[MUSIC] Statistics plays a significant role across the physical and social sciences. And it's arguably the most salient point of intersection between diverse disciplines. >> Statistics is the common language of science. Scientists use statistics to convert data into useful information. This is exactly what you will do in this course. Through your own original research, you will convert existing data into useful information. You use data to tell a story that's of interest to you, and of value to others. Statistics is there for a process, where we are collecting data, summarizing data, and interpreting data. The process of statistics starts when we identify what group we wanna study or learn something about. We call this group the population. The word population, and throughout its entire course, is not just used to refer to people. It is used in a more broad statistical sense. Where population refers to an entire group you want to focus upon. This can be an entire group of people or animals or insects, or inanimate objects like apartment buildings or craters on Mars. [MUSIC] >> For example, we might be interested in the opinions of the population of US adults about the death penalty. [MUSIC] How the population of mice react to a certain chemical. [MUSIC] The average price of the population of all one bedroom apartments in a certain city. Population, then, is the entire group that's the target of our interest. In most cases, the population is so large, that as much as we want to, there's absolutely no way that we can study all of it. A more practical approach would to be to examine and collect data only from a sub-group of the population, which we call a sample. We call this first step which involves choosing a sample and collecting data from it, producing data. Since for practical reasons we need to compromise and examine only a subgroup of the population rather than the whole population, we should make an effort to choose a sample in such a way that it will represent the population as well. [MUSIC] James Thompson has been studying pollination success of an obscure flower that blooms at high altitudes, the glaciered lily. We're looking at a high altitude species. And as people interested in global change and climates have realized this is where we might first see things like species doing poorly because the situations have changed, and in fact there's a lot of focus on high elevation research in the general context of climate change. >> There are millions of these flowers across the Rockys. And Professor Thompson can not study them all, he has to choose a sample. >> If I'm to say anything accurate those data have to really reflect what's happening out here. So for instance when I look at a sample of flowers I have to be thinking all the time about whether I'm selecting a set of flowers that's adequately representative of the whole of what I wanna talk about. [MUSIC] >> This is true whether we're studying flowers, craters on Mars, or the opinions of US adults regarding the death penalty. Our sample would not represent US adults, if we only asked Republicans or only asked Democrats. Such a sample would not represent the population. Data sets can be very different depending on what is being studied. This data can take the form of answers to survey questions, tables of numbers such as crater details, or in the case of glacier lilies, observations collected over many years. Essentially, I've asked a very simple question. What causes a flower to be a success? Does it get pollinated? Does it set a fruit? Does it make seeds? How many seeds does it make? >> To make sense of this data, it needs to be summarized in a meaningful way. This is called exploratory data analysis. Exploratory data analysis often reveals new ways to think about the data. >> As frequently happens in science, the more carefully I looked, the more things I saw to interest me. >> Exploratory data analysis helps scientists refine their questions. And sometimes even reveal entirely new questions. >> If climates are changing, relationships between plants and pollinators and other mutually beneficial relationships, those may be disrupted. >> Scientists studying climate change have often wondered what effect a warming climate will have on the relationship between plants and animals. Is it possible that small changes in climate could have a big impact on these relationships? Exploratory data analysis suggests that that is a question Professor Thompson might be able to answer using 30 years of data. This leads up to the final step, inference. What can we infer about the population as a whole from the data in our sample? Remember, after exploratory data analysis, we're able to ask specific questions of our data. Inference is where we come full circle with the hope of revealing new knowledge about the population. So what can Professor Thompson infer about Glacier Lilies? What his data revealed is that glacier lilies and the bees that pollinate them are becoming separated in time. As the climate warms, lilies bloom sooner before the bees arrive. >> My paper on glacier lilies, as far as I can tell, is the first demonstration of it or the first even plausible demonstration of it. It's not an easy thing to show. It's an easy thing to say, hey, this could happen. My long term data sets have allowed me to do is to say, yeah, and it looks like it has happened. >> James Thompson was able to explore his data to show how climate change causes plants and animals to become disconnected in time. You too will be looking at large data sets and asking new questions of interest to you. You won't be creating new data, but you will create new knowledge through exploratory data analysis and inferential data analysis. Statistics education is most often conducted within a discipline specific context or as generic mathematical training. Our goal is instead to create meaningful dialogue across disciplines. Ultimately, this experience will help you on your way to engaging in interdisciplinary scholarship at the highest levels.
