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This study was designed to compare the effects of Team Assisted Individualization (TAI) and Student Teams-Achievement Divisions (STAD) on fourth grade students' academic achievement in and attitudes towards mathematics. Seven classes of a school were randomly selected for this experimental study. Two of these were given instruction through TAI; two through STAD, and the remaining three were treated as a control group. For the purpose of the data analysis regarding academic achievement, the 3X1 covariance analysis was used to compare the groups. As a result of this comparison, both the TAI and STAD methods were found to have positive effects (d=1.003 for TAI and d=0.40 for STAD) on students' academic achievement in mathematics. The pairwise comparisons showed that the TAI method had a more significant effect than the STAD method. The scores for the attitude towards mathematics were analyzed by using non-parametric statistics. As a result of this analysis, no significant difference was observed regarding students' attitudes towards mathematics.

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Differencing estimator, Differencing matrix, Multicollinearity, Ridge regression estimator, 62G08, 62J07,

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized difference-based almost unbiased ridge estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, a new generalized difference-based weighted mixed almost unbiased ridge estimator is proposed. The performance of this estimator over the generalized difference-based weighted mixed estimator, the generalized difference-based estimator, and the generalized differencebased almost unbiased ridge estimator in terms of the mean square error matrix criterion is investigated. Then, a method to select the biasing parameter k and nonstochastic weight ω is considered. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset. KeywordsDifference-based estimator • Generalized ridge estimator • Generalized difference-based weighted mixed almost unbiased ridge estimator • Partially linear model • Weighted mixed estimator

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Key Words & Phrases: nonnegative matrices, generalized inverse intra-block estimator; combined intra-inter-block estimator.ABSTRACT A necessary and sufficient condition for g--to be a nonnegative matrix is presented when A, B and 4-5 are assumed to be nonnegative matrices. To demonstrate the applicability of the theorem, the intra-block and combined intra-inter-block estimators of the treatment effects for an incomplete block model are compared