Valuing constitutes an important aspect of mathematics pedagogy and hence student learning outcomes. This study surveyed 416 students from Cape Coast, Ghana to explore what senior high school students in this country in West Africa valued in their study of mathematics. The data collected were analyzed using principal component analysis. The results suggest that Ghanaian senior high school students found connections, understanding, fluency, learning technologies, feedback, instructional materials, open-endedness and problem-solving important in their mathematics learning. Implications of the findings for curriculum delivery in mathematics and future research opportunities are also discussed.
The paper addresses the issue of identifying the maximum safe dose in the context of noninferiority trials where several doses of toxicological compounds exist. Statistical methodology for identifying the maximum safe dose is available for three-arm noninferiority designs with only one experimental drug treatment. Extension of this methodology for several experimental groups exists but with multiplicity adjustment. However, if the experimental or the treatment groups can be ordered a priori according to their treatment effect, then multiplicity adjustment is unneeded. Assuming homogeneity of variances across dose group in normality settings, we employed the generalized Fieller’s confidence interval method in a multiple comparison stepwise procedure by incorporating the partitioning principle in order to control the familywise error rate (FWER). Simulation results revealed that the procedure properly controlled the FWER in strong sense. Also, the power of our procedure increases with increasing sample size and the ratio of mean differences. We illustrate our procedure with mutagenicity dataset from a clinical study.
We adopt a granular approach to estimating the risk of equity returns in sub-Saharan African frontier equity markets under the assumption that, returns are influenced by developments in the underlying economy. Four countries were studied -Botswana, Ghana, Kenya and Nigeria. We found heterogeneity in the evolution of volatility across these markets and also that two-regime switching volatility models describe better the heteroscedastic returns generating processes in these markets using the deviance information criteria. We backtest the results to assess whether the models are a good fit for the data. We concluded that, the selected models are the most suitable for predicting the volatility of future returns in the markets studied.
In this article we consider identification of maximum safe dose (MSD) in a dose response study for distribution-free endpoints. Where the maximum safe dose is the highest dose level that does not exceed the median toxicity of the zero dose by a predetermined margin. A nonparametric confidence set-based approach was proposed, that is we incorporate Mann-Whitney method with the partitioning principle in a step-down fashion for safety evaluation. A comprehensive study of the familywise error rate for our new procedure was compared with the dose response (DR) procedure via a Monte Carlo simulations. An example from preclinical trial in genetic toxicology was used for illustrative purpose.
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