Posted on Wednesday, 18th January 2012
Please post a comment or question on Chapter 2 and/or Section 3.1
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January 18th, 2012 at 12:31 pm
I wasn’t sure where to post before, so this is a re-post of my question:
Chapter 2 discusses how data transformations can be used to make the data more regular/normal, but doesn’t completely describe how to decide which transformation to use? Is there a real method to selecting transformations of data, or do we begin with the natural log transformation, and if that doesn’t make the data normal, we try other transformations? Is there any way to know before collecting the data what type of transformation might be needed?
January 18th, 2012 at 1:24 pm
(1) I understand that statistical models can describe the variability in the data, but can a model explain the source of the variability? For example, if we know variability in a dataset can arise because of many reasons and we are interested knowing how much each of those reasons contribute to the variability or whether one predominates, can a model help us?
(2) I don’t entirely understand the argument on Page 41: “log-transformed growth measurements usually have fairly symmetrical distributions”, especially how it pertains to the Central Limit Theorem.
January 18th, 2012 at 1:34 pm
1. It’s not clear to me why the CLT can be stated as “if we add up many small, independent effects their sum will be approximately normally distributed.” I understand why independence is necessary and that we need a large amount of independent events, but why the “small” effects? Also, in the example given, I don’t understand how growth could be independent (it seems like the growth one day is directly related to the growth the day before – if the growing thing is lacking nutrients, all of the growth during that time will be stunted)
2. The part about why log transformations often results in a normal distribution was unclear. Is this a function of how the math works out or is it a function of how nature happens to work out?
January 18th, 2012 at 8:04 pm
In the last part of the details section on page 35, I am not sure what assumptions are being made on the covariance matrix, /Sigma. Does the unbiased version of the estimator apply to only the assumption of identical variances of x_i’s or what form would the unbiased estimator take without such an assumption (for the diagonal or full-matrix version of /Sigma)?
January 18th, 2012 at 9:17 pm
Sorry, second comment. The ending of the paragraph on PSA and Bayes’ Theorem (pg 57) is frustratingly cut short. It seems that the positive patient was suddenly incorporated in the false-positive population.
January 18th, 2012 at 10:08 pm
In discussing transformations of data in Chapter 2, you and your coauthors emphasize how such transformations can produce more elegant or tractable descriptions of data than the untransformed values themselves. While I understand how expressions of linear rather than multiplicative relationships can demonstrate these qualities in descriptions of data, I also consider how the visual impact of the actual multiplicative or proportional relationships may be diminished (if not eliminated) by the same transformations. While linear relationships may communicate to a reader information identical to the information communicated by proportional relationships, framing the relationships as proportional seems to me like it could tell stronger stories about the relationships than framing the relationships as linear could. In this way, I have to wonder whether in certain cases the impression of proportional data as proportional may matter more than the information of the same data as proportional, and whether choosing not to transform otherwise elegant data could behoove an analyst in his/her research.
January 18th, 2012 at 10:58 pm
Regarding section 2.2.2: I’m not sure I understand the rationale behind using non-logarithmic transformations for some data. E.g., a square-root transformation, used on spike counts, is said to be a “variance-stabilizing transformation”—and I don’t really understand what this means, or, more importantly, WHY it’s preferable to a log transformation. This might be a minor point, but I’d like to understand it.
January 18th, 2012 at 11:31 pm
1. Histograms of different bin sizes give different impressions of data. So for a specific histogram, how do we know what bin size is appropriate?
2. Will some features of the data lose during transformation?
3. I have seen a lot of data normalization from research articles. Is it a way to manipulate data? What role does normalization play?
4. What’s the meaning of ‘strength of transformation’?
January 19th, 2012 at 2:02 am
I really appreciated the usage examples for the logarithmic transformation, especially the description of power laws using learning rates.
January 19th, 2012 at 2:36 am
In chapter 2, the value of exploratory analysis is emphasized, with one example being transformations for visualization. However, it seems to me that this approach encourages the researcher to try to find a representation that “quiets” the interesting parts of the data by forcing it into the mold of the normal distribution. Might this sometimes result in the wrong statistical methods being used to evaluate the data, resulting in an incorrect scientific conclusion? Or is the time-tested central limit theorem (and thus the normal distribution) so useful and that it should always be sought out?
January 19th, 2012 at 7:59 am
In the example problem on page 55 (example 3.1.1), we conclude that the two neurons are not independent because the probability of their intersection is more than double (read: not equal to) the product of the product of the two neurons’ probabilities. This seems to be a large difference between the two computed probabilities, so independence can be confidently discarded. However, when the two values are much closer to one another, does that affect our confidence in their independence? In other words, if the two computed probability values are not equal but much closer to one another, we can still assume independence? Or is there a certain threshold for which we may consider dependence between the two events?
January 19th, 2012 at 8:22 am
On page 41, section 2.2.1, top of the page, the summary of the central limit theorem: How can a single sum be a distribution? If we add many small, independent effects, don’t we just get one number?
On page 45, section 2.2.2, the ideas of “less strong than” and “strengthen the transformation” are unclear to me.
Example 2.2.4 “Because the instantaneous potential is generated from both agonist and antagonist muscle fibers”. What does agonist and antagonist mean in this context? If it’s on the same muscle, are there really antagonist fibers? Is this not an effect of a propagating action potential reaching 2 electrodes in series?
January 19th, 2012 at 9:04 am
On page 58, example 3.1.2, can we talk a little bit about the terms sensitivity and specificity, especially in regards to “true positives” and “true negatives” and statistical power and the p value
January 19th, 2012 at 9:35 am
Good introduction; I liked the continued examples throughout the chapter. One minor note: as I understand it, an EMG signal is not generated from a combination of potentials from both agonist and antagonist fibers as suggested in example 2.2.4. I believe the positive and negative characteristics of the waveform are simply due to the inward and outward flow of currents surrounding an active zone of propagating action potentials down the muscle fibers.
With regard to Bayesian Statistics, I often hear that Bayes’ rule is “conditioned on a prior.” Is there a particular term in the equation that’s considered the prior?