Much has been written about the relationship between students’ SAT test scores a
ID: 1720114 • Letter: M
Question
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?
Is this correlation evidence that having a 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.
Explain why correlation alone is rarely sufficient to demonstrate cause.
Explanation / Answer
Solution:
Correlation
Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For example, height and weight are related; taller people tend to be heavier than shorter people. The relationship isn't perfect. People of the same height vary in weight, and you can easily think of two people you know where the shorter one is heavier than the taller one. Nonetheless, the average weight of people 5'5'' is less than the average weight of people 5'6'', and their average weight is less than that of people 5'7'', etc. Correlation can tell you just how much of the variation in peoples' weights is related to their heights.
when correlation is strong and positive
A positive correlation is a relationship between two variables such that their values increase or decrease together.
Direct relations ship exists between xand y
in this case take y=sat scores =dependent variable
x=income =independent variable
so when correlation between x and y is strong positive means
y increases if x also increases
y dcreases if x also decreases.
Explanation:
Correlation is expressed on a range from +1 to -1, known as the correlation coefficent. In a perfect positive correlation, expressed as +1, an increase or decrease in one variable always predicts the same directional change for the second variable. If two variables sometimes but not always change in tandem, the correlation is expressed as greater than zero but less than +1. Values below zero express negative correlation: As the value of one variable increases, the other decreases. Zero indicates a lack of correlation: There is no tendency for the variables to fluctuate in tandem either positively or negatively.
What does this correlation tell you?
Correlation statistics represents relationships between data instead of cause. Thereforefirst and foremost, this correlation tells you that there is definitely a relationship between SATscores and high family income. Specifically, it tells us that the higher the family’s income, it ispredicted then that the SAT scores of that individual to be high
There’s a common tendency to think that correlation between variables means that one causes or influences the change in the other one. However, correlation does not implycausation. There may be an unknown factor that influences both variables similarly.
Is this correlation evidence that high SAT scores are a cause of higher income? Or, does this tell you something else? Explain your answer.
Answer:
No. For one, there is a difference between correlation and cause. Correlation shows arelationship but it does not distinguish if one variable causes the other to happen. There is noevidence that the high income causes the high scores, but that there is a relation
Explain why correlation alone is rarely sufficient to demonstrate cause.?
Ans:
Correlation is a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable.
Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events. This is also referred to as cause and effect.
Theoretically, the difference between the two types of relationships are easy to identify — an action or occurrence cancause another (e.g. smoking causes an increase in the risk of developing lung cancer), or it can correlate with another (e.g. smoking is correlated with alcoholism, but it does not cause alcoholism). In practice, however, it remains difficult to clearly establish cause and effect, compared with establishing correlation.
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