# Essays on Measurement and Analysis for Business Decision Making through Similarities and Differences of Analysis of Variance and the T-Test Statistics Project

The paper “ Measurement and Analysis for Business Decision Making through Similarities and Differences of Analysis of Variance and the T-Test” is a   fascinating variant of statistics project on statistics. According to Girden, when applying the one-way Anova test, it is important to note that the F value can only be proven reliable under certain assumptions. These assumptions are: values in each group assume a normal curve possibilities of different population means standard deviations of populations are equal Two-way Analysis of variance The two-way Anova test is more or less an extension of one-way Anova (Kothari 256).

It is employed to examine the kind of influence various independent variables have on just a single dependent variable. As one-way Anova determines the considerable effect one independent variable has, two-way Anova measures the same effects in cases involving several independent variables each with its own multiple observations (Kothari 257). In addition to determining the major effects each independent variable contributes, the two-way ANOVA test identifies any considerable interaction effect existing among independent variable. A researcher might for instance want to examine the effect that sex and race have on wages.

The researcher may further want to elaborate if disparities in wages are due to differences in sex alone or differences in race alone or if differences are attributable to certain combinations of both race and sex – do interaction effects exist? Example: A research was carried out to determine the impact of high protein meal on physical performance in adolescents during a fitness test. Half of the students were given high protein breakfast while the other have had low protein breakfast. All subjects underwent a fitness test afterward and the results recorded.

Better performance was represented by high scores. Question: Are there significant effects or interaction effect? Answer: We first create an Anova table; From the values of F, it is clear that there are considerable effects for protein levels (F=8.89 (1,16), p< .01). Significant effects also appeared for gender (F=20.00 (1,16), p< .01). However, there was not a major interaction effect (F=2.22 (1,16), not significant). Therefore based on the above data, it is possible to conclude that high protein meals will result in high fitness scores. Also, young men appear to have considerably high fitness scores than their women counterparts. Nested Analysis of varianceAnother type would be the nested analysis of variance.

This is normally used when the researcher has a single measurement variable and more than two nominal variables (Kothari 270). Nesting therefore means that each value of individual nominal variables can only be found in assemblage with just one value of a nominal variable that is at a higher level. Each group in nested ANOVA is split into subgroups, making it an extension of the one-way ANOVA test. Theoretically, the choosing of these subgroups is done at random and from a bigger category of subgroups (Acock 189).

A good example would be in testing the null hypothesis “ stress and calm rats both have a similar amount of glycogen in their muscles. ” If the researcher a number of stressed rats, a number of calm rats and a single glycogen measurement extracted from each rat, then one-way ANOVA would be appropriate. However, the researcher may not know the reasons behind such variations and this is where nested ANOVA comes in handy. Its application will make it possible to group the rat cages into stressed and calm rats, and every cage would represent a subgroup with each rat’ s glycogen level of one rat representing one observation in that particular subgroup.

This example is a two-level nested ANOVA with the first level being the groups and the subgroups, the various cages, representing the second level. Nested ANOVA gives room for the addition of more levels that can be added when in case of accuracies are of concern. It is, however, important to note that if the different levels are distinctions with apparent interests and not random, then it would be wise to avoid the use of nested ANOVA (Acock 191).