![]() ![]() Here again is a summary of the values of SS and SC obtained so far. SC wg(g) = ∑ ( X gi Y gi ) ( ∑ X gi )( ∑ Y gi ) The components for each group ("g") are calculated as: Calculations for the Covariance of X and YĬross-products of X i and Y i for each subject in each of the three groups, along with other summary data required for the calculation of SC T and SC wg:Ĭalculation of SC for the total array of data: Values of X along with the several summary statistics required for the calculation of SS T( X) and SS wg( X).ģ. ![]() Values of Y along with the several summary statistics required for the calculation of SS T( Y), SS wg( Y), and SS bg( Y): Calculations for the Dependent Variable Y The only structural difference is that now the number of groups is k=3.ġ. The computational format for the one-way ANCOVA is the same here as for Example 1. So once again we encounter the what-if question: What would have happened if the three groups had all started out on the same footing? The measure of how well the subject has learnedĪs you can see from the means in the X columns, the investigator was right in her expectations concerning different group levels of basic computer familiarity: 13.0 and 13.8 for groups A and B, versus 10.1 for group C. [The covariate whose effects the investigator X = the prior measure of basic computer familiarity The following table shows the measures on both variables laid out in a form suitable for an analysis of covariance, with The groups instructed by Methods A and B both reside in fairly affluent neighborhoods, while the group instructed by Method C comes from a less privileged part of town. Our researcher was also well aware that her three groups, drawn from three different schools, might be starting out with substantially different levels of basic computer familiarity, in consequence of the average socio-economic differences that she knows to exist among the schools. The rationale is fairly obvious: the more familiar a subject is with basic computer procedures, the more of a head start he or she will have in learning the elements of computer programming remove the effects of this covariate, and you thereby remove a substantial portion of the extraneous individual differences. Well aware of the broad range of pre-existing individual differences that are likely to be found in situations of this sort, our curriculum researcher took the precaution of measuring her subjects beforehand with respect to their pre-existing levels of basic computer familiarity. ![]() The reason for this shortfall is of course the degree of variability within the groups, which is quite large in comparison with the mean differences that appear between the groups. A simple one-way ANOVA performed on this set of data would yield a miniscule F=0.40, which falls far short of significance at the basic. As it happens, however, these differences, considered in and of themselves, are well within the range of mere random variability. Given the differences among the means of the three groups, you might think at first glance that Method B has the edge over Method A, and that Methods B and A are both superior to Method C. The following table shows the measure of how well each of the 36 subjects, 12 per group, learned the prescribed elements of the subject matter. Each group, within the setting of its home school, then received a six-week course of instruction in one or another of the three methods. To assess the relative merits of three methods of instruction for elementary computer programming, a curriculum researcher randomly selected 12 fifth graders from each of three elementary schools in a certain school district. ![]()
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |