Statistical Research Methods and Selection of Statistical Tests

Factorial ANCOVA

In this statistical analysis there is more then one dependent variable and there are more then one co-variate. For example if one wants to study the sentence of race and type sentence controlling for prior convictions and seriousness of offenses then Factorial ANCOVA is is a useful statistical research design and statistical test to verify the significance at a particular significant level. The same statistical process as mentioned above for the one-way ANCOVA is used as a statistical test process.

One-way MANOVA compared with discriminant analysis

Say a researcher want to study the effect of race on the length of sentences and drug dependency then one-way MANOVA or discriminant analysis is most suitable then other statistical designs and test process. If one wants to predict the race depending on the level of sentence and drug dependency then it is a discriminant analysis not the one way MANOVA. This is the difference between MANOVA and discriminant analysis. In discriminant analysis a discriminant function is tested using eigenvalues, percentage of variance, canonical correlations and Wliks lamda and degrees of freedom and the p-value. This p-value is used to determine whether the discriminant function is significant or not. The discriminant eigenvalues functions is used in MANOVA to calculate the MANOVA statistics and f-values from these statistics. The MANOVA statis tice are as follows:

Pillai’s Trace = sum of ( k i / ( 1+ k i) )

Wik’s lamda = 1/ (1 + k i ) repeat until all the eigenvalues.

Hotelling’s Trace = sum of k i where ki is the eigenvalue for the discriminant function.

Roy’s largest root = k i maximum of the eigenvalues for all discriminant function based on the data.

All these MANOVA statistics have an f-value and p value. These are on the rank order of conservativeness with respect to type 1 error.

Factorial MANOVA, one-way MANCOVA and Factorial MANCOVA

The factorial MANOVA is used when there are 2 or more independent non-metric variables and two or more independent variables. When some extraneous variables are used as co-variates then one-way MANCOVA or factorial MANCOVA is used. In addition, the statistical analysis also analyze uni-variate and multivariate analysis based on the MANOVA statistics in an elaborate way.

Summary

As discussed above, the statistical research design depends on the research issue and its complexity and the number of independent, dependent and extraneous variables to be considered. In addition, all these statistical techniques depends on certain assumptions and these assumptions must be applicable to the data concerned. In analyzing all these factors and applying the statistical process and testing statistics and selection of samples in a considered way a researcher can use these statistical techniques to draw conclusions about a population characteristics from a sample study.

mple study.