# Introduction for Chi-Square study

Psych 2002C   Instructions for Exercise 3a (Introduction for Chi-Square study)

This exercise will utilize the approach that we used in the previous two exercises.  This approach is one in which you  work “backwards” in the sense that you start with a particular kind of analysis (so far, we used t-test and ANOVA) and then develop a study which utilizes that particular kind of analysis for its results. Like in the previous exercises your method will be derived from existing studies and your results will be derived in a “backwards” fashion from the outcome predicted by your hypothesis. Note, you must choose a different study area from that used in exercises 1a/1b. and 2a/2b.

In this part (3a) you will be writing the Introduction (literature review and hypothesis). However, you will not complete the Chi-square calculations until you get to part 3b. However, for this part it is not necessary to know the computational methods, only the general rationale. You may wish to choose a Chi-square Goodness of Fit or a Chi-square test of independence (called “association” in video module). The first one (using a single variable) design is easier to construct, but the second one (using two variables) design gives you more to discuss.

A note on Chi-square. So far, you have been analyzing data that represents measurements on some dependent measure. The numbers actually represented the amount of something (like the level of depression, the size of a brain, the length of sleep, etc.). For chi-square the numbers will not be measuring a dependent measure, but instead will be simply a count (frequency) of people (or events) that fall in a certain category. Hence, you will be working with categorical or  frequency  data. So, when you are preparing your hypothetical study, ask yourself, “Will my numbers be simple frequencies (correct), or will they be measurements (incorrect)?”

The “Goodness of Fit” tests simply looks at how some real data (called “observed frequencies”) matches up with what was predicted to be the frequencies under the null hypothesis (called “expected frequencies). For example, one might have a null hypothesis that equal numbers of men and women go into veterinary medicine. Therefore, if there are 80 students graduating from a vet school we would expect 40 to be men and 40 to be women. However, suppose we actually see that the class consists of 56 women and 24 men (a 70%/30% split). There is a mismatch between what we expected and what we see. The chi-square goodness of fit test will tell us if the mismatch is big enough to be significant (indicating a real gender difference in this profession) or not significant (just due to chance variation from one year to the next).

The chi-square “test of independence” uses the same basic way of comparing the observed and expected frequencies, but is set up so as to see if two different variables are affecting one another (described as an “association” or “contingency” in other books). To take the example of vet students above, suppose we wondered if a student’s gender has an effect on what kind of veterinary medicine they practice (small animal (suburban) or large animal (farm)). There are two variables here: gender and type of practice; we wonder if they are independent or associated (if one is contingent upon the other). The basic rationale is such: If 70% of the current vet students are women, then 70% of those going into suburban practice should be women and 70% of those going into farm practice should be women. If it turns out that the actual numbers of men and women that we observe going into the two sub-specialties are quite different from expected, then it shows that they are not independent but rather are related (an association between gender and choice of sub-specialty). Of course, the analysis all boils down to a number (the chi-square value) that you can check for significance in a table.

Finding a study to base yours on. If you have no idea what might interest you, first go to one the sites (or one of your own choosing) below for good ideas of what is going on currently. You can use key terms that you find here when you go to PsychInfo, Google scholar or Summon to locate an original study.

http://www.apa.org/news/psycport/index.aspx    APA site for current news

http://www.sciencedaily.com/    Use “Mind/Brain” tab

Once you have a general idea of what you want to look for, go to PsychInfo (or alternatives–see below) and search for “key words” (button above main search box brought up when you hit “Search form”). If your key word does not register, then trying searching for it in “Thesaurus” to find perhaps a better word for what you are looking for.

Once you have succeeded in getting a list of articles related to a certain topic, you can “search in current results” (button under main search box) to look for the key word “chi-square”. If you want to get a little more detailed, try adding the terms “goodness of fit” or “test of independence”. A quick reading of the abstract will allow you to see if the study is the kind of thing you may want to look at more closely. If you like it, it will become the first building block of the introduction to your study. Try to avoid studies that have overly-complex designs and analyses (you know what I mean here; you probably feel they are all that way).

Two convenient alternatives to PsychInfo are Google Scholar (http://scholar.google.com/) and a program on the library’s Home page called Summon. In these, you simply put in a number of key terms (e.g., autism, head size, chi square) and they will return the references. NOTE—the full text of the article is often designated by a “pdf” or “html” box off to the right of the main listings.

Having found a starting article you will build your literature review and hypothesis in the same way as you did in exercise 1a. Your key articles will mention areas that need follow-up research. Moreover, you will think of ways in which you could investigate some aspect of the study more completely. Just remember that as you construct your hypothesis you need to keep in mind that you will need to make a Method section (part of exercise 2b). So you should select a topic that will allow you to borrow some of the techniques and measurements that you have read about. It is not wise to attempt to dream up these kinds of things when you are not actually working in the field. Note that any borrowing should be restricted to specific techniques in the Methods section (and nowhere else in the report) that you cannot put into your own words.

Since your Introduction will include at least 5-6 references you should attach a formal references page (with proper APA format) at the end. The most critical thing is that it reviews the literature and presents your hypothesis in a clear and complete fashion.