Question 1: 300 words
By now you are adept at calculating averages and intuitively can estimate whether something is “normal” (a measurement not too far from average) or unusual (pretty far from the average you might expect). This class helps to quantify exactly how far something you measure is from average using the normal distribution. Basically, you mark the mean down the middle of the bell curve, calculate the standard deviation of your sample and then add (or subtract) that value to come up with the mile markers (z scores) that measure the distance from the mean.
For example, if the average height of adult males in the United States is 69 inches with a standard deviation of 3 inches, we could create the graph below.
Men who are somewhere between 63 and 75 inches tall would be considered of a fairly normal height. Men shorter than 63” or taller than 75” would be considered unusual (assuming our sample data represents the actual population). You could use a z score to look up exactly what percentage of men are shorter than (or taller than) a particular height.
Think of something in your work or personal life that you measure regularly (No actual calculation of the mean, standard deviation or z scores is necessary). What value is “average”? What values would you consider to be unusually high or unusually low? If a value were unusually high or low—how would it change your response to the measurement?
Question 2: 300 words
Two or more samples are often compared when we suspect that there are differences between the groups—for example, are cancer rates higher in one town than another, or are test scores higher in one class than another? In your chosen field, when might you want to know the mean differences between two or more groups? Please describe the situation (what groups, what measurements) including how and why it would be used.
Question 3: 325 words
One goal of statistics is to identify relations among variables. What happens to one variable as another variable changes? Does a change in one variable cause a change in another variable? These questions can lead to powerful methods of predicting future values through linear regression.
It is important to note the true meaning and scope of co
elation, which is the nature of the relation between two variables. Co
elation does not allow to say that there is any causal link between the two variables. In other words, we cannot say that one variable causes another; however, it is not uncommon to see such use in the news media. An example is shown below.
Here we see that, at least visually, there appears to be a relation between the divorce rate in Maine and the per capital consumption of margarine. Does this imply that all ma
ied couples in Maine should immediately stop using margarine in order to stave off divorce? Common sense tells us that is probably not true.
This is an example of a spurious co
elation in which there appears to be a relation between the divorce rate and margarine consumption but, it is not a causal link. The appearance of such a relation could merely be due to coincidence or perhaps another unseen factor.
What is one instance where you have seen co
elation misinterpreted as causation? Please describe.