Correlation Analysis of Standarized Testing Data I need some insight on how to correctly analyze some data using correlations. 
The nature of the data and research endeavor is as follows:
I have two independent samples of different sizes that contain four different data points per observation reflecting scores of four different standardized testing measurements. For the sake of conversation the data sets will be N1 and N2 and the tests will be A, B, C and D. Essentially, measure A is a test that is issued to students once a year at the end of the year and B C and D are issued mid-year. The basic research question is: Do students scores of the midyear tests of B, C and D correlate to the scores on test A?    
I need advice on what how to properly conduct this analysis. 
Sample Sizes: N1 = 54  N2 =56
I need to know what type of correlation to conduct and why and how to determine that the results of that correlation procedure are statistically significant. I do not need to compare the between the samples. I need to conduct correct analysis for the test A compared to tests B C and D for each sample independently. 
I have some statistical understanding, I am just confident somebody on this forum has much a much more fluid and comprehensive understanding of how to best approach this. 
FYI: I am using SAS software to conduct my analysis. 
 A: the most suitable approach to your analysis will depend on the question you are trying to address. The following answer considers your objective is to (exclusively) measure the correlation between A score and other scores, as you stated, in a predictive manner, not causal. It means that after estimating the parameters of the model, you will be able to obtain some good estimates for B, C and D scores given that you only know A score. I am not familiar with SAS, but I am sure you can implement the following approach, called linear regression:
$Yscore_i=\beta_0+\beta_1 Ascore_i+\varepsilon_i$
where $i=\{1, 2, 3, \ldots, N\}$ is an "id" that uniquely identifies each individual in your sample; $Ascore_i$ is the score obtained by individual $i$ on test $A$; $Yscore_i$ may assume $Bscore_i$, $Cscore_i$ or $Dscore_i$; and $\varepsilon_i$ is some random part of $Yscore_i$ that cannot be explained by $Ascore_i$. Roughly speaking, $\hat{\beta}_1$ (the "hat" indicates $\hat{\beta}_1$ is an estimative of the real value of $\beta_1$) indicates how $Ascore_i$ relates to $Yscore_i$ on average. I imagine SAS output automatically displays p-values and confidence intervals, so you will be able to check for statistical-significance.
Remember that even when those scores are statistically correlated (and they probably are), this correlation might vanish or even change signal (Simpson's paradox, though it's not really a paradox) when you add other control variables to your regression, such as students' background. Also note that scores of individuals in the same class might be correlated with each other, which leads us to an extensive discussion of clusters and clustered standard errors. At last I highlight that, for causal inference purposes, on estimating the model above you are assuming some strong hypothesis hold, such as $Ascore_i$ and $\varepsilon_i$ are not correlated. It implies that the only thing that matters to determine $Yscore_i$ is $Ascore_i$, something I strongly believe is not true. If any of those topics are of your interest, you shall ask latter providing further details of your intended analysis.
All the best!  
