Transcript Class 2
Basics of Data Cleaning Why Examine Your Data? • Basic understanding of the data set • Ensure statistical and theoretical underpinnings of a given m.v. technique are met • Concerns about the data – Departures from distribution assumptions (i.e., normality) – Outliers – Missing Data Testing Assumptions • MV Normality assumption – Solution is better • Violation of MV Normality – Skewness (symmetry) – Kurtosis (peakedness) – Heteroscedascity – Non-linearity Negative Skew 8 6 4 2 0 0.00 .50 1.00 1.50 2.00 GPA 2.50 3.00 3.50 4.00 Positive Skew 8 6 4 2 0 0.00 .50 1.00 1.50 2.00 GPA 2.50 3.00 3.50 4.00 Kurtosis Mesokurtic Leptokurtic Platykurtic Skewness & Kurtosis SPSS Syntax FREQUENCIES VARIABLES=age /STATISTICS=SKEWNESS SESKEW KURTOSIS SEKURT /ORDER= ANALYSIS. Z values = Statistic Std Error Critical Values for z score .05 +/- 1.96 .01 +/- 2.58 Statistics age N Skewness Std. Error of Skewness Kurtosis Std. Error of Kurtosis Valid Missing 140 4 .354 .205 -.266 .407 Skewness = .354/.205 = 1.73 Kurtosis = -.266/.407 = -.654 Homoscedascity s21 m1 s22 m2 s23 m3 s24 m4 s 21 = s 22 = s 23 = s 24 = s 2e When there are multiple groups, each group has similar levels of variance (similar standard deviation) Linearity 1 Zscore(PERF) 0 -1 -2 -3 -4 -5 -6 -3 -2 -1 0 1 Zscore(STRESS) 2 3 4 Testing the Assumptions of Absence of Correlated Errors • Correlated errors means there is an unmeasured variable affecting the analysis • Key is to identify the unmeasured variable and to include it in the analysis • How often do we meet this assumption? Data Cleaning • Examine – Individual items/scales (i.e., reliability) – Bivariate relationships – Multivariate relationships • Techniques to use – Graphs non-normality, heteroscedasticity – Frequencies missing data, out of bounds values – Univariate outliers (+/- 3 SD from mean) – Mahalanobis Distance (.001) Graphical Examination • Single Variable: Shape of Distribution – Histogram – Stem and leaf • Relationships between two+ variables – Scatterplot Histogram 60 50 Frequency 40 30 20 10 Mean = 11.8008 Std. Dev. = 10.1035 N = 364 0 0.00 10.00 20.00 30.00 yrsexp 40.00 50.00 Scatterplot 60.00 50.00 yrsexp 40.00 30.00 20.00 10.00 0.00 10.00 20.00 30.00 40.00 50.00 age 60.00 70.00 80.00 Frequencies race Valid Missing Total Frequency white, not hispanic 290 african american/black 31 asian/pacific islander 19 hispanic 19 other 9 9.00 1 Total 369 System 2 371 Percent 78.2 8.4 5.1 5.1 2.4 .3 99.5 .5 100.0 Valid Percent 78.6 8.4 5.1 5.1 2.4 .3 100.0 Cumulative Percent 78.6 87.0 92.1 97.3 99.7 100.0 Outliers • Where do outliers come from? – Inclusion of subjects not part of the population (e.g., ESL response to vocabulary test) – Legitimate data points* – Extreme values of random error (X = t + e) – Error in observation – Error in data preparation Univariate Outliers • Criteria: Mean +/- 3 SD • Example: Age – Mean = 34.68 – SD = 10.05 • Out of range values > 64.83 or < 4.53 Univariate Outliers 50 Frequency 40 30 20 10 Mean = 34.6784 Std. Dev. = 10.04525 N = 370 0 20.00 30.00 40.00 50.00 age 60.00 70.00 Multivariate Outliers Mahalanobis Distance SPSS Syntax Regression Var = case VAR1 VAR2 /statistics collin /dependent =case / enter /residuals = outliers(mahal). Critical Values (case with D > c.v. is m.v. outlier) two variables - 13.82 three variables - 16.27 four variables - 18.46 five variables - 20.52 six variables - 22.46 Approaches to Outliers • • • • • • Leave them alone Delete entire case (listwise) Delete only relevant variables (pairwise) Trim – highest legitimate value Mean substitution Imputation 2 2 1 1 Zscore(EXAM) Zscore(EXAM) Effects of Outliers 0 -1 -2 -3 -4 0 -1 -2 -3 -2 -1 Zscore(HMWRK) r = .50 0 1 -3 -4 -3 -2 -1 Zscore(HMWRK) r = .32 0 1 Effects of Outliers 25 N = 500, no outlier N = 501, outlier present 20 N = 401, outlier present N = 301, outlier present N = 201, outlier present N = 101, oulier present 15 N = 51, oulier present N = 26, outlier present Interviews 10 5 0 0 20 Publications Major Problems: Missing Data • Generalizability issues • Reduces power (sample size) • Impacts accuracy of results – Accuracy = dispersion around true score (can be under- or over-estimation) – Varies with MDT used Dealing with Missing Data • • • • • • Listwise deletion Pairwise deletion Mean substitution Regression imputation Hot-deck imputation Multiple imputation Dealing with Missing Data In Order of Accuracy: • Pairwise deletion • Listwise deletion • Regression imputation • Mean substitution • Hot-deck imputation Dealing with Missing Data MDT Pros Cons Listwise deletion Easy to use High accuracy Reduces sample size Pairwise deletion Easy to use Highest accuracy Problematic in MV analyses; non-positive definite correlation matrix Mean substitution Easy to use Saves data; preserves sample size Moderate accuracy Attenuation of findings Regression imputation (no error term adjustment) Saves data; preserves sample size Moderate accuracy Difficult to use Can’t use when all predictors are missing Hot-deck imputation Saves data; preserves sample size Lots of bias & error Transformations Distribution • Moderate deviation from normality • Substantial deviation from normality • Severe deviation; esp. jshape • Negative skew Best Transformation to Try • Square Root • Log • Inverse • “Reflect” (mirror image), then transform • Interpretation of transformed variables?