Study Strategies for Graduate Statistics
Many graduate students have anxiety about taking statistics or research methods courses. They may recall undergraduate statistics as being difficult or they might be concerned that they aren’t good enough at math or that math was too long ago. One researcher found that up to 80 percent of graduate students have anxiety about taking statistics courses (Onwuegbuzie, 2004). The good news is that other researchers have found that this anxiety diminishes quickly during a course in statistics.
While the anxiety may be temporary, the study skills for statistics may be different from those you’re used to within your own field. Here is an overview of some general strategies. Below are some more specific skills for solving homework problems.
Stay focused on the big picture. The purpose of statistics is not to answer strange math puzzles, it’s to understand and reason about variability in the world around us. As a grad student, there is a good chance you will be conducting your own quantitative research and you’ll certainly be reading and evaluating the research literature in your field, at least some of which may be quantitative in nature. Keeping this in mind may help you focus your efforts on the important aspects of statistics rather than the computational details.
Study regularly. Since the concepts in probability and statistics build upon each other and each concept takes time to fully comprehend, cramming is not a successful strategy for statistics. Without regular study, you won’t be able to integrate and synthesize the ideas into your thinking. Even if you can only find 15 minutes on a hectic day, that is a day which you’ve maintained your level of knowledge, rather than forgotten information.
Focus on the interrelationships among concepts and definitions. Compare and contrast similar sounding definitions (e.g. a random event versus a random variable). Concept mapping can be invaluable to keep your thinking organized. At the end of the course what you’ll take with you is an understanding of concepts and tools for understanding variability, not mathematical details.
Talk about statistics and research. Ask questions in class or after class. Organize study sessions. Compare notes with classmates. One of the most challenging skills is being able to translate ordinary language into statistical ideas. The more you talk about statistics, the easier it will be to acquire these skills.
Find a mentor/tutor before you need one. It might seem like going-it-alone is more efficient but working with someone with more experience can make learning new and confusing material from outside your area of study much more effective. Connecting with this person in the first weeks will make it easier to reach out when you do want to review a concept or troubleshoot a problem.
Recruit a more advanced grad student in your program, or perhaps from a different department. Many campuses have a statistical consulting service, though they rarely provide coursework support, they may be able to refer you to someone appropriate. A few universities like ASU have free services for postgrad statistics learners—they may be housed in the library, academic support program (i.e. math centers), or with the math department. Ask around.
Don’t let notation scare you. Culturally, we often represent the ideas of difficult topics through strange mathematical notations scribbled on a chalkboard. Yet, we represent simple and easy with the abc’s. Keep in mind that each new symbol or letter encapsulates some concept. It has a definition and usually simple English "translation" or way to read it. These are typically not difficult to learn or understand, but it can be frustrating when you encounter them before you’ve learned the definition.
By the way, the Greek letter capital sigma, Σ, simply means "add". It is basically just +, which I’m sure you learned with your abc’s. Where the plus sign adds the two numbers on either side, sigma notation adds a whole bunch of items. Pretty simple, no?
Focus on the future. If you might be conducting quantitative research for your thesis or dissertation, an introductory class is only a necessary starting point. Many students find that a single statistics class from their first year is insufficient two to five years down the road when they attempt to conduct their own research. If you might be using quantitative skills in your profession or for your research, I would encourage you to grow your statistical thinking skills. Consider taking intermediate level statistics courses, teach an undergraduate research methods section, work for lab or center that conducts quantitative research, or tutor next year’s class. Many universities offer statistics workshops on select topics. There are several programs that offer two to five day summer workshops on various research topics (e.g. ICPSR Summer Program).
How to Study and Solve Homework Problems
Prepare for lectures. Read the slides or relevant textbook section before class. Don’t worry if you don’t fully comprehend it: the purpose is to start thinking about where the content is going. If you have an hour to read through the material, great! But even a few minutes of exploring will help prime your learning. Concentrate on the material during class. If you don’t understand something, ask. This may even prompt others to ask questions when they don’t understand something.
Study without distraction. Statistics problem require a lot of working memory (e.g. focused attention). Avoiding distraction while studying. Getting enough sleep, good nutrition, maintaining strong social connections, and regular exercise are also great ways to optimize your mental resources.
Don’t skip the hand calculations. Yes, these are tedious and annoying. But doing one example by hand takes the mystery out of statistics and improves comprehension. Further, the time spend working through the formula will likely make you a more advanced reader of formulas—statistical formulas have their own "roots", "stems", and "suffixes" which you’ll begin to recognize. Hopefully, you will not be asked to memorize more than a handful of formulas.
Bring the right tools. Solving math or statistics problem typically involves a set of knowledge and skills particular to that problem. You’ll want to gather together those mental tools you’ll likely to need for a given problem by reviewing notes, slides, and textbooks. Keep an eye out for important concepts, formulas, and procedures. You don’t have to be an expert in each, just familiar enough to know where to go, should you need it. Then, read through the question carefully enough to understand what is being asked and begin to use your tools to solve the problem. You may need to seek out additional resources during problem solving, but you should have a basic toolkit to work from. Any idea, formula, math skill that you need to solve the problem (that you don’t already know) should be written down on a running list of review material.
Check your work. Learning statistics typically involves working problems that rely on the covered material. Checking your solutions provides instant feedback on whether you’re on the right track. For longer problems, you might even check your work in steps (Did I choose the right procedure? Did I do the computations correctly? Is my interpretation of the result correct?). Use excel to check your computations or statistical software to check results. Keep a running list of the types of mistakes you make.
Resolve misconceptions. Misconceptions are par for the course in statistics. Learning statistics is discovering and correcting your own misconceptions. If you get a wrong answer on an exercise, and it isn’t a basic math error, look to your understanding of the most relevant topic and the concepts on which it relies.
Make a game of it. See how far you can work an exercise without going back to solutions or examples. In the beginning, you may not get very far. In fact, you may not even be able to set up the problem without help. Over time, you’ll improve your ability to work problems.
Be wary of extreme frustration. Working on challenging problems is bound to cause mild frustration. If you notice your frustration level rising, consider taking a short break, asking for help, set the task aside until the next day. If done sparingly, sometimes skipping a problem is reasonable—maybe come back to it a week or two, it might be much easier then. Severe emotional reactions can prevent you from being able to solve the problem by taxing your ability to focus—don’t try to barrel through it.
Be aware of mathematics study skills. A few statistics classes are more rigorous and mathematical. These courses would be more theorem and proof based which requires mathematical sophistication. This sophistication can be acquired by anyone, but it has some additional study strategies not presented here. You may wish to seek them out.
For test preparation, do many practice problems. While conceptual understanding is the most important goal, being able to solve problems during an exam often requires near instant recall of how to perform a given procedure or analyze a situation. The best way to perform well is with lots of practice drills in conditions as similar as possible to the test. Old problems or examples can be re-solved after a few days if you run short on problems.
- Onwuegbuzie, A. J. (2004). Academic procrastination and statistics anxiety. Assessment & Evaluation in Higher Education, 29(1), 3-19. doi:10.1080/0260293042000160384