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Complex ANOVA Study


Analysis of variance is a statistical technique used when comparing elements of data of multiple samples, the variances of the data samples are used to compare the symmetry of items of data in the samples. When the t test is used to compare multiple data samples, there are high chances of committing type 1 errors, to improve the accuracy of the test, the ANOVA technique is preferable, Miller (1997).

The research question will be to establish the relationship between the discipline of students and the level of academic performance. The ANOVA methodology is suitable for this test, because the data will be collected from three samples selected randomly; symmetry of the results will be tested using their variances for more accuracy as compared to other statistical tests such as the t test. The null hypothesis will be that there is no relationship between academic performance and discipline while the alternative hypothesis for the study will be there is a relationship in discipline of students and their level of academic performance. The generic random or experimental errors will be expected.


Three samples selected randomly will be used for this study. The population for study will be grade six students at a Chicago institution. A procedure for selecting the samples will be applied to ensure that the samples are representative of the population. The grade six classes will first be stratified according to performance into three strata; a sample of six students will then be selected from each stratum for the study. The participants will be between the ages of ten and thirteen, to ensure all the sexes are represented; the samples will be made of three girls and three boys.


The variables of the study will be academic performance and discipline level. Ordinal scale will be the most appropriate; the levels of discipline and academic performances will be assigned numerals in a scale, the discipline level will be on a scale of one to ten, figures for the academic performance will be obtained from the school’s examination department. The data for discipline levels will be continuous while that for the level of academic performance will be discrete. A scale of 1-10 will be used for the discipline levels, the discipline will be established by observing the behavior of the learners, for example noise making, absenteeism or late class  attendance.

Well behaved participants will score high in the discipline scale while poor behaved learners will score low. The levels of academic performance will be ready from the examinations segment of the school. The main data collection technique which will be applied for the study will be observation; the discipline of the pupils will be rated on this. Some aspects of discipline that will be used will include: the neatness of the participants, their class attendance, attention in class, and their degree of absenteeism.


After the study is empirically carried out, data from the three samples will be available for statistical testing. The ANOVA technique will be used for analyzing the data in terms of the variation. The parity of performance will be expected in accordance to the discipline patterns of the pupils.

Post-hoc tests will be conducted if different data sets portray similar characteristics, in-depth study into the finer details of the participants will then be conducted to establish the perceived characteristics. The variances of the data in relation to the level of discipline of the pupils will be used to draw conclusions for the study; High variation will be expected from the mean performance for students with very high levels of discipline and those having very low levels of discipline. The variances in performance obtained will then be used for testing the hypothesis.


The expected biases will be, for the highly performing pupil’s discipline might be overrated and that of the poorly performing underrated, to avoid these biases the researchers will not identify the participants’ individually so that they won’t know from whom they are collecting the data. Assumptions are expected to be made on the discipline levels, because it will be difficult to establish the exact discipline level from the created ordinal scale, this may reduce the accuracy of the data collected.

Random errors are also expected to sprout from the ANOVA technique because they are generic to this style. The conclusion of the proportionality between performance and discipline level can be established from this study, however the intervals in discipline projecting the intervals in the levels of academic performance will be hard to establish and base the conclusion on. The practical significance of the results will be improving the performance of the learners, the results will be provided to the school’s administration; they can then improve performance by enforcing measures to improve the discipline of the learners. Improving the discipline of the learners will go a great extend in improving their respective performances.


Miller, G. R. (1997). Beyond ANOVA: Basics of applied statistics. New York, NY: Chapman     and Hall

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