Understanding and protecting vulnerable children is key to helping them become productive members of society. The Department of Health and Human Services sponsored the National Survey of Child and Adolescent Well-Being (NSCAW) to better understand the lives of children who come into contact with the child welfare system. This paper uses the NSCAW data to investigate the role of maternal depression and maternal substance abuse on a child's cognitive stimulation scores for a subset of the children. An investigation of the survey methodology and the actual data led to some manipulation of the data and assumptions for the analysis. The differences between design and model based analyses of survey data were explored. The two analyses were applied to the cognitive stimulation scores. For the model based analysis, two models were developed, one which used the weights at each stage of model building and one which did not use the weights at each stage. The models had conflicting results. Two recommendations were made to improve upon the model based analysis. First was to obtain information about the weights after each stage of adjustment. The second was to model the different strata separately. The design based analysis (design based-model assisted) used the two models created in the model based analysis and re-examined them using design based techniques. The design based analysis had similar results to the model based analysis. The two models in the design based setting also provided conflicting results regarding the question of interest. To determine which is better, the question of which "regression line" provides better data reductive properties needs to be addressed.