Goals for students in an introductory course

I am studying Statistics for business at introductory level, and having difficulty in handling the amount of information, partly because I am coming back to study after 5 years and I didn't do much stats at school.

I don't understand binomial distribution, inference and all the types of "errors" on my textbook. I did pretty well on the first 2 assignments, based on the excel templates provided by the course and some common-sense thinking.

My question is What are some key points that I should know about statistics? Would appreciate any help.

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Roughly speaking there are two stages in a statistical experiment: before the experiment and after the experiment. In the binomial case, before the experiment we say: "we will observe a realization of a binomial random variable with unknown proportion parameter $\theta$", after the experiment we observe the realization and the question is "what can we say about $\theta$ ?". The "before" stage is probability theory rather than statistics, maybe you should make efforts to understand this point. –  Stéphane Laurent Jun 1 '12 at 6:05
It depends. Is your goal to get a working understanding of statistics or to pass the course? :) –  MånsT Jun 1 '12 at 7:20
@MånsT Ideally understanding statistics will help me to pass the course –  Filype Jun 1 '12 at 7:31
Following on @MånsT 's comments - if your main goal is to pass the course, then it would help if you told us the syllabus and maybe the text you are using. For broader understanding - quite a lot of intro. stats. is "common sense thinking" supplemented by a few key ideas and formulas and such. –  Peter Flom Jun 1 '12 at 10:39
We are using an online book that was written by one of our senior lecturers, I am studying sampling distributions at the moment and finding it pretty hard –  Filype Jun 4 '12 at 1:31

The American Statistical Association is actively involved in addressing this question. Its Guidelines for Assessment and Instruction in Statistics Education (GAISE) project has recently issued two reports. One of them describes what introductory college-level statistics teaching should cover.

The stated goals are numerous and general. You can read them at http://www.amstat.org/education/gaise/GAISECollege_Goals.pdf. They range from

Students should believe and understand why variability is natural, predictable, and quantifiable

to

students should know how to interpret statistical results in context.

It is noteworthy that they nowhere mention "binomial," "distribution," or "errors," whereas "inference" is mentioned prominently, as in

Students should understand the basic ideas of statistical inference, including ... statistical significance [and] ... the concept of confidence interval.

Please be aware that not all introductory statistics courses will follow these guidelines. Courses are taught in various departments for different purposes to a variety of student populations. Some of them, for instance, aim to teach technical methods to students who will later be required to apply them. The best resources for learning the objectives of any particular course of study are (a) its syllabus and (b) the introduction to the textbook, if any. It wouldn't hurt to consult the instructor, either: they should have, ready at hand, a clear and complete answer to this question!

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This is a good answer. But does the ASA differentiate what should be emphasized as special topics related to disciplines. i think people work in medical clinical trials need to know certain things that wouldn't be important in business or marketing and conversely business students would need to know things that people in the medical arena would not. –  Michael Chernick Jun 1 '12 at 23:13
. My canonical examples are survival analysis and equivalence testing in medicine (particularly pharmaceutical research) is not so important to MBA students but time series analysis is important to MBA students but not really very important in medicine (I don't include longitudinal analysis under the category of time series even though it involves repeated measurement over time). Longitudinal data analysis is something that people in medicine do need to know something about but may not be important in some other disciplines. –  Michael Chernick Jun 1 '12 at 23:21