Multivariate Analysis of Covariance, Slides of Statistics

Download Multivariate Analysis of Covariance and more Slides Statistics in PDF only on Docsity!

MULTIVARIATE ANALYSIS OF

COVARIANCE

(MANCOVA)

Topic 1

JAMES MATT CARAAN

statistical technique that is the extension of analysis of covariance (ANCOVA). Basically, it is the multivariate analysis of variance (MANOVA) with a covariate(s). In MANCOVA, we assess for statistical differences on multiple continuous dependent variables by an independent grouping variable, while controlling for a third variable called the covariate; multiple covariates can be used, depending on the sample size. Covariates are added so that it can reduce error terms and so that the analysis eliminates the covariates’ effect on the relationship between the independent grouping variable and the continuous dependent variables. MANCOVA

WHAT ARE COVARIATES/COVARIANCE?

Covariance is a measure of how much two random variables vary together.

It’s similar to variance, but where variance tells you how a single variable

varies, co-variance tells you how two variables vary together. A covariate

can be one of these two variables. It is any variable that effects how your

independent variables act upon your dependent variables. For example,

confounding variables are covariates.

In multivariate analysis of covariance (MANCOVA), all assumptions are the same as in MANOVA, but one more additional assumption is related to covariate: Independent Random Sampling: MANCOVA assumes that the observations are independent of one another, there is not any pattern for the selection of the sample, and that the sample is completely random.

Level and Measurement of the Variables: MANCOVA assumes that the independent variables are categorical and the dependent variables are continuous or scale variables. Covariates can be either continuous, ordinal, or dichotomous.

ASSUMPTIONS IN MANCOVA

IN SIMPLER VIEW GROUPS OUTCOME

Loyalty

Number of Attacks

OTHER VARIABLES

Time Spent

Care or Company

VIDEO

Non-parametric tests are the mathematical methods used in statistical hypothesis testing, which do not make assumptions about the frequency distribution of variables that are to be evaluated. WHAT ARE NONPARAMETRIC TESTS? The word non-parametric does not mean that these models do not have any parameters. The fact is, the characteristics and number of parameters are pretty flexible and not predefined. Therefore, these models are called distribution-free models.

NON-PARAMETRIC METHODS

The sign test is used to compare the continuous outcome in the paired samples or the two matches samples. Null hypothesis, H0: Median difference should be zero Test statistic: The test statistic of the sign test is the smaller of the number of positive or negative signs. Decision Rule: Reject the null hypothesis if the smaller of number of the positive or the negative signs are less than or equal to the critical value from the table. SIGN TEST

Mann Whitney U test is used to compare the continuous outcomes in the two independent samples. Null hypothesis, H0: The two populations should be equal. Test statistic: If R1 and R2 are the sum of the ranks in group 1 and group 2 respectively, then the test statistic “U” is the smaller of: MAN WHITNEY U TEST Decision Rule: Reject the null hypothesis if the test statistic, U is less than or equal to critical value from the table

Wilcoxon signed-rank test is used to compare the continuous outcome in the two matched samples or the paired samples. Null hypothesis, H0: Median difference should be zero. Test statistic: The test statistic W, is defined as the smaller of W+ or W-. Where W+ and W- are the sums of the positive and the negative ranks of the different scores. Decision Rule: Reject the null hypothesis if the test statistic, W is less than or equal to the critical value from the table. WILCOXON SIGNED-RANK TEST

ADVANTAGES &

DISADVANTAGES OF NON-

PARAMETRIC METHODS

The disadvantages of the non-parametric test are: Less efficient as compared to parametric test The results may or may not provide an accurate answer because they are distribution free DISADVANTAGES OF NON-PARAMETRIC TEST

WHEN DO WE USE NON-

PARAMETRIC TESTS?