For instance, if I were to look at the amount of money organizations are spending on R&D per year and then look at the amount of money one particular organization is spending. How can I compare and analyze it's spending behavior compared to that of the group? Is there an accepted approach? Looking for anything that will point me in the right direction. Thanks!
Simply if you can check mean difference with help of t or z test based on data size
Thank you all for your inputs!
Ruth Maria Tappin , how would I use ANOVA to compare one versus the populatoin?
Milan B. Vemić , before I create something new, I wanted to see if there was something that was already done. The problem with doing it the way you say is that I'm looking at trend comparisons. However, Anjay kumar Mishra sort of gives me an idea that perhaps I can compare derivatives together with t tests. But again, I will go down a "custom" path if I need to, but is anyone aware of any research that compared one to many in terms of trends?
This is elementary statistics. You have a sample of R&D expenditures and have calculated a mean (average) and standard deviation. You now want to know how much one observation deviates from the group. Simply calculate the deviation of that sample standardized by the standard deviation, which will tell you how many standard deviations it is away from the mean: Z=(x-mu)/sigma. The sign tells you on which side you are on, ahead (+) or behind (-).
I must not be phrasing the question correctly because Greg Olsen you misunderstood my ask and did not read my follow up. I am looking not to compare averages, but one company's PATTERN of behavior against the overall industry TREND--meaning longitudinal behavior. For example, companies overall may be increasing spending from years 2010-2011, flattening 2012-2013. If company A started increasing it's spending 2008-2009, it's AHEAD of the trend. My question is how do I assess whether and to what extent any individual company is ahead of overall industry trends.
Sorry I didn't read the follow up. You have two time series on some sampling interval (quarterly?). To show qualitatively that company A is ahead of the S&P or whatever is to show plots of the log of the two time series side by side. If you are making an argument that there is a causal relationship you could use a multivariate method (see Chapter 8 of Tsay, Analysis of Financial Time Series, 2nd ed.) to see if company A predicts S&P. Be careful about the various assumptions of the different models. Can it be modeled as a linear trend and random walk? Is there seasonality? Is the time series strongly or weakly stationary (see Chapter 1 and 2 of Tsay)? These determine the right kind of model to use.
If you are not making a causal argument, but want to see how the two trends differ, run your decomposition and then compare the trend lines graphically. That will give you a good sense qualitatively of the underlying trends, versus the cyclical variations and noise.
Greg Olsen thank you, that's very helpful! I will look into the methods and sources you mention.
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