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I'm from a social science background and, like you, I often find myself hopelessly lost when it comes to what feels like very basic concepts in statistics. I think that's partly due to how statistics is taught in all non-mathematics disciplines - in theory we're taught how to use and evaluate quite complex statistical procedures, but with only 1-2 hours per week teaching, it's impossible for our lecturers to cover the fundamental building blocks that help us to understand what's actually going on.

Because of this, I've recently started a few MOOCs on Coursera, and I've found these massively helpful for covering research methods and statistics in far more depth than my undergraduate and postgraduate lecturers ever had time to delve into. In particular, a couple of courses I'd recommend are:

• Methods and Statistics in Social Sciences - This is particularly focused on quantitative methods in the social sciences (including quite a bit on behavioural and self-report research) so I'm not sure if it will be directly relevant with respect to neuroimaging and cognitive neuroscience, but this gives a great introduction to research methods in general. I've actually only done the first course in this series (Quantitative Research Methods), but they're very comprehensive and well made, so I'm confident that the whole series will be useful for any researcher.
  
• Probability and statistics: To p or not to p? - This one is a little bit more maths-heavy so might be a bit intimidating if you don't find that sort of material easy, but it's a good introduction to some of the core concepts in quantitative research, including some you mentioned (e.g. probability distributions). You don't really have to fully engage with or grasp the maths for it to be useful either.
  
  In terms of textbooks, I personally use Andy Field's Discovering Statistics Using R, and find that very helpful. Field is a psychologist who is very open about his difficulties with learning statistics, and I've found it quite useful and re-assuring to learn from someone with that mindset. He's also tried writing a statistics textbook in the form of a graphic novel, An Adventure in Statistics: The Reality Enigma, so if that sounds like something that might help you, check it out.
  
  I think a few people from a 'purer' statistics background are a bit more critical about Field's books because they're not as comprehensive as a book written by, for example, a statistics professor - and there might be some advice in there that's a little bit out-of-date or not quite correct. He also has a very hit-and-miss cheesy sense of humour, which you'll either love or find very annoying. But I think he takes the right sort of approach for helping people who aren't necessarily mathematically-inclined to dip their toes into the world of statistics.

You need Intuitive Biostatistics. It's written specifically for scientists and medical professionals without a math background to learn how to interpret data in scientific papers. I'm a PhD student in cell bio and it is invaluable. The only thing it might not cover super in-depth is probability, but it pretty much covers the gamut of everything else without delving into the mathematics behind everything. The guy who wrote it also makes the Graphpad Prism software, which a lot of bioscientists use for data analysis.

For the next step, I highly recommend JB Statistics videos. They are the best moderate math level explanations for the common concepts I have yet come across. Especially watch the sampling distribution playlist several times to fully comprehend the CLT.

Some other advice I wish I was told before I started learning statistics: 1) Statistics is the inverse of probability. 2) Statistics is unintuitive and hard to understand. You will have to read some things dozens of times and from different people's wording to fully understand a concept (looking at you, p-values). Best of luck.

Beginner Resources: These are fantastic places to start for true beginners.

Introduction to Probability is an oldie but a goodie. This is a basic book about probability that is suited for the absolute beginner. Its written in an older style of english, but other than that it is a great place to start.

Bayes Rule is a really simple, really basic book that shows only the most basic ideas of bayesian stats. If you are completely unfamiliar with stats but have a basic understanding of probability, this book is pretty good.

A Modern Approach to Regression with R is a great first resource for someone who understands a little about probability but wants to learn more about the details of data analysis.

​

Advanced resources: These are comprehensive, quality, and what I used for a stats MS.

Statistical Inference by Casella and Berger (2nd ed) is a classic text on maximum likelihood, probability, sufficiency, large sample properties, etc. Its what I used for all of my graduate probability and inference classes. Its not really beginner friendly and sometimes goes into too much detail, but its a really high quality resource.

Bayesian Data Analysis (3rd ed) is a really nice resource/reference for bayesian analysis. It isn't a "cuddle up by a fire" type of book since it is really detailed, but almost any topic in bayesian analysis will be there. Although its not needed, a good grasp on topics in the first book will greatly enhance the reading experience.

> I'm trying to create a forecasting model to predict ...was hoping someone could point me in the right direction with documentation, vignetts, papers that could help me figure this out, or ideas on how you would approach this problem.


Well you are in luck, there is an entire book that answers what you are trying to accomplish, and spells out the steps how to do it.


https://www.amazon.ca/Introductory-Time-Paul-S-P-Cowpertwait/dp/0387886974/ref=sr_1_1?keywords=introductory+time+series+r&qid=1574873740&sr=8-1

It may also be available for free through other means.

The specific chapters you want will probably be two and three (correlation, and forecasting strategies), though the rest of the book will likely be beneficial as well.

> I have some but I am not super well versed in the matter. (with regards to R and programming skills)

If that’s the case, it might be difficult to implement what is in the book. It assumes you know R at probably around a low/mid level. But if you power through you should be able to get some good out of it.

