Can having a pet improve your health? It's a question that's fascinated scientists and pet owners for years, but the latest research seems to suggest that no, maybe it can't.

The study showed that children in households who had cats and dogs were healthier overall in a number of ways – but after accounting for controlling factors, it also showed that the cats and dogs were unlikely to be the reason why.

The findings are a counter argument to many other studies that have found a link between pets and healthiness, but members of the team from the RAND Corporation, a research nonprofit, say they were surprised by the results too.

"We could not find evidence that children from families with dogs or cats are better off either in terms of their mental wellbeing or their physical health," says one of the researchers, statistician Layla Parast.

"Everyone on the research team was surprised – we all have or grew up with dogs and cats. We had essentially assumed from our own personal experiences that there was a connection."

One of the reasons this new study is worth taking note of is that the sample size is so large: it looked at 5,191 households in total, using data from the California Health Interview Survey collected in 2003. That's bigger than many other pet and health studies.

What also sets this research apart are the advanced statistical calculations used to control for multiple factors that could also boost a child's wellbeing, including being in a higher income family, living in a wealthier area, or the type of family housing.

As expected, the kids with pets were doing better overall: they tended to have better health in general and slightly higher weights, and were more likely to be physically active. They were even noted as being more obedient.

But when the findings were adjusted to account for a bunch of other variables that can influence wellbeing, the health differences between the pet-owning households and the non-pet-owning households almost completely disappeared.

Those results will seem strange to anyone who's felt the happiness of owning a pet, including the RAND researchers themselves.

"I've talked to a lot of friends of mine whose reaction was like yours and mine: No!," Parast told James Hamblin at The Atlantic. "This can't be true. What kind of 'science' are you doing?"

One possibility is that owning a pet signifies better health rather than causing it, but there's some hope for those of us who are still sure that pets really can be good for us.

To begin with, the data in this research only looks at a snapshot of children's health at one particular point in time, rather than over months or years.

And the team behind the analysis says further studies would be required to get a definitive answer on whether pets are responsible for better health, with some participants given pets and others not, and wellbeing tracked over 10 years or more.

"We're not completely ruling out that pet ownership leads to good health," Parast told The Atlantic. "We're just saying you need to step back and see that people who own pets are different from people who don't in a whole lot of ways."

What's more, Parast says owning a pet brings the joy of companionship and a host of other benefits that aren't necessarily recorded in standard measurements of health like BMI and the time we spend being active.

So there's hope yet for the hypothesis that owning a cat or a dog can improve your health – we just need more evidence for it.

"It would be great to have a reason to hand out cuddly puppies to everyone who needs better health," Parast told The Atlantic.

"I would be completely in favour of that. But there's no scientific evidence right now that shows that."

The research has been published in Anthrozoos.