The Chi-Square Statistic


We have been talking about statistics, and how to understand the statistics piece of a research article. Today we will start looking at the most common statistical tests used in health-care research. We will not talk about how to do these tests. Instead we will focus on how and why these tests are used. We will begin with the Chi-square.

Chi-square is used to analyze the difference in proportions for categorical data. If you remember, categorical data is information with discrete groups like race, sex, or the rating out of ten given to pain during pushing stage. A proportion is simply the number in the group who experienced something.

Do you remember  when I put the data into a two by two table to find out if the odds were different between groups? This is essentially what a chi-square does. But where chi-square differs is in telling you if the difference between the two groups is considered “too big” to be due to random chance.

Remember, the whole point of statistics is to help you decide if what you are seeing could be the result of random variation.  Chi-square does this by looking at the overall numbers, and comparing them to the numbers for each group.

Birth Worker Survey

For example, in the Birth Worker Survey, we asked participants to rate their agreement with the statement “Midwives should not need to be licensed to practice.”  There was 32 responses and they varied from strongly disagree to strongly agree.  If we collapse the groups into agree or disagree, and remove the neither agree nor disagree group,  we have 7 participants who agree and 17 who disagree. The Two by Two table looked like this:


Midwife Non-midwife Total
Agree 3 4 7
Disagree 2 15 17
Total 5 19 24

There is a big size difference between these groups, so how do we know if the difference is real, or just a result of the random variation?  We use a chi-square statistic.  Chi-square will first look at our total numbers of agree and disagree to find out what we should expect in the boxes for the individual groups.  The expected value is compared to the actual distribution to see how closely they resemble the overall distribution.

The total distribution shows that 29% of participants agreed with the statement. In the groups, 60% of midwives and 21% of non-midwives agreed with the statement.  Because we have such a small number of respondents, I have to use the Fisher Exact method of calculating the chi-square — this doesn’t affect the outcome, it is simply a more robust calculation when you have a small sample and would expect to have less than 5 in any box of the square. Using this method I get a chi-square statistic and p-value.  We will talk about p-value later, but it is the measure of how likely this even is to happen given the null hypothesis (or what is considered status quo).  So the p value tells me how likely I am to see this outcome if there is no difference between midwives and non-midwives beliefs on this statement.

My p-value is 0.6644, which means that if there were no difference between the two groups, I would be likely to get this result.  Therefore, we conclude that this data fails to support a difference in beliefs about midwifery licensing between midwives and non-midwives.

In the Literature

You will see chi-square statistics in many types of studies.  While it doesn’t fit all types of research questions, it is nearly always used to compare participant characteristics if there are two or more groups in a study. You will often find a table with participant characteristics broken down by exposure category, and the chi-square results demonstrating the ways in which the groups are similar or dissimilar.

In this study on dance in labor, the researchers used chi-square as part of the analysis of pain and satisfaction with pain relief.

Coming up

Next time we will dive deeper into Odds and Risk Ratios, and later this week we will look at an example from the scientific literature to review the chi-square.