It can be difficult to find good studies about Natural Family Planning on the internet. The list below contains some of the most important and influential studies for NFP, so you can read the data yourself from the primary source and figure out what's best for you and your family.
A paper by Dr. Richard Fehring (of Marquette University) published on the USCCB (United States Conference of Catholic Bishops) website. It provides an overview of the history of the Marquette method and a summary of studies about its effectiveness.
Pages 13-14 are worth calling out since they summarize the rules of the Marquette Method nicely.
Also, the last page of the PDF contains a table that's really useful — it summarizes the efficacy observed by several different NFP studies of the Marquette Method. For example, you could compare this against the table provided by Contraceptive failure in the United States (also linked below). If you compare the charts, you'll see that the Marquette Method performs better than condoms in both typical and perfect use.
This is a Marquette University study published by Dr. Richard Fehring. The goal of the study was to research the effectiveness of the Marquette Model over a 2-year period while comparing use of the ClearBlue fertility monitor to mucus observation methods. As you can see in the link, the results showed that the fertility monitor proved more effective at avoiding unintended pregnancy, with only 6 out of 212 women who used the monitor experiencing an unintended pregnancy after two years.
This article, published in the Journal of Reproductive Medicine (2009), compares the Marquette Method to the Creighton Method. Of course, many people are interested in comparing these methods to know which is more effective. The results of this study indicate that the Marquette Method is more effective when trying to avoid pregnancy.
This manuscript, published in 2011 by James Trussell, PhD, provides information about the failure rates of (non-NFP) contraceptive methods. That's really useful because we can use it to compare against NFP methods of avoiding pregnancy to get an idea of how effective everything is in comparison. For example, compare the failure rates in this study against those in The Marquette Model: An Evidenced-based Electronic Hormonal Fertility Monitor Aided Method of Family Planning.
This web page, from the Centers for Disease Control and Prevention, includes information about the typical use failure rate of different birth control methods. The page says the typical use failure rate of condoms is 13% and oral contraceptives 7%, citing Contraceptive Technology, 21st ed. The same page cites a study, Effectiveness of Fertility Awareness-Based Methods for Pregnancy Prevention: A Systematic Review, that finds the typical use failure rate of the monitor-only Marquette Method to be 2-6.8%. So, by the CDC's own research, the effectiveness of fertility awareness methods is on par with or better than that of condoms or oral contraceptives.
This isn't exactly a research study, but it still felt appropriate to include it on this page. This is essentially a text book about the Marquette Method of NFP, published by the creator of the Marquette Method, Dr. Richard Fehring. Although it's intended for Marquette Method instructors, it can be a great resource if you want to study the Marquette Method in depth yourself and get a better understanding of how and why the Marquette Method works with your body.