# Statistics? What do they really mean?

Statistics can often scare us without really understanding what they actually mean…… Dr Robin Turner shares more on what to look for…

We met Robin during a workshop that we all attended for PC4… the Primary Care Collaborative Cancer Clinical Trials Group that was established in February 2009 and is funded by Cancer Australia… Our conversation lead to this wonderful opportunity for Robin to shed some light on what Claudine and I have always found challenging… Understanding STATISTICS! For those going through cancer or any health challenge, we are often faced with statistics in the form of percentage e.g. 50% chance of… ratios e.g. 1in 2… or 4 times more likely to… But what does it really mean? Thank you Robin for taking the time to bring some very valuable things to look for…

## Profile information

Your Name | Dr Robin Turner |

City of Residence | Sydney, Australia |

Occupation or Experience | I’m a biostatistician working in public health research at UNSW Australia. I have a PhD in statistics, a Masters of Biostatistics and a BScHons in Physics |

Web Links | https://sphcm.med.unsw.edu.au/people/dr-robin-turner |

Your Passions/Interests | My passion is to ensure that the research I’m involved in is high quality and leads to improving people’s lives. I also enjoy developing statistical methods and teaching statistics. |

**Often we get statistic in terms of percentages or ratio’s e.g. 50% of the population or 1 in 2 will be affected by cancer… So what are statistics and how can we better understand what they mean?**

Fundamentally a statistic is just a summary measure of data collected usually from a sample (we also have statistics done on populations for example the population census). Because of the variety of types of data and settings where the data is collected from, there are a variety of different measures used to summarise this information.

Percentages are common measures to describe how many out of 100 will have a particular characteristic. In the example given above “50% of the population … will be affected by cancer”, people may not necessarily have an inherent understanding of percentages and may find it useful to think about it as out of every 100 people in the population, 50 will be affected by cancer. These often get converted to things like “1 in 2” where they have converted the fraction 50/100 to 1 in 2 by dividing 50 by 50 and 100 by 50 to make it out of 2 people instead of 100 people.

**Confused?** There is no standard way of reporting things so the same statistic might be reported in a multitude of ways. One way to help understanding is to either ask for or convert the number into “out of 100 people how many would be affected by cancer” this version is often easier to understand.

But what I have glossed over is how relevant is this percentage to me? The key to this is how many people was this out of and are those people the same as me or different to me? What do I mean by this, in the example of 50% of the population affected by cancer – what do we mean by population? Is that all people of all ages in the world? In Australia? Older people? Younger people? Males? Females? High risk? Low risk? Understanding where the number has come from and who it is based on may help you understand how relevant the number is for you.

**What are the indicators that a particular statistic is relevant to us or not relevant?**

There are a couple of important aspects about whether a statistic is relevant or not. Is the statistic based on people similar to me? Is it from a study that the people would have similar characteristics to me and therefore is likely to apply to me also? Do I believe the study that the statistic comes from? Is it a large well designed study and have the results been replicated?

** For someone going through cancer or any other health issue, what questions can be asked to better know where our doctors get their statistics around side effects, survival, treatment and recurrence so that better decisions around choices can be made?**

Excellent question. What I would want to understand is what level of evidence is there to support those statistics and what uncertainty is there around the estimate. So statistics as a discipline is really about making sense of data when there is uncertainty present. There will never be a statistic that is 100% precise and known exactly but there will be an accompanying measure of precision around that. Ideally there should be high quality evidence with high precision (small uncertainty).

**When researching on the internet, what are the indicators that the source of the statistic is reliable and accurate?**

This is a really difficult question to answer in this day and age! I’m fairly cynical when I look for information on the internet, it’s very easy for non-science to be presented as science or for science to be taken out of context. As a statistician I’m looking to see that the study design was appropriate for the question being asked, that the statistics have been done correctly and other measures of quality show that the study is good quality. I think without training in these areas it’s very difficult to assess information. I also have to rely on content experts to understand what could be a major problem for a particular study that wouldn’t just be a purely statistical issue. It’s difficult to give advice outside the statistical area where my skills lie.

**What other message do you feel is important to give around statistics in relation to health and wellbeing?**

Think about the plausibility of numbers and where they come from. Anyone can create a statistic but an expert (actually a team of experts covering all the skills needed for the area) will adjust for important factors to ensure the correct statistic is estimated. Often we see statistics given to sell products, I’m thinking of some of the ads on TV and then the fine print will say it was based on for example 4 people. Check to make sure the statistic comes from a large enough sample to be meaningful, small samples will be very imprecise.

**If someone was told they had a 4 times greater chance of getting bowel cancer – what does that actually mean?**

This is an example of a ratio measure/statistic and these are often the hardest measures to understand. The example here of having 4 times greater chance of having bowel cancer sounds scary but because we don’t know the actual risk of getting bowel cancer I.e. Is it 1 out of 10, 1 out of 1000 or some other level of risk, then it’s very difficult to assess what this ratio means. So if your risk of bowel cancer without the implied risk factor was 1 out of 10, then saying your risk is 4 times greater means your risk is actually 4 x 1 out of 10 so it’s now 4 in 10. For me this would be a big increase in actual risk of having cancer. But often risk is much much smaller than that, often we’re talking about risk of 1 in 1000 (or even smaller!). Then if your risk is 4 times greater then it’s now only 4 in 1000, which to me is a much smaller increase in risk. So if you’re given a ratio measure like this, I would always ask for it to be converted into absolute risk, so out of 100 people (or 1000 or which ever number makes most sense to you) how many would get bowel cancer and if the risk is 4 times higher or however many times higher or lower how many would get cancer. This should help you understand what your actual risk is and whether a particular increase is a big or small increase in actual risk.

These ratio measures are very common, because the way we analyse studies is primarily set up to estimate ratio measures, we don’t often then convert back into absolute risk. So you may come across these quite frequently so it’s important to remember that the decision you make based on it will depend on the actual absolute risk (I.e. Is it 4 in 10, or 4 in 1000, or 4 in 1000000 or some other amount compared to the original risk I.e. 1 in 10, 1 in 1000 or some other amount) not necessarily the ratio measure itself.