NYC Charter School Performance on the 2012-13 State Exams

1. Bivariate Correlations

2. Linear Regression Analysis

3. Multiple Regression Analysis

Bivariate Correlations

Bivariate Correlation

Paersone Correlation or Co-efficient of correlation

Scale level of measurement

p<0.05 Significant Correlation

Researcher can be 95% confident that the relationship between these two variables is not due to chance

Denoted by r

-1 ≤ r ≤ +1 0 ------- ±0.3 No Relation

±0.3 ------- ±0.5 Weak Relation

±0.5 ------- ±0.8 Moderate Relation

±0.8 ------- ±1 Strong Relation

1 is total positive correlation, 0 is no correlation, and −1 is negative correlation

The closer the value is to -1 or +1, the stronger the association is between the variables

Linear Regression Analysis

Outlier There should be no significant outliers. Outliers are simply

single data points within your data that do not follow the usual pattern.

The problem with outliers is that they can have a negative effect on the regression equation that is used to predict the value of the dependent (outcome) variable based on the independent (predictor) variable.

Multiple Regression: Model Suma. R tells the reliability & mathematical relationship.1. R Square (co-efficient of determination) tells the

percentage of accuracy.2. Also percentage of variation that can not be controlled i.e.3. (1-R Square)i. Adjusted R2, It can be negative & always less than or

equal to Rii. Adjusted R2 will be more useful only if the R2 is

calculated based on a sample, not the entire populationiii. Adjusted R2 increases only if the new term improves the

model more than would be expected by chance

ANOVA ANOVA table tests whether the overall regression

model is a good fit for the data. p<0.05 The table shows that the independent variables

statistically significantly predict the dependent variable, F(3, 16) = 32.811, p < .0005 (i.e., the regression model is a good fit of the data)

Coefficients

How much the dependent variable varies with an independent variable , when all other independent variables are held constant.

T value less than ±2 is not important Significant value of x