Strategies for Identifying Outliersand Managing Missing Data
R. Michael Haynes, PhD [email protected]
Tarleton State University
A PRIORI MARCH 1, 2012Assistant Vice President for Student Life Studies
POST HOC FEBRUARY 29, 2012Executive Director of Institutional Research
Assistant ProfessorEducational Leadership and Policy Studies
Outlier analysis in multiple regression class
Data inspection (missing data) was a key aspect of dissertation
Try to incorporate at the very least “a nod” to data inspection in any assessment/project completed
A little background...
Identifying input errors
Indentifying spurious data points (an answer of “6” on a 1-5 Likert scale)
Makes your findings more sound
Good practice as recommended by the American Psychological Association (Wilkerson & APA Task Force on Statistical Inference, 1999)
Why is it important to evaluate your data set?Can help in…..
Desired Outcomes
Knowledge of various data inspection methods visual range of data set
Methods for managing missing data list wise deletion
pair wise deletion mean replacement linear trend point
Criteria for identifying outliers/spurious data points standardized residuals/predicted values
standard deviation diagnostics Cook’s D values
Data inspection methods
VisualCan alert you to missing casesMost beneficial with smaller datasets where review of individual cases is possible
Data inspection methodsSPSS minimum/maximum values functionQuick method of inspecting range of larger data sets
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
Learning Community 884 0 1 .14 .343
You are taking this survey: 874 1 3 2.01 .139
Recoded response to high
school graduation year
variable HGRADYR
883 1 4 3.94 .367
Valid N (listwise) 873
What to do about missing values?SPSS options
Exclude cases listwise: Only cases with valid values for all variables are included in the analyses.Exclude cases pairwise: Cases with complete data for the pair of variables being correlated are used to compute the correlation coefficient on which the regression analysis is based. Degrees of freedom are based on the minimum pairwise NReplace with mean: All cases are used for computations, with the mean of the variable substituted for missing observations
(SPSS Inc., 233 S.Wacker Drive, Chicago, IL, 60606)
Problems with these options…
Listwise excludes all values for a case missing even 1 variable value…throws the baby out with the bath water!
Pairwise only utilizes variables for which both values are present
Can lead to distortion of findings through selection bias
(King, Honeker, Joseph, & Scheve, 1998)
More preferred options…Choose “Transform” -> “Missing Values”
Enter variables with missing values into “New Variable” boxUnder “Name and Method”, select one of the following:
Series MeanMean of Nearby PointsMedian of Nearby PointsLinear InterpolationLinear Trend at Point
I prefer the last option, Linear Trend at Point
Linear Trend at Point
Uses the theory of regression to calculate coefficients based upon existing values
Generates a replacement value for each case on each variable
More robust than simply replacing with mean
Identifying outliers… what is an outlier?
An unusual score in a distribution that is considered extreme and may warrant special consideration (Hinkle, Wiersma, & Jurs, 2003)
...a data point distinct or deviant from the rest of the data (Pedhazur, 1997)
Why is it important to identify potential outliers?
Can skew findings which in turn can skew conclusions/decisions/programming
Can help identify case in dire need of additional programming/resources…..finding that lost raft at sea!
As mentioned earlier, can assist in identifying data entry errors
Strategies for identifying outliers in your dataset
Standardized predicted and residual scores
Strategies for identifying outliers in your dataset
Strategies for identifying outliers in your dataset
Residuals 3 standard deviations away from meanRule of thumb….”99% of your dataset should fall within + or – 3 standard deviations from the mean”
Casewise Diagnosticsa
Case
Number Std. Residual
Percent Hispanic
Enrollment Predicted Value Residual
75 -4.091 .180 .54883 -.368829
88 -3.195 .020 .30811 -.288109
175 -4.068 .060 .42682 -.366818
a. Dependent Variable: Percent Hispanic Enrollment
Strategies for identifying outliers in your dataset
Cook’s D valuesConsiders each variables relationship to the other variables in the dataset (Pedhazar, 1997)Cook’s D values greater than 1 could be suspect
Strategies for identifying outliers in your dataset
Cook’s D valuesConsiders each variables relationship to the other variables in the dataset (Pedhazar, 1997)Cook’s D values greater than 1 could be suspectSaves values to dataset
OK, so what if some of your cases don’t pass this 3 prong approach and it’s not a data entry error?
Discard the case? Rejects the notion that the data “is what it is…”“Tightens-up” the model to be more representative of the norm
Keep it in?Distorts the whole for a special circumstanceDepending upon your research question, could bring attention to a group needing special consideration
Either way, can be addressed in limitations/conclusions/need for further research
References
Hinkle, D.E., Wiersma, W., & Jurs, S.G. (2003). Applied statistics for the behavioral sciences (5th ed.). Boston, MA: Houghton Mifflin Company
King, G., Honaker, J., Joseph, A., & Scheve, K. (1998). Listwise deletion is evil: What to do about missing data in political science [Electronic version]. Society for Political Methodology: American Political Science Association, Washington University in St. Louis, St. Louis, MO. Retrieved February 2, 2009, from http://polmeth.wustl.edu/workingpapers.php?order=dateasc&title=1998&startdate=1998-01-01&enddate=1998-12-31
Pedhazur, E. J. (1997). Multiple regression in behavioral research (3rd ed.). South Melbourne, Australia: Wadsworth.
Wilkinson, L. & Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanation. American Psychologist, 54, 594-604.