Surviving the statistics course.

The whole syllabus rests on about four ideas

Variation exists, so any two groups will differ a little by chance alone. Some differences are larger than chance comfortably explains. How confident you are depends on how many observations you have and how spread out they are. And a difference being real is not the same as it being important.

Almost everything else — the tests, the assumptions, the output — is machinery for answering those four questions in particular situations. Students who hold onto them find that new tests are variations rather than new topics. Students who memorise procedures find that every week contains a new and unrelated thing.

Choosing a test is a decision tree, not a memory exercise

Nobody in practice recalls thirty tests. They ask three questions and the answer falls out. What kind of outcome do you have — a number, a category, a rank? How many groups are you comparing, and are they independent or the same people measured twice? Are you comparing groups or looking at a relationship between variables?

Write that tree on one page and keep it beside you. It is more useful than any amount of revision, and it is the thing that makes an exam question about which test to use straightforward rather than terrifying.

• ✦What is the outcome: continuous, categorical, or ranked?
• ✦How many groups, and are they independent or paired?
• ✦Comparing groups, or examining a relationship?
• ✦Do the assumptions hold, and what do you do when they do not?
• ✦What does the result mean in the actual units of your field?

Reading output without fear

The panel of numbers your software produces contains about four things that matter and a great deal that does not. Find the test statistic, the p-value, the effect size and the confidence interval, and ignore the rest until you need it.

The p-value tells you how surprising your result would be if there were genuinely no effect. It does not tell you the effect is large, or important, or that your hypothesis is true. The effect size tells you how big, and the confidence interval tells you how precisely you know it. Being able to say all three in a sentence is what a marker is looking for, and it is a much smaller skill than it appears.

Say what it means in your own field's units

This is where marks are won and it is not statistical at all. A significant reduction in readmissions is a phrase. Roughly four fewer readmissions per hundred patients per quarter, with the true figure plausibly between one and seven, is a finding somebody can act on.

Translating output back into the units of your practice demonstrates that you understood it rather than ran it. It also protects you at a defense, where the question is almost never how the test works and almost always what you think it shows.

The honest use of software, and of help

Let the software compute. That is what it is for and no course is testing your arithmetic. What every course is testing is whether you can choose the right procedure, check whether its assumptions hold, and interpret what comes out.

So the rule worth holding yourself to is that you should be able to explain every number in your assignment in plain language before you submit it. Output you cannot account for is a liability rather than an answer, particularly in a course where the next assignment builds on this one. Where a mentor works through it with you, that explanation is the deliverable — the numbers were always the easy part.

Tell the guild your tale.

Name the course, the program and the date it is due. A mentor credentialed in that subject reads it and replies with counsel and a figure within two hours. The reading costs nothing, and sometimes the answer is an honest no.