SAMPLE BIAS RELATED TO HOUSEHOLD ROLE

This article develops a two-stage statistical analysis to identify and assess the effect of a sample bias associated with an individual’s household role. Survey responses to questions about the respondent’s role in household finances and a sampling design in which some households have all members take the survey enable the estimation of distributions for each individual’s share of household responsibility. The methodology is applied to the 2017 Survey of Consumer Payment Choice. The distribution of responsibility shares among survey respondents suggests that the sampling procedure favors household members with higher levels of responsibility. A bootstrap analysis reveals that population mean estimates of monthly payment instrument use that do not account for this type of sample misrepresentation are likely biased for instruments often used to make household purchases. For checks and electronic payments, our analysis suggests that it is likely that unadjusted estimates overstate true values by 10–20 percent.

Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions

In general, although some random variables such as wind speed, temperature, and load are known to have multimodal distributions, input or output random variables are considered to follow unimodal distributions without assessing the unimodality or multimodality of distributions from samples. In uncertainty analysis, estimating unimodal distribution as multimodal distribution or vice versa can lead to erroneous analysis results. Thus, whether a distribution is unimodal or multimodal must be assessed before the estimation of distributions. In this paper, the bimodality coefficient (BC) and Hartigan’s dip statistic (HDS), which are representative methods for assessing multimodality, are introduced and compared. Then, a combined HDS with BC method is proposed. The proposed method has the advantages of both BC and HDS by using the skewness and kurtosis of samples as well as the dip statistic through a link function between the BC values in BC and significance level in HDS. To verify the performance of the proposed method, statistical simulation tests were conducted to evaluate the multimodality for various unimodal, bimodal, and trimodal models. The implementation of the proposed method to real engineering data is shown through case studies. The results demonstrate that the proposed method is more accurate, robust, and reliable than the BC and original HDS alone.