RStudio Workshop Series: Inferential Statistics

The next thing we might want to talk about is inferential statistics. I didn't include any code in this portion, because the rest of our workshop series is focusing one thing at a time, one test at a time, for our inferential statistics. What is an inferential statistic? This is when you wish to make inferences about data or conduct what we call “hypothesis testing”. So a lot of folks think when they think inferential statistics, they think p-values. If you've ever done a stats class, you probably know what a p-value is; we're going to talk about that. We generally calculate inferential statistics when we're interested in the wider population. We might have a sample, but we generally don't care about the sample, we got the sample because we care about the information for the wider population. There are many ways to calculate inferential statistics, and that's the focus of the rest of the workshop series. So next, in two weeks from now, we're doing a chi-square test, for example. Which is one kind of inferential statistic.

If you were at week one, I did include a handout at the very end of the Word document with my flow chart to help you pick the correct inferential statistic. Let me open that for you now. So we're not going to cover this in detail today, but there are so many different inferential statistics you could choose that I've made a little flow chart to help you pick. And we'll be using this during the rest of the workshop series as well to help us figure out which statistic we might be using. So this is something you could use as an example, if you want to, and again, it's from the workshop from two weeks ago. If you missed that workshop and you'd like this handout, let me know [lplater@uoguelph.ca] and I can e-mail it to you.  

All right, we're almost done today, folks. Just a little bit more. So generally speaking, if you get a p-value, you are doing inferential statistics. So a chi-square, a correlation, a t-test, an ANOVA, a regression. Those are all examples of inferential statistics and we're covering all of those: some this semester, some next semester. What is a p-value? This is something a lot of people get incorrect, because the language is really confusing. So I've left you the confusing language, and we're going talk about it. A p-value is the probability (really important! P-value is a probability) or the likelihood of obtaining the observed data (so your sample data) or more extreme data, given that the null hypothesis (or H0 or H-naught) is true. It's a dense, dense definition. A p-value is a probability, and we get this probability assuming that the null hypothesis is true. Well, what the heck is the null hypothesis? The null hypothesis is the hypothesis saying “nothing's happening”; there's no difference, there's no correlation, there's no relationship between our variables. On the flip side, we also have what we call the alternative hypothesis. This is the hypothesis we're looking for evidence to talk about. Is there a difference? Is there a correlation? Is there some sort of relationship happening? So when we talk p-values, the biggest thing you need to remember, and we'll cover this for the rest of our workshop series as well…but if “p” is less than your alpha [α] value, which is a fancy statistical term to say, most folks and most departments and most fields use α is equal to .05. If p is less than (<) .05, you have found what we say “statistical significance”; you can “reject the null hypothesis”. There is something happening: there is a difference or a correlation or a relationship. 

We also have if p is greater (>) than your alpha [α] level or if p is greater than (>) .05, we can say this is not statistically significant, and the language we use is we “fail to reject HO”, we “fail to reject the null hypothesis”. We cannot say whether there is a difference; we cannot say whether there is a correlation; we cannot say whether there is a relationship. 
That is your super fast, easy, quick introduction to inferential statistics. And if you want to know a little more, that's what the rest of the workshop series is for. We're going to pick on one test at a time and do that test one bit at a time in RStudio. So in two weeks we're doing chi-square, two weeks after that we're doing correlation.