Academic research statistics

statistics 

1.  
2. Paired-sample t-test between “math scaled score” and “Terra Nova 4^th grade math score”
   1. The null hypothesis is that there is no difference between the maths scaled score and the Terra Nova 4^th grade math score. 
   2. My conclusion is that there is definitely a difference between both grades. The null hypothesis is rejected!

 ANOVA comparing math scaled score among different ethnic groups

1. 1. The null hypothesis is that the averages in the math tests among ethnic groups are similar (or the same).
   2. The independent variable is the ethnic group characteristic, and the dependent variable is the math scaled score.
   3. My conclusion is that there is a difference in math scaled scores between different ethnic groups, as can be seen by the very large difference between the sum of squares between ethnic groups and within them.

1. Multiple regression with “math scaled score” as dependent variable and “gender”, “ELA scaled score”, and “Terra Nova 4^th grade math score” as independent variables.
   1. The null hypotheses are that the independent variables don't affect the dependent one (math scaled score) and that it is the same regardless of these independent variables.
   2. My conclusions are that there is a difference due to the independent variables, as it is seen that even after calculating the regression, the residual aspect is still strong enough to make a difference, suggesting that the independent variables do affect the outcome of the math scaled test.
   3. The independent variable that is the best predictor of the math scaled score is the ELA scaled score. Its standard error is small and so is his beta value.