Much has been written about the relationship between students' SAT test scores and their family's income. Generally speaking, there is a strong positive correlation between income and SAT scores. Consider and discuss the following questions as you respond:
- What does this correlation tell you?
Solution:
The correlation between the two variables explains the amount of relationship exists between the two variables. If we get the high positive correlation coefficient then we say that there is a strong positive linear relationship or association exists between the given two variables. If there is a high negative correlation then we interpret this as a strong negative linear association exists between the two variables. In the high positive correlation, as the first variable increases, the second variable also increases. For the given example, as the SAT scores increases the income also increases and as the SAT scores decreases, the income decreases. This means there is a high or strong positive correlation exists between the income and SAT scores.
- Is this correlation evidence that having a high family income causes one to have high SAT scores?
Solution:
This correlation does not evidence that the high family income causes one to have high SAT scores at the given level of significance. This does not means it is happens all times, there would some little possibility of having a high family income does not causes to have high SAT scores. We are talking about in-general phenomenon about the relationship and we do not apply this relationship to each and every one person. We can say that there is a 95% possibility of having high family income causes one to have high SAT scores.
- Is this correlation evidence that high SAT scores are a cause of higher income? Or, does this tell you something else? Explain your answer.
Solution:
Yes, the correlation evidence that high SAT scores are a cause of higher income. For the given example, the SAT scores is the independent variable and the income is the cause or dependent variable. Also, it is important to understand that the results are generalized and we cannot claim 100% surely. We claim the statement about correlation exists between high SAT scores and higher income at the given level of significance.
- Explain why correlation alone is rarely sufficient to demonstrate cause.
Solution:
As we discuss in the above discussion that we cannot apply the correlation results at the personal level and this is the general phenomenon about the relationship. This correlation explains the general relationship between the two variables and due to this reason the correlation alone is rarely sufficient to demonstrate cause.
Questions about Post:
What do you think would be the (dependent) variable to cause the income to be higher? Is it safe to say that ongoing research would be considered since correlation is not always accurate? Do you think that the conclusion of this discussion would be different if this was measured on a personal basis than a generalized platform?
Response: