Statistics for coffee and poop are surprisingly hard to come by. Few studies have looked into this in depth. (It's a bit of crappy topic for a PhD thesis.)
In one of the few studies that looked at this, Brown et al found that 29% of the 99 health volunteers they studied reported that coffee induces a "desire to defecate" within 20 minutes.
This effect was more common in women, with 63% of women reporting this effect. Brown et al noted that this gender difference was indeed statistically significant. (p < 0.01)
Source: Effect of coffee on distal colon function.
Timing of the Coffee Laxative Effect
Researchers then tested each person in the study who reported a laxative effect of coffee by looking at their bowel activity as they drink coffee.
Upon drinking coffee, each volunteer experienced strong and immediate movement of their bowels as registered on the scientists' instruments.
By around 15-20 minutes, this effect reached its maximum.
By around 1 hour, it was over.
When they tried the same experiment with hot water; the same patients did not experience any effect showing that this laxative effect likely came from something inside the coffee.
Coffee as a Medicine: Surgical Recovery
Coffee's laxative effect is so scientifically legitimate, that some some smart researchers have tried using it to speed up surgical recovery.
When patients get bowel surgery, their bowels stop moving for up to a few days. This keeps people in the hospital and delays their recovery. With each hospital costing thousands of dollars, this issue has significant financial implications as well.
A meta-analysis of 6 trials covering 601 patients found that patients who drank coffee during their surgery recovery had their first bowel movement 9 hours faster. (CI: -16.97 to -2.99) Coffee helped these patients' bowels return to normal significantly faster.
Coffee also helped patients return home faster. Their hospital stays were around 0.74 days shorter than patients who did not drink coffee. (CI: -1.14 to -0.33)
Effect of postoperative coffee consumption on gastrointestinal function after abdominal surgery: A systematic review and meta-analysis of randomized controlled trials
Related Article: Coffee + Lifespan
Coffee is not just good for surgical patients, it's been shown to correlate with a longer life as well for men and women. We don't exactly know the mechanisms, but it does go to show that drinking coffee is probably pretty good for you.
Related Article: Caffeine + Calorie Burn
Coffee also may help with losing weight and preventing diabetes. Researchers found that out of the thousands of patients they followed in the UK, those that drank coffee and lost weight had a lower risk of diabetes compared to those who did not regularly drink coffee