Inferential Statistics Today and next thursday

Check in Method Draft due today 3 rd article assignment is posted –It is due November 29 th For Tuesday: Articles for in-class discussion –These are popular media articles about problems in research, it should be a fun discussion –Please come with one question or comment about each article –I will bring snacks!

Before we get to statistics… Proposal draft –More about writing an introduction

The structure of an introduction 1st paragraph –A general introduction of the problem with some references 2nd paragraph –Often begins with theory or empirical studies 3rd paragraph –May continue this…and more paragraphs if necessary

More introduction 4 th paragraph…and perhaps more –Identifies where you will add to the research –May focus on methods, or limitations or previous studies 5 th paragraph –Summarizes what you have said in brief –States the research questions or hypotheses clearly and in moderate detail

Now back to statistics Inferential statistics: Today –Null and alternate hypotheses –Type I and Type II error –The “normal curve” the “empirical rule” and probability –The Chi-squared test

Stating hypotheses Comes before any statistics Uses basic language But requires careful thinking about the language you use Thinking that stems from the scientific approach –We never prove anything –We only find support for it

Hypothesis testing Divides a study into two possible outcomes –Study does not only mean experiment –Can mean survey, observation, etc. Support for the “null hypothesis” or… Support for the “alternate hypothesis” You can only end up with one or the other

The null hypothesis Is usually what we don’t want to find support for –Note, we do not say it is what we “disprove” –We can say that we “reject” it Perhaps a commonly accepted status quo A stereotype What we believe to be untrue What was true once and is no longer true

The alternate hypothesis What we propose is actually the case Usually we have some reason to think that things aren’t just “status quo” Its what we hope will emerge from our study or data –We say we “find support for it” But if it doesn’t emerge in our data –We “fail to find support for it” –We “fail to reject” the null hypothesis

The null hypothesis College students have high rates of casual sex –This could be a stereotype –A pop culture myth –Could have some research data to support it That is perhaps outdated –Could be true, but we the researcher think it isn’t

The alternate hypothesis College students do not have high rates of casual sex –Maybe we have qualitative interviews that suggest casual sex is a myth –Maybe we think that problems with STDs has changed people’s behavior

Now, back to statistics Inferential statistics –Making guesses about what is happening in the population based on what we see in our sample –How can we do this

Type I and Type II error Hang on to your logic hats These make most sense when you know some statistics This is just a conceptual introduction

Type I error When I believe that my alternate hypothesis is supported But actually the support is a statistical accident And actually I’m wrong.

Type I error I do a study I propose that people are smarter than cats (this is my alternate hypothesis) My sample data do show that people are smarter than cats But actually this is a statistical accident Cats actually are smarter than people This is a type I error

Type 2 error When, after my study, I believe that my alternate hypothesis was NOT supported But actually the lack of support was a statistical accident –Often due to small sample size This is a type two error

Type I and type II error Science tends to focus on Type I error We agree that a chance of type I error 5% of the time is OK Type 2 error is harder to predict exactly –We usually agree that type 2 is OK 20% of the time A more strict cutoff for Type I error is probably good since we tend to favor our own beliefs and think we are right

Type I and Type II error are both bad Do you want to be the person who thinks you have discovered the cure for HIV but really you haven’t? Do you want to be the person who really does discover the cure for HIV but concludes you haven’t? Neither option is very appealing

The empirical rule Is a series of probability statements about data Is based on how data occur within the normal distribution The empirical rule forms the conceptual basis for a lot of inferential statistics