Also be aware that according to some of the reviews. the source code and data does not appear to be online any more. That makes direct copy and pasting the examples difficult, but if you are applying it to your own data set only, that might be less of an issue.

Its a pretty good book (its the one I read on forecasting originally), and it will get you going in the might direction but its not perfect and you might be able to find a more current one with available sample data. Read the reviews.

Get started and let me know how it goes :)

EDIT

All of the data, as well as functions and R code are indeed available online. Just had to look for it:

http://www.maths.adelaide.edu.au/emac2009/

Edit 2:

Here is are a few newer books as well. I skimmed it quickly and it may or may not be better:

http://db.ucsd.edu/static/TimeSeries.pdf

Again, you are looking at autocorrelation and forecasting. This one may lean a bit more on the math side.

/EDIT

I TFed an intro undergrad course that used Alan Agresti's Statistical Methods for the Social Sciences. I didn't read much of it, but the students seemed to like it. He also has another book that's probably also pretty good. The intro course for non-stats students at my graduate school is Applied Statistics for the Behavioral Sciences, which might also be worth a look. If those are too technical or hands-on, then the "for Dummies" book might also be a good choice - it's in very plain language and tries to keep things relevant to real-life examples.

Many of the bigger-picture "whys" become more apparent when you have a solid grounding in probability theory and the theory behind statistical inference, though. Some of them don't have very satisfying answers, either (Q: Why p = 0.05? A: Convention). In my opinion, the more you understand statistics, the more you realize it's less about finding exact answers than it is about quantifying imprecision. That can be hard for a layperson to wrap their head around!

Since you are still in college, why not take a statistics class? Perhaps it can count as an elective for your major. You might also want to consider a statistics minor if you really enjoy it. If these are not options, then how about asking the professor if you can sit in on the lectures?

It sounds like you will be able to grasp programming in R, may I suggest trying out SAS? This book by Ron Cody is a good introduction to statistics with SAS programming examples. It does not emphasize theory though. For theory, I would recommend Casella & Berger, many consider this book to be a foundation for statisticians and is usually taught at a grad level.

Good luck!

There is a bunch of engineering stats books out there. The one we teach out of at my uni is the one by Devore. I think it does a good job of teaching what it does. I know Ross has an engineering stats book out there, and so does Montgomery, and they are both people who have written good books in the past. The one by Ross seems to have some good topics in it from reading the table of contents.


Also, you probably want to pick up a regression book. I like the one by Kutner et al., but it is ungodly pricey. This one has a free pdf. I don't like a lot about it, but the first few chapters of every regression book are pretty much the same.

If you want to go deep into statistical theory, there is Casella and Berger as well.


For programs, I know MATLAB has a stats package that should be sufficient for the time being. If you want to go further in stats, you might want to consider R because it will have vastly more stats functions.

I know this is a boring suggestion, but nothing beats the old, venerable Schaum's Outlines for their combination of problems, solutions, and inexpensiveness. If you are just starting, perhaps start with this one, and once you get some exposure to the basics you'll have a better idea of what you might want to pursue next- perhaps the next step would be analysis using a computer instead of by hand.

Lots of us have free YouTube videos on the basics that you can reference if/when you need them as you go. Try me or Kahn Academy, there are many others. Let me know if this idea doesn't fit with what you had in mind, and I can try to point you in a different direction.

> the first half of my degree was heavy on theoretical statistics,

Really? Wow, I'm impressed. Actual coverage of even basic theoretical stats is extremely rare in psych programs. Usually it's a bunch of pronouncements from on high, stated without proof, along with lists of commandments to follow (many of dubious value) and a collection of bogus rules of thumb.

What book(s) did you use? Wasserman? Casella and Berger? Cox and Hinkley? or (since you say it was heavy on theory) something more theoretical than standard theory texts?

I'd note that reaction times (conditionally on the IVs) are unlikely to be close to normal (they'll be right skew), and likely heteroskedastic. I'd be inclined toward generalized linear models (perhaps a gamma model -probably with log-lnk if you have any continuous covariates- would suit reaction times?). And as COOLSerdash mentions, you may want a random effect on subject, which would then imply GLMMs

This book is a amazing:
Discovering Statistics Using R
by Andy Field

If you are doing self-study, it is easy to lose momentum. This book is hilarious, personal, and transcends the textbook genre.

Amazon Link

I'm a big fan of The Drunkard's Walk. Also, the author Leonard Mlodinow (PhD in physics from Berkeley) has a number of other really good books on different scientific fields.

The best to start with Theoretical understanding would be: The Elements of Statistical Learning: Data Mining, Inference, and Prediction

If you prefer to understand along with computation implementation, go with this: An Introduction to Statistical Learning: with Applications in R

Incorporating expert opinion into a Bayesian model is usually done through prior distributions instead of an additional feature. (As an aside, doing so is considered subjective Bayesian inference versus objective Bayesian inference).

