RESEARCH DESIGN AND STATISTICS

Research Design and Statistics

Research Design and Statistics

Section I

MANOVA

Multivariate analysis of variance (MANOVA) is a generalized form of univariate analysis of variance (ANOVA). It is used in cases where there are two or more dependent variables. As well as identifying whether changes in the independent variable(s) have significant effects on the dependent variables, MANOVA is also used to identify interactions among the dependent variables and among the independent variables. Where sums of squares appear in univariate analysis of variance, in multivariate analysis of variance certain positive-definite matrices appear. The diagonal entries are the same kinds of sums of squares that appear in univariate ANOVA. The off-diagonal entries are corresponding sums of products. Under normality assumptions about error distributions, the counterpart of the sum of squares due to error has a Wishart distribution.

Difference between effect size and the p value

In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity. An effect size calculated from data is a descriptive statistic that conveys the estimated magnitude of a relationship without making any statement about whether the apparent relationship in the data reflects a true relationship in the population. In that way, effect sizes complement inferential statistics such as p-values. Among other uses, effect size measures play an important role in meta-analysis studies that summarize findings from a specific area of research, and in statistical power analyses.

The concept of effect size appears already in everyday language. For example, a weight loss program may boast that it leads to an average weight loss of 30 pounds. In this case, 30 pounds is an indicator of the claimed effect size. Another example is that a tutoring program may claim that it raises school performance by one letter grade. This grade increase is the claimed effect size of the program. These are both examples of "absolute effect sizes," meaning that they convey the average difference between two groups without any discussion of the variability within the groups. For example, if the weight loss program results in an average loss of 30 pounds, we do not know if every participant loses exactly 30 pounds, or if half the participants lose 60 pounds and half the participants lose no weight at all.

Standard Error

The standard error of a method of measurement or estimation is the standard deviation of the sampling distribution associated with the estimation method. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate.

Analysis of covariance

Analysis of covariance (ANCOVA) is a general linear model with one continuous outcome variable (quantitative) and one or more factor variables (qualitative). ANCOVA is a merger of ANOVA and regression for continuous variables. ANCOVA tests whether certain factors have an effect on the outcome variable after removing the variance for which quantitative predictors (covariates) account. The inclusion of covariates can increase statistical power because it accounts for some of ...