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JAQM Volume 14, Issue 2 - June 30, 2019
Contents
Discriminating Value of Item and Test
Satyendra Nath CHAKRABARTTY
The paper proposes new measures of difficulty and discriminating values of binary items and also test consisting of such items. The measures consider length of two vectors and angle between them. Relationships between difficulty and discriminating values of items and test were derived including relationship between test reliability and test discriminating value. Quantitative evaluation of discriminating value of Likert item and questionnaire have been presented for seven dissimilarity measures which can be computed from a single administration of the questionnaire and using the permissible operations for a Likert scale i.e. considering only the frequency or proportion for each cell of the Item-Response category matrix. Important features of the methods discussed along with comparison of the proposed methods in terms of desired properties. Each proposed method is monotonic subject to satisfying specific condition which is different for different approaches. Theoretical derivation of condition for monotonically increasing was undertaken separately for each method. Based on theoretical advantages, measure based on CV appears to be best method for discriminating values of Likert items and scale. Both the conditions for zero discriminatory value of an item are satisfied by CV. Moreover, it is easy to estimate population CV and undertake other statistical inferences.
Small Count Data and Outlier Analysis: An Exploratory Study of Patient Safety
Alexander PELAEZ, Elaine R. WINSTON, Nooshin NEJATI
Small count data presents challenges for analytics and requires significant data inspection. Outliers may become a problem for small count data and are often overlooked. A single outlier may have a strong effect on small count data because of the difficulty in identifying the nature of the outlier. In the healthcare industry, small count data often represent life-threatening incidences, such as rare diseases or “never events” in surgeries. The focus of this research is on data sets that report retained surgical devices. Any single outlier may have an impact on performance. Accurate identification of outliers is essential to healthcare providers. This paper examines two approaches for outlier identification of retained surgical devices data. A proposed method is based on the impact a potential outlier has on the variance of the data. The results of this method are compared to a chi-square distribution to identify potential outliers. The method reported a significantly lower number of outliers in comparison to Tukey fences. The results show that using the variance difference method provides a lucid and conservative approach to outlier identification. In the case of retained surgical devices, outliers may represent variation in the quality of surgical care provided at hospitals. The variance difference method has the potential to help with the accurate representation of small count data.
Power Pranav Distribution and its Applications to Model Lifetime Data
Kamlesh Kumar SHUKLA
In this paper, a two-parameter power Pranav distribution (PPD), of which Pranav distribution introduced by Shukla (2018) is a special case, has been proposed. Its important statistical properties including shapes of the density, moments, coefficient of variation, skewness, kurtosis and index of dispersion have been obtained and presented graphically. Hazard rate and stochastic ordering of the proposed distribution have also been studied and discussed. The maximum likelihood estimation has been discussed for estimating its parameters. Simulation study of PPD has also been carried out. Application and goodness of fit of the proposed distribution has been discussed with a real lifetime datasets from engineering and biology. Its fit was found satisfactory over two parameter power Ishita distribution (PID), power Akash distribution (PAD), power Lindley distribution (PLD) and one parameter Pranav distribution.