As a quick overview, Bayesians usually make inference on the posterior distribution - a combination of the prior distribution (in your case, expert opinion), and the likelihood. As a really basic example, consider a setting where you have data on MI outcomes (no covariates at this point) - a series of 1's and 0's. A frequentist would likely take the mean of the data. As a Bayesian, you would consider this binomial likelihood and likely combine it with a beta prior. The default (non informative) prior would be to use a beta(1, 1) distribution. However, if in a prior dataset, you had observed four patients, three with an MI and one without, you could use a prior of beta(1+3, 1+1). See here for more details on beta-binomial.

In the above example, it's easy to incorporate prior information because we used a conjugate prior. While probably not exactly what you are doing for your dissertation, here's an overview of a conjugate prior with a linear regression from wikipedia. There are many more resources online for this that you can find by searching for something along the lines of "bayesian linear regression subjective conjugate prior". For a more detailed (introductory) overview of bayesian statistics, check out this book.

To be honest, as much as I'm a Bayesian, I think that creating an automatic model that incorporates expert opinion will be really difficult. Usually, subjective priors are chosen carefully, and there not always as interpretable as the beta-binomial posterior presented above. I think this goal is possible, but it would require a lot of though about how the prior is automatically constructed from a data set of surgeon's predictions. If you have any followup questions/would like more resources, let me know!

Edit: I guess I never really addressed the issue of predictive models. However, the difficult part will be constructing the prior automatically. If you can do this, predicting outcomes will be a simple change to make, especially in the case of linear model.

There is a good book about teaching statistics by Andrew Gelman and Deborah Nolan: Teaching statistics: A Bag of Tricks.

I will second this. I used this book for my year of undergrad foundations of probably and stats.
I also really like Casella and Berger's 'Statistical Inference.'

https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126

you can check the following book on Biostatistics


Essentials of Bio-Statistics: An overview with the help of Software

https://www.amazon.com/dp/B07GRBXX7D E-book

ISBN: 978-1723712074

At least re: random variables, events, PDF, and CDF, I like the diagrams from Prof. Joe Blitzstein's textbook:

http://i.imgur.com/aBkgHGC.jpg

This is a classic. I took a grad level course with this textbook and every problem is nasty. But yes, it is really a classic.

Also, I just begun Data Analysis Using Regression and Multilevel/Hierarchical Models by Andrew Gelman and Jennifer Hill. Love his interpretation of linear regression. Linear regression might sound like basics, but it lays the foundation work for everything else and from time to time I feel compelled to review it. This book gave me a new way to look at a familiar topic.

If you are familiar with any statistical programming language/packages, I would highly suggest you implement the learnings from any books you have.

I haven't read it, but there's a book written about what p-values are: https://www.amazon.com/p-value-Stories-Actually-Understand-Statistics/dp/0321629302

Get this book: Guerrilla Analytics: A Practical Approach to Working with Data

Although I am not a statistician myself and given your background, some of my recommendations would be:

• All of Statistics for a concise treatment of well....all of statistics :p
  
  
• [Introduction to Statistical Learning/Elements of Statistical Learning] (https://www.amazon.com/Introduction-Statistical-Learning-Applications-Statistics/dp/1461471370/ref=sr_1_1?s=books&ie=UTF8&qid=1493070885&sr=1-1&keywords=introduction+to+statistical+learning) avaliable for free in the internet if you are interested in applying statistical methods with Machine Learning
  
  
• Introduction to Probability for a intro to probability theory which underlies most of statistics.
  
  
• One of either [Python Data Science Handbook] (https://www.amazon.com/Python-Data-Science-Handbook-Essential/dp/1491912057/ref=sr_1_1?s=books&ie=UTF8&qid=1493071026&sr=1-1&keywords=python+data+science+handbook) or [R for Data Science] (https://www.amazon.com/Data-Science-Transform-Visualize-Model/dp/1491910399/ref=sr_1_1?s=books&ie=UTF8&qid=1493071056&sr=1-1&keywords=r+for+data+science) for building programming chops in your language of choice Python or R.
  
  This should probably be enough for now but if you need more recommendations just say so :)
  
  Regarding the time series question, it's not my area of expertise but since time series analysis ends up employing many statistical methods, I think it can be considered an area of statistics (Statisticians around here correct me if I am wrong :P)

You can do a significance test. But 1 in 20 randomization checks will be statistically significant. So if your test is significant, you don't know if randomization failed, or if you were unlucky.

And if a randomization check is not significant, that doesn't tell you much. It just tells you that you failed to detect failures of randomization.

So don't try. Design robust randomization procedures that you believe in (using telephone randomization, opaque envelopes, whatever). If you don't have complete faith in your randomization, you don't believe it, no matter what.

Link (behind a paywall): http://www.bmj.com/content/319/7203/185.1.full I think the clinical trials book by Torgerson and Torgerson covers this: https://www.amazon.com/Designing-Randomised-Trials-Education-Sciences/dp/0230537359 (But so should any decent book on clinical trials).