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4E$E$&E$E$E$E$E$[6[6+&^E$E$E$6E$E$E$E$dConcept of Multivariate analysis of variance (MANOVA)
It is one of advanced statistical procedures that dealing with more than tree variable, by this method we can test the significance of differences between the mean of two or more dependent variables
MANOVA is simply an ANOVA with several dependent variables, obtain a multivariate F value.
It unlike ANOVA that used the univariate technique (only dependent variable could be analyzed with more than two groups. Multivariate analysis of variance is the multivariate ANOVA technique for analyzing more than two groups, so MANOVA calculates a vector of means, a centroid for each group, and a grand centroid for all groups. MANOVA, the within-group variability must also be calculated for each dependent variable. Unlike ANOVA, where the F statistics reported for MANOVA, the most common method used for determining statistical significance is WILKs Lambda (multivariate F value).
It was developed for use in experiential situations in which at least one indendent variable was manipulated
It is stastical procedure used to test the significance of differences between the means of tow or more groups on two or more dependent variables
It is extension of ANOVA procedures to more than one dependent variable
Advantages over ANOVA:
By measuring several dependent variables in a single experiment, there is a better chance of discovering which factor is truly important.
It can protect against Type I errors that might occur if multiple ANOVAs were conducted independently.
It can reveal differences not discovered by ANOVA tests.
Disadvantages
More complicated design than ANOVA
Multivariate analysis of covariance (MANCOVA)
This procedure is similar to using ANCOVA when a covariate is identified for ANOVA test, multivariate analysis of covariance (MANCOVA) is utilized within covariate is identified as part of MANOVA test . if there are multiple dependent variables with more than two treatment groups and the researcher would like to control for a covariate or confounding issues or a difference in baseline characteristics ,then a MANCOVA could be used .
Also by this procedure allows for the control of extraneous variables (covariates) when there are two or more dependent variables
Concept of covariance (ANCOVA)
It is one of the most widely used as multivariate technique
It is procedure that controlling unwanted variables, ancova can accomplish this control function by statistically removing the effects of the extraneous variable on the dependent variable
This procedure is good example of a related procedure ,it combines features of ANOVA and regression
The main role of this procedure is that it permits statistical control of extraneous variables.
This way permitting a more precise estimate of group differences(when randomization process is used
It is used to analyze independent variable that include both categorical and interval level data.
It also useful for researchers who want to adjust for baseline difference amoung the different treatment groups or therapies
The important assumption to ANCOVA is that there is no relationship between the covariate and the treatment variables
ANCOVA provide a way to combine ANOVA and regression technique when research involves categorical independent variable
ANCOVA used in three areas:
In quasi-experimental (observational) designs, to remove the effects of variables which modify the relationship of the categorical independents to the interval dependent.
In experimental designs, to control for factors which cannot be randomized but which can be measured on an interval scale. Since randomization in principle controls for all unmeasured variables, the addition of covariates to a model is rarely or never needed in experimental research. If a covariate is added and it is uncorrelated with the treatment (independent) variable, it is difficult to interpret as in principle it is controlling for something already controlled for by randomization. If the covariate is correlated with the treatment/independent, then its inclusion will lead the researcher to underestimate of the effect size of the treatment factors (independent variables). .
In regression models, to fit regressions where there are both categorical and interval independents.
Odds Ratio
Definition - in a retrospective study the objective is to compare cases and controls with respect to the presence of a reported risk factor.
Odds ratio used in retrospective studies estimates prevalence (only the likelihood of being sick ,prevalence, in contrast to estimate which referred to the likelihood of becoming sick ,incidence .
Odds ratio: the ratio between the HYPERLINK "javascript:parent.see('odds')" odds that an event occurs in two groups or two sets of circumstances.
To understand the odds ratio
It is value to approximation or as estimator to the relative risk
When a retrospective case-control study design is used , the relative risk can be estimated by using the odds ratio, so , in using the odds ratio as an estimator of relative risk , one must assume that the control group is representative of the general population , the cases are representative of the population with the disease, and the frequency of the disease in the population is small
Diseasefactor
Exposed factor
presentabsenceABNot exposedCD
The calculation of the odds ratio is by multiplying the number of cases with the disease and exposed to the factor by the number of cases without the disease and not exposed to the factor, and divided this number by the number of cases with the disease without exposure to the factor multiplying by those case without the disease but exposed to the factor.
Odds ratio is= EMBED Equation.3
Logistic regression
It is one of nonparametric test; logistic regression is similar to linear regression. The main difference is that logistic regression does not require the dependent variable or outcome variable to be measured on an interval or ratio scale so in this case logistic regression would be preferred to linear regression. It can be used when assumption two of linear regression is not met
Logistic regression allows one to predict a discrete outcome, such as group membership, from a set of variables that may be continuous, discrete, dichotomous, or a mix of any of these.
It is analyze procedure that uses maximum likelihood estimation for analyzing relationship between multiple independent variable that is categorical (nominal-level measure) where it can also transforms the probability of an event occurring into odds that , is , into ration of one events probability relative into probability of a second event
The result, probabilities that range between zero and one in actuality are transformed into continuous variables that range between zero and infinity
Logistic regression also considered as procedure that uses maximum likelihood estimation for analyzing relationships between multiple independent variables and dependent variable that is categorical (.i.e., a nominal-level measure)
The types of logistic regression:
The logistic regression can be performed as simple logistic regression (one dependent variable and one independent variable
Multiple logistic regressions (one dependent variable and more than one independent variable.
Reference:
Richard F. Morton et al. A study guide to epidemiology and biostatistics.
Patrick M.Malone et al .Drug information a guide for pharmacists.
Denise F.Polit et al .Nursing research principle and method
internet.
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