Undergraduate students’ errors on interval estimation based on variance neglect

Interval estimation is an important topic, especially in drawing conclusions on an event. Mathematics education students must possess the skill to formulate and use interval estimation. The errors of mathematics education students in formulating wrong interval estimates indicate a low understanding of interval estimation. This study explores the errors of mathematics education students in interpreting the variance in the questions regarding selecting the proper test statistic to formulate the interval estimation of mean accurately. Respondents in this study involved 36 students of mathematics education (N = 9 males, N = 27 females). This research is qualitative research with a qualitative descriptive approach. Data collection was carried out using the respondents’ ability test and interviews. The respondents’ ability test instrument was tested on 36 students and declared valid where r-count r-table with r-table of 0.3291, and declared reliable with a Cronbach Alpha value of 0.876 0.6. Through an exploratory approach, data were analyzed by categorizing, reducing, and interpreting to conclude students' abilities and thinking methods in formulating interval estimation of the mean based on the variance in questions. The results showed that mathematics education students neglected the variance, so they could not determine the test statistics correctly, resulting in error interval estimates. This study provides insight into the thinking methods of mathematics education students on variance in interval estimation problems in the hope of anticipating errors in formulating interval estimation problems.

Teaching: confidence, prediction and tolerance intervals in scientific practice: a tutorial on binary variables

Background One of the emerging themes in epidemiology is the use of interval estimates. Currently, three interval estimates for confidence (CI), prediction (PI), and tolerance (TI) are at a researcher's disposal and are accessible within the open access framework in R. These three types of statistical intervals serve different purposes. Confidence intervals are designed to describe a parameter with some uncertainty due to sampling errors. Prediction intervals aim to predict future observation(s), including some uncertainty present in the actual and future samples. Tolerance intervals are constructed to capture a specified proportion of a population with a defined confidence. It is well known that interval estimates support a greater knowledge gain than point estimates. Thus, a good understanding and the use of CI, PI, and TI underlie good statistical practice. While CIs are taught in introductory statistical classes, PIs and TIs are less familiar. Results In this paper, we provide a concise tutorial on two-sided CI, PI and TI for binary variables. This hands-on tutorial is based on our teaching materials. It contains an overview of the meaning and applicability from both a classical and a Bayesian perspective. Based on a worked-out example from veterinary medicine, we provide guidance and code that can be directly applied in R. Conclusions This tutorial can be used by others for teaching, either in a class or for self-instruction of students and senior researchers.

Predictor of reliability indicators for nanoelectronic heterostructure devices with transverse current transfer under conditions of limited experimental information based on Bayesian inversion

Predictor of the reliability indicators of resonant tunneling diodes with a generalization of the methodology for nanoelectronic heterostructure devices with quantum confinement and transverse current transfer has been developed. The advantage of the developed software is the possibility of interactive input of additional experimental information for further calculation of point and interval estimates of the reliability indicators of semiconductor devices using Bayesian inversion, which allows predicting these indicators under conditions of limited experimental information.

1483A meta-analysis of the serial interval and generation time of COVID-19 transmission

Background Variation of the estimated serial interval and generation time introduces heterogeneity in COVID-19 transmission models. We conducted a systematic review and meta-analysis to estimate more precise serial intervals and generation times of COVID-19. Methods A literature search was conducted using the WHO Global COVID-19 Literature database from 1 January 2020 to 30 April 2021. A single reviewer performed the data extraction. A random-effects model was used to pool the estimates. Subgroup analysis was performed to check the estimates for heterogeneity by geographical region and the presence of lockdown measures. Results A total of 222 articles were retrieved of which 73 articles were included based on the selection criteria. Serial intervals were reported in 65 articles that provided 75 unique estimates from 16,805 transmission pairs. Generation intervals were reported in 9 articles that provided 9 unique estimates from 1,150 transmission pairs. The pooled serial interval was 5.00 days (95% CI: 4.68, 5.33). The pooled generation time was 4.37 days (95% CI: 3.58, 5.16). The serial interval estimates did not vary by either geographical region (P > 0.05) or the presence of lockdown measures (P > 0.05). Conclusions This analysis provides more precise pooled serial and generation intervals that may decrease misspecifications of future transmission models. Key messages Epidemiological parameters are crucial components in estimating the dynamics of COVID-19 transmission. Periodically updating serial and generation time intervals are important to reduce model misspecification for a new disease such as COVID-19.

Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

This paper theoretically investigates the asymptotic properties of maximum likelihood estimates of GaGLM, and discusses some properties about Gamma distribution. It can provide theoretical foundation for expanding the application scope of gamma distribution based regression model, and benefit the further interval estimates, hypothesis tests and stochastic control design.The existence of the Gamma function in Gamma distribution makes correlation analysis certain specificity, and few researchers do relevant theoretical research. To complement this part, we established the asymptotic properties and the application condition of maximum likelihood estimates of GaGLM. In addition to this, we also discussed the propertis of the Fisher information matrix ,and n-order moment of Z and log(Z).

Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

This paper theoretically investigates the asymptotic properties of maximum likelihood estimates of GaGLM, and discusses some properties about Gamma distribution. It can provide theoretical foundation for expanding the application scope of gamma distribution based regression model, and benefit the further interval estimates, hypothesis tests and stochastic control design.The existence of the Gamma function in Gamma distribution makes correlation analysis certain specificity, and few researchers do relevant theoretical research. To complement this part, we established the asymptotic properties and the application condition of maximum likelihood estimates of GaGLM. In addition to this, we also discussed the propertis of the Fisher information matrix ,and n-order moment of Z and log(Z).

Null Hypothesis Significance Testing: A Brief Review

Null hypothesis significance testing (NHST) dominates the interpretation of quantitative data analysis in education, psychology, and other social science fields (Shaver, 1993). Meanwhile, the use of NHST has been under enduring and intense criticisms (Carver, 1978; Cohen, 1997; Cumming, 2013; Thompson, 1993, 1996, 1999). In 2015, the journal, Basic and Applied Social Psychology (BASP; Trafimow & Marks, 2015) banned the use of NHST, reigniting another round of intense discussions about whether continue using the NHST technique. In the present paper, I have elaborated the definition of NHST and six most commonmisinterpretations/false beliefs, and suggested reporting strategies, including reporting effect size along with its interval estimates. Finally, I briefly commented on the causes of misconceptions