Experimental research has had a long tradition in psychology and education. The experimental method formally surfaced in educational psychology around the turn of the century, with the classic studies by Thorndike and Woodworth on transfer.
Friday, October 21, 2011
ANOVA on residual scores
ANOVA on residual scores
Residual scores represent the difference between observed posttest scores and their predicted values from a simple regression using the pretest scores as a predictor. An attractive characteristic of residual scores is that,unlike gain scores, they do not correlate with the observed pretest scores
Thursday, October 20, 2011
The T-Test
The T-Test
This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the analysis for the posttest-only two-group randomized experimental design. The t-test assesses whether the means of two groups are statistically different from each other.
The t-value will be positive if the first mean is larger than the second and negative if it is smaller. Once you compute the t-value you have to look it up in a table of significance to test whether the ratio is large enough to say that the difference between the groups is not likely to have been a chance finding. To test the significance, you need to set a risk level (called the alpha level). In most social research, the "rule of thumb" is to set the alpha level at .05. This means that five times out of a hundred you would find a statistically significant difference between the means even if there was none (i.e., by "chance"). You also need to determine the degrees of freedom (df) for the test. In the t-test, the degrees of freedom is the sum of the persons in both groups minus 2. Given the alpha level, the df, and the t-value, you can look the t-value up in a standard table of significance (available as an appendix in the back of most statistics texts) to determine whether the t-value is large enough to be significant. If it is, you can conclude that the difference between the means for the two groups is different (even given the variability).
Wednesday, October 19, 2011
ANCOVA : Covariate
In econometrics, the term "control variable" is usually used instead of "covariate". In a more specific usage, a covariate is a secondary variable that can affect the relationship between the dependent variable and other independent variables of primary interest. In statistics, a covariate is a variable that is possibly predictive of the outcome under study. A covariate may be of direct interest or it may be a confounding or interacting variable. The alternative terms explanatory variable, independent variable, or predictor, are used in a regression analysis.
An example is provided by the analysis of trend in sea-level by Woodworth (1987). Here the dependent variable (and variable of most interest) was the annual mean sea level at a given location for which a series of yearly values were available. The primary independent variable was "time". Use was made of a "covariate" consisting of yearly values of annual mean atmospheric pressure at sea level. The results showed that inclusion of the covariate allowed improved estimates of the trend against time to be obtained, compared to analyses which omitted the covariate.
ANCOVA Assumptions
ANCOVA Assumptions
In statistics, analysis of covariance (ANCOVA) is a general linear model with a continuous outcome variable (quantitative, scaled) and two or more predictor variables where at least one is continuous (quantitative, scaled) and at least one is categorical (nominal, non-scaled). 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 the variability.
Like any statistical procedure, the interpretation of ANCOVA depends on certain assumptions about the data entered into the model. For instance, the F-test assumes that the errors are normally distributed and homoscedastic. Since ANCOVA is a method based on linear regression, the relationship of the dependent variable to he independent variable(s) must be linear in the parameters.Simplifying assumption (not necessary to run ANCOVA): homogeneity of regression which says that the relationship between the covariate and the dependent variable should be similar across all groups of the independent variable.
In ANCOVA, assumptions include at least one categorical independent variable and at least one interval or metric independent variable. The categorical independent variable is called a factor, whereas the metric independent variable is called a covariate.
In ANCOVA assumptions, the most common use of covariate is to remove extraneous variations from the dependent variable. This is because in ANCOVA assumptions, the effect of factors is of major concern.
Like ANOVA, ANCOVA assumptions have similar assumptions. These assumptions are as follows:
The variance that is being analyzed or estimated should be independent, which also holds true for ANCOVA assumptions.
In ANOVA, the variable which is dependent in nature must have the same variance in each category of the independent variable. In the case of more than one independent variable, the variance must be homogeneous in nature, within each cells formed by the independent categorical variables, which also holds true for ANCOVA assumptions.
In ANOVA, it is assumed that the data upon which the significance test is conducted is obtained by random sampling, which also holds true for ANCOVA assumptions.
When analysis of variance is conducted on two or more factors, interactions can arise. An interaction occurs when the effect of independent variables on a dependent variable is different for different categories, or levels of another independent variable. If the interaction is significant, then the interaction may be ordinal or disordinal. Disordinal interaction may be of a no crossover or crossover type. In the case of the balanced designs, while conducting ANCOVA assumptions, the relative importance of factors in explaining the variation in the dependent variable is measured by omega squared. Multiple comparisons in the form of a priori or a posteriori contrast can be used for examining differences among specific means in ANCOVA assumptions.
ANCOVA assumptions also assume the homogeneity of regression coefficients which is based on the fact that the regression coefficient for every group present in the data of the independent variable should be same. If this fact of ANCOVA assumptions is violated, then the ANCOVA assumption will be misleading.
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Wednesday, October 12, 2011
ANOVA : Analysis of Variance
ANOVA : Analysis of Variance
In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes t-test to more than two groups. Doing multiple two-sample t-tests would result in an increased chance of committing a type I error. For this reason, ANOVAs are useful in comparing two, three or more means.
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