A Literature Example
In this study, Pregnancy outcome in women with previous one cesarean section, the authors did many statistical comparisons of the data. One comparison is easily understood with a chi-square – does having a previous vaginal delivery increase the success rate of VBAC?
So, here are the things we need to answer this question:
Hypothesis: Women attempting a TOLAC with a previous vaginal delivery are more likely to have a successful VBAC than women attempting a TOLAC without a vaginal delivery.
Null Hypothesis: Women attempting a TOLAC with a previous vaginal delivery are no more likely to have a successful VBAC than women attempting a TOLAC than women attempting a TOLAC without a vaginal delivery.
Using the data provided by the study we get this table:
|Vaginal Delivery||No Previous Vaginal Delivery||Total|
From this table we can learn the following things:
A total of 115 with a previous cesarean delivery attempted VBAC.
Of those attempting a VBAC, 71.3% had a previous vaginal delivery.
Of those attempting a VBAC, 83.4% were successful.
When we examine data, we see 89% of the women with a previous vaginal delivery were successful at VBAC, while 69.7% of women without a previous vaginal delivery were successful at VBAC. This appears to support the assertion that a previous vaginal delivery increases the odds of a successful VBAC, but the sizes of the groups are very different. Is it possible this difference is within the expected variation of chance? Using the chi-square statistic will help us decide.
Online Statistics Software
Open a new window with Open Epi, online statistics calculator that you can use to assess the results of studies. Select a Two by Two Table from the side menu, and select the button for Enter New Data. Look at the blank table. You will see one side of the table says “Disease” while the other says “Exposure.” Don’t let that worry you. These are old terms from when epidemiology was all about identifying the cause of things like polio. Where it says disease, it means the event of interest. In general, the exposure will be on the top, and the disease will be on the left. If your table doesn’t look like that, you can select settings and change it. You should notice a + and a – for both exposure and disease/event of interest. The + means it is present and the – means it is not present.
Go ahead and enter the data. In this question, a previous vaginal delivery is our “exposure” because we want to know if having one changes the odds of VBAC. And in this table, a successful VBAC would be our “disease” because it is our event of interest. You could just as easily have not successful VBAC as your “disease,” it just depends on how you ask the question.
After the data is entered in the chart, click calculate. This will open a page with the Chi-Square measures of association. My calculations say the p-value is less than .05, which means the difference is more than we would expect by chance if the null hypothesis were true.
The Chi-Square value is 6.3218. This number is compared to a chi-square table to give the p-value (we’ll talk about those later) of 0.01195. This tells us the difference is statistically significant – or highly unlikely to happen if the null hypothesis is true. So we will reject the null hypothesis, the risk is not same for both groups of women.
If you scroll down on the results, you will see the risk results, and the risk ratio. You will see the risk ratio is 1.277, which means the “risk” of having a successful VBAC is 28% higher for women with a previous vaginal birth.
The odds ratio is 3.527. This means the odds of having a successful VBAC is 3.527 higher if the woman has had a previous vaginal birth.
You will also notice the confidence intervals listed for the estimates of risk and odds ratios. We will talk about those when we talk about p-values next week.