The Basics of Statistics

So the other day, I was talking to someone about one of the studies I was planning on posting about. I mentioned one of the results, and he said he'd really like to see the means and standard deviations. I thought to myself, "Alright, I'll put those in the post," but when I actually started writing the post, I began to fear that including standard deviations might just be confusing to people who don't have any background in statistics. So I left them out. But I didn't feel very good about leaving them out. So I decided to take action, and write a series of posts on the basics of the sorts of statistics that are used in the research I and other behavioral science bloggers post about.

I've now written 8, yes 8 of them. The topics I have so far are:

  1. Normal Distributions
  2. Standardized Normal Distributions and Z-Scores
  3. Samples, Sampling Distributions, and t-Distributions
  4. Confidence Intervals
  5. Hypothesis Testing With Confidence Intervals
  6. T-Tests

Plus there are two posts that are just examples that you can work through. Anyone familiar with statistics will notice that I've left out a whole bunch of stuff, and if you'll read the posts, you'll notice that I've left out or glossed over even more, but my purpose isn't to provide a complete blog course on statistics in the behavioral sciences. I just want to give people the basics, so that they can read posts and perhaps even the results sections of some of the papers cited in posts, and have a good idea of what's going on. I've written them all over the last 2 days because I've been sick, which means I've been bored. Since I've written them quickly, I've probably made some mistakes. If you notice any, point them out to me. I'll put up the first post Friday, and the rest every 2 or 3 days until we get through them all.

I'm not really sure how far I should go. After t-tests, I'll probably do correlations and then significance tests related to correlations. The next natural step after that would be ANOVA, and I'm not really sure how to explain ANOVA in a blog post except at a really superficial level. If I figure it out, I'll do ANOVA. I'll probably end with non-parametric tests. If you think I'm missing something vital in this list, let me know that too.

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I wonder if something about power, effect size and degrees of freedom would be useful

Austin, I talk about df, of course, 'cause you need to to understand t-distributions and anything that uses them. But I didn't talk about power and effect size. Maybe I'll do that in a separate post, getting into the details of hypothesis testing with statistics a little more (Type I and Type II errors, for example).