ISOMERISM: IS THERE MISCONCEPTION?

Nine articles have been analyzed containing research results on misconceptions about isomerism. Analysis was conducted to examine the potential to causes emergence of the misconception. The analysis result are expected to be useful for teachers in learning for the same concepts. At least the teacher can avoid misconceptions that have happened before and innovate to find the right learning strategy. Isomerism can be categorized as a defined concept so that students are expected to be able to use rules for the purpose of classifying objects or events. The analysis showed 31 misconceptions experienced by grade 11 students to prospective chemistry teachers on isomerism concept. Thirty-one misconceptions are classified into three groups based on students' abilities needed to understand the concept of isomerism. The three groups are: (1) understanding the definition and application of rules; (2) spatial understanding; and (3) microscopic understanding. At this time only eleven misunderstandings were discussed, namely misunderstandings whose causes belong to the group (1). As an indicator caused misconception is inability of the sample to classify objects/events based on the attributes or characters indicated by the object/event. To teach a defined concept, it is recommended to use a strategy that contains detailed explanatory definitions and rules, examples and non-examples, and the elaboration process. In order to increase student reasoning, it is recommended to use a isomerism concept logic scheme

Improved Inference under Heteroscedasticity of Unknown Form Using a New Class of Bootstrap and Nonparametric Estimators

It is well-known that use of ordinary least squares for estimation of linear regression model with heteroscedastic errors, always results into inefficient estimates of the parameters. Additionally, the consequence that attracts the serious attention of the researchers is the inconsistency of the usual covariance matrix estimator that, in turn, results in inaccurate inferences. The test statistics based on such covariance estimates are usually too liberal i.e., they tend to over-reject the true null hypothesis. To overcome such size distortion, White (1980) proposes a heteroscedasticity consistent covariance matrix estimator (HCCME) that is known as HC0 in literature. Then MacKinnon and White (1985) improve this estimator for small samples by presenting three more variants, HC1, HC2 and HC3. Additionally, in the presence of influential observations, Cribari-Neto (2004) presents HC4. An extensive available literature advocates the use of HCCME when the problem of heteroscedasticity of unknown from is faced. Parallel to HCCME, the use of bootstrap estimator, namely wild bootstrap estimator is also common to improve the inferences in the presence of heteroscedasticity of unknown form. The present work addresses the same issue of inference for linear heteroscedastic models using a class of improved consistent covariance estimators, including nonparametric and bootstrap estimators. To draw improved inference, we propose adaptive nonparametric versions of HCCME, bias-corrected versions of nonparametric HCCME, adaptive wild bootstrap estimators and weighted version of HCCME using some adaptive estimator, already available in literature, namely, proposed by Carroll (1982). The performance of all the estimators is evaluated by bias, mean square error (MSE), null rejection rate (NRR) and power of test after conducting extensive Monte Carlo simulations.