The big question for this segment is, how do we effectively use statistics in critical thinking, decision making and future forecasting? [MUSIC] Critical thinking is a pattern of careful, rational, evidence-based thought. It's how we should aspire to think when determining our beliefs and choosing our actions. In particular, we want to take a rational approach to decision making and to predicting future trends. What has that got to do with statistics? Well, plenty. Statistics is all about observing the world around us and building and testing models of the world. That is conceptual structures which describe and predict what we see. Humans use conceptual models to understand and interact with the world. That's just what thinking is. Statistics gives us objective and reliable tools for studying and refining our models. And if the conceptual models we rely on are more accurate. Then decisions and predictions that make sense in the model are more likely to work well in the real world. The main tools of statistics are descriptive statistics, statistical modeling, and hypothesis testing. Descriptive statistics is about describing data, averages, measure of variability, histograms to show the frequency of various values, that sort of thing. With statistical modeling, we can describe relationships between variables. That is, between measured quantities or categories. Hypothesis testing is then used to evaluate the discrepancies between our models and reality. So we know when the models need more work. Many public debates ebb and flow on anecdotal, emotive and rhetorical currents. Think of the debates around vaccinations, homeopathy, gun control and global warming. As a statistician, I believe that if the general public had a better understanding of random variation and just a little knowledge of how statistics work. Then they would be harder to mislead. A good example of this is the autism scare around the vaccine for measles, mumps, and rubella. In 1998, the prestigious British medical journal, The Lancet, published a deeply flawed article by Andrew Wakefield and colleagues. Suggesting that the MMR vaccine can cause autism in young children. The Lancet later retracted the article and Wakefield was eventually barred from practicing medicine. The scientific community has thoroughly debunked both the original article and any link between vaccinations and autism. Nevertheless in the two decades since Wakefield's article. An anti-vaccine movement has flourished, with cherry-picked data, celebrity spokespeople, and shallow science journalism contributing to lower vaccination rates. Scattered outbreaks of previously controlled diseases and the deaths of hundreds of children. Much blame can be given to news media for perpetuating the confusion through the illusion of balanced coverage. Suppose a news article mentions extensive scientific studies finding no connection between vaccines and autism. But for balance, also interviews emotional parents who are convinced that vaccines are to blame for their children's autism. Effectively, they are asking the public to make up their own minds about the strength of the evidence on both sides, but that's exactly what statistics does. It gives objective reliable measurements of the strength of evidence. If the public understood that pure chance implies many children will be diagnosed with autism shortly after vaccination. And that statistics can take a very large sample into account and detect, with great sensitivity, any connection between vaccination and autism. Then this debate would have been put to rest years ago, saving many children's lives. When you're choosing between two or more possible strategies or courses of action. You need to think about the outcomes that each of those strategies are likely to lead to. And how desirable or undesirable each of those outcomes would be. Weighing the merits of the various possible outcomes is a subjective task. For instance, a strong economy today, and a healthy environment tomorrow are both important. But how should we balance those goals against each other? Statistics cannot tell us what's important in life, but if we can decide what we want, then statistics can help us make it happen. Remember before, I said that statistical modelling characterizes relationships between variables. For decision making, if we can build a model based on the choice we make, the resulting outcome, and perhaps some intermediary variables. Then we have a probabilistic model of how good or bad the result of each of our possible choices will be, and we can choose the best. Consider a traffic engineering example. Suppose we're trying to choose the signal timings at an intersection, so as to minimize the overall average waiting time for drivers. Using observation and statistics, we can build an accurate model of traffic density and driver behavior. And then simulate traffic passing through the intersections under various configurations. From the simulation results, we can estimate the relationship between signal timings and the average waiting time. Timing the lights on that basis should get everyone where they're going faster. Like any other kind of statistical estimation, predicting future trends relies on a model. Some kind of simplified theory about how the data we observe are generated. A familiar example of prediction, modern meteorology goes back about a century and a half to the development of the telegraph and the first networks of weather observation stations. Since then, weather prediction has continued to improve in its accuracy. The improvement is due to three factors working together. Firstly, more data. The ever growing historical weather data record, and the increasing number of weather stations and satellites, and the richness of the data they produce gives us much more information to work with. Secondly, better models. Meteorologists have built increasingly accurate predictive models, relying on advancements in physics and other relevant sciences. And they validated and refined the models on the basis of their agreement with collective data. Thirdly, computers. Modern weather prediction begins with a current snapshot of the Earth's oceans and atmosphere. And uses a computer model to simulate the changes in temperature, air pressure, humidity, etc, over a period of time. Increasing computer power allows more detailed simulations and better predictions. In more recent years, interest has grown in longer term climate prediction. In principle, the methods are the same. Build a computer model of the world's current climate and simulate its development over the coming decades using knowledge from physics, chemistry and biology. It's a lot hotter because we're trying to predict further ahead but also because we need to anticipate how ecological systems will behave in novel circumstances. No one's saying it's easy, but statistics is a key tool in building ecological and climatological models that are comprehensive and robust enough to make the best possible predictions. Statistical methods amplify our cognitive abilities. Strengthening our critical thinking by giving us powerful objective tools to make decisions and predictions. Embracing these tools will keep us well informed and in control of our destiny. [MUSIC]