Markov Chain Monte Carlo procedures) injects random error into the process then average parameter estimates across data sets or... analyze individual data sets Schaefer, J.L., & Graham, J.W. (2002). Missing data: Our view of the state of the art. -Psychological Methods, 2, 147-177.

11. Outliers Univariate vs. Multivariate outliers Primary reasons for outliers incorrect data entry individual is not from the population of choice Detecting univariate outliers for dichotomous variables: uneven (90-10) splits for continuous variables: z-scores greater than 3.29 (p < .001) or larger deleted z-scores greater than 3.29

12. Outliers continued graphical methods: histogram, box plot, normal probability plots, etc. Detecting multivariate outliers using Mahalanobis (MAHAL) distance distance of a case from the centroid (??) of remaining cases centroid = where the means for all target variables intersect statistically test cases using ?2 ? = .001, df = # target variables

13. Outliers continued can also use indices of leverage, discrepancy, & influence forms of MAHAL What to do with outliers determine if they are part of the sample create dummy-coded variable (outlier/nonoutlier) run analyses on other variables (demographics) determine if you will delete case or modify score data transformations (to come later)

14. Normality Univariate vs. Multivariate Normality Check distributions at the univariate level skewness and kurtosis (statistical tests) check (detrended) expected normal probability plots compares expected to observed values Can use Mardia�s coefficient to test for multivariate normality Assume robustness???!!!!

15. Linearity The dreaded straight-line (Pearson�s r) Diagnosed primarily from bivariate scatterplots lowess fit line What to do if nonlinearity exists? transform variables dichotomize use nonlinear statistical methods

16. Homoscedasticity and Homogeneity of Variance-Covariance Matrices Homoscedasticity for ungrouped data: variability in scores for one continuous variable is the same at all values of a second i.e., you have similar distributions I will attempt to draw Homogeneity of Variance-Covariance for multivariate data (Box�s M test) for grouped data

17. Data Transformations Used to reduce outlier impact and improve distribution of data These are not universally recommended! interpretative problems Types of transformations square root: good for moderate departures from normality makes larger numbers smaller I attempt to draw yet again a beautiful, positively-skewed distribution

18. Data Transformations continued log: good for substantial departures from normality base 10 function ? x = 10y ? 100 = 10y makes smaller numbers larger, and vice versa dichotomization: when nothing else works

19. Data Transformations continued Direction of deviation (skew) is important reflect for negative skew add �1� to largest score to form a constant subtract each original score from the constant transform as previous the interpretative direction has also changed Can also add a value of one to each score if you have scores of less than one important when taking square root or log, respectively decimals give you larger numbers and negative numbers, respectively.

20. Multicollinearity and Singularity Multicollinearity = variables are too highly correlated Singularity = variables are redundant Correlations > .70 are generally problematic These both inhibit matrix inversion! Like you care! run your analyses and see if the computer throws-up Procedure: calculate collinearity diagnostics squared multiple correlations (VIF), tolerance

21. Steps for screening (un)grouped data Analyses include regression, canonical correlation, factor analysis, SEM "Steps": check distributions for normality, univariate outliers, missing data check plots for linearity and homoscedasticity transform variable(s) if needed calculate Mahalanobis distance (multivariate outliers) if identified, delete or modify outliers deal with missing data rerun everything if you use a form of substitution

22. Steps for screening grouped data Analyses include MANOVA, Discriminant Function Analysis, and Multigroup CFA and SEM Steps are the same as with ungrouped data just do parallel screening within each substantive subgroup that you care about e.g., within gender groups, ethnic groups, experimental groups, etc.