Challenges: Paper Compilation and Mad Dollar $igns

When I first looked at my assignment for this exam and found "Challenges in Statistics" next to my name I was a little dismayed. Isn't everything in statistics a challenge in statistics? I asked myself, but I realized this was the section of the text which dealt with gaussian distributions and outliers, probably the two statistical challenges I've actually faced since beginning this course. I have encountered both of recent in looking through a large old data set which I am trying to re-interpret for a paper I am writing. The data was generated by an old tech in the lab who isn't in the state anymore, and one challenge I had in approaching the data statistically and anticipating how I could display my data was that I didn't know about the distribution. I hadn't worked with these cells before, and I had only done a similar, but not exactly the same protocol. Reading about normality tests reminded me that I had that option, and now I remember what the "skewness" and "kurtosis" values are useful for in prism. Similarly, I struggled with outliers and how to treat potential outliers, because normally I would only reject an outlier if I had reason to believe that my own experimental error or some other thing outside my control had biased this outlier. However, since this wasn't my data, I also didn't perform the experiments! I had to make some educated choices with my PI, trying to remain informed with the Grubb's test.

 

In addition to the lab, the issue of distribution also affects my day-to-day money management. I'm a grad student who likes to invest my modest stipend in stocks. As someone who is fairly new to trading securities, one comfortable way into the world of Wall Street was via statistics. The same challenges in statistics which face scientists also face economists and stock traders. When there is real money on the line, it helps to have some of these statistical tools on my side, to help temper any bias. Given that I am trading in real companies with significant reputations, it's hard not to get emotionally involved in any of my holdings. However, if I can set some rules and use some of the tools in this section of the text, I can increase my overall profit through bullish and bearish. For example, check out this Forbes article which underscores how a normal distribution of the DJIA 30 indicates a healthy market (also see figure).

Displaying an individual stock's performance in what we hope is a normal distribution or finding standard deviation can indicate the volatility of a stock, correlated to risk. This value can also be similar to beta, the value many investors use to indicate volatility/risk, although it should be mentioned that this is not how beta is calculated. Lastly, many trading algorithms on Wall Street and financial theories anticipate a gaussian distribution of stock prices in order to maximize alpha or gains adjusted to the overall performance of the market. Thus, skew and kurtosis are important for investors to keep track of! The role of normal distribution, skew, and kurtosis in investing is simply summed up in this post, for those interested.