I believe that Mexico would not end up owning California because USA's ambition for manifest destiny was way to strong. The USA would have found a way to take back California because they were so determined to own land from coast to coast. Thomas even went against his own morals to purchase the Louisiana Territory. That's how strongly the states wanted that land.
The correlational method is a research method in which two variables are measured for each participant and the extent to which those variables are related is measured.