Today we're going to continue our discussion of statistical models by showing how we can find if there are differences between multiple groups using a collection of models called ANOVA. ANOVA, which stands for Analysis of Variance is similar to regression (which we discussed in episode 32), but allows us to compare three or more groups for statistical significance.

Do you think a red minivan would be more expensive than a beige one? Now what if the car was something sportier like a corvette? Last week we introduced the ANOVA model which allows us to compare measurements of more than two groups, and today we’re going to show you how it can be applied to look at data that belong to multiple groups that overlap and interact. Most things after all can be grouped in many different ways - like a car has a make, model, and color - so if we wanted to try to predict the price of a car, it’d be especially helpful to know how those different variables interact with one another.

Today we're going to finish up our discussion of Bayesian inference by showing you how we can it be used for continuous data sets and be applied both in science and everyday life. From A/B testing of websites and getting a better understanding of psychological disorders to helping with language translation and purchase recommendations Bayes statistics really are being used everywhere!

There is a lot of excitement around the field of Big Data, but today we want to take a moment to look at some of the problems it creates. From questions of bias and transparency to privacy and security concerns, there is still a lot to be done to manage these problems as Big Data plays a bigger role in our lives.

Today we're going to discuss the Binomial Distribution and a special case of this distribution known as a Bernoulli Distribution. The formulas that define these distributions provide us with shortcuts for calculating the probabilities of all kinds of events that happen in everyday life. They can also be used to help us look at how probabilities are connected! For instance, knowing the chance of getting a flat tire today is useful, but knowing the likelihood of getting one this year, or in the next five years, may be more useful. And heads up, this episode is going to have a lot more equations than normal, but to sweeten the deal, we added zombies!

Today we're going to start our two-part unit on data visualization. Up to this point we've discussed raw data - which are just numbers - but usually it's much more useful to represent this information with charts and graphs. There are two types of data we encounter, categorical and quantitative data, and they likewise require different types of visualizations. Today we'll focus on bar charts, pie charts, pictographs, and histograms and show you what they can and cannot tell us about their underlying data as well as some of the ways they can be misused to misinform.

Today we're going to talk about Chi-Square Tests - which allow us to measure differences in strictly categorical data like hair color, dog breed, or academic degree. We'll cover the three main Chi-Square tests: goodness of fit test, test of independence, and test of homogeneity. And explain how we can use each of these tests to make comparisons.

Today we’re going to talk about confidence intervals. Confidence intervals allow us to quantify our uncertainty, by allowing us to define a range of values for our predictions and assigning a likelihood that something falls within that range. And confidence intervals come up a lot like when you get delivery windows for packages, during elections when pollsters cite margin of errors, and we use them instinctively in everyday decisions. But confidence intervals also demonstrate the tradeoff of accuracy for precision - the greater our confidence, usually the less useful our range.

We may be living IN a simulation (according to Elon Musk and many others), but that doesn't mean we don't need to perform simulations ourselves. Today, we're going to talk about good experimental design and how we can create controlled experiments to minimize bias when collecting data. We'll also talk about single and double blind studies, randomized block design, and how placebos work.

Today we’re going to talk about data relationships and what we can learn from them. We’ll focus on correlation, which is a measure of how two variables move together, and we’ll also introduce some useful statistical terms you’ve probably heard of like regression coefficient, correlation coefficient (r), and r^2. But first, we’ll need to introduce a useful way to represent bivariate continuous data - the scatter plot. The scatter plot has been called “the most useful invention in the history of statistical graphics” but that doesn’t necessarily mean it can tell us everything. Just because two data sets move together doesn’t necessarily mean one CAUSES the other. This gives us one of the most important tenets of statistics: correlation does not imply causation.

Today we're going to talk about degrees of freedom - which are the number of independent pieces of information that make up our models. More degrees of freedom typically mean more concrete results. But something that is statistically significant isn't always practically significant. And to measure that, we'll introduce another new concept - effect size.

Today we're going to wrap up our discussion of General Linear Models (or GLMs) by taking a closer looking at two final common models: ANCOVA (Analysis of Covariance) and RMA (Repeated Measures ANOVA). We'll show you how additional variables, known has covariates can be used to reduce error, and show you how to tell if there's a difference between 2 or more groups or conditions. Between Regression, ANOVA, ANCOVA, and RMA you should have the tools necessary to better analyze both categorical and continuous data.

Geometric probabilities, and probabilities in general, allow us to guess how long we'll have to wait for something to happen. Today, we'll discuss how they can be used to figure out how many Bertie Bott's Every Flavour Beans you could eat before getting the dreaded vomit flavored bean, and how they can help us make decisions when there is a little uncertainty - like getting a Pikachu in a pack of Pokémon Cards! We'll finish off this unit on probability by taking a closer look at the Birthday Paradox (or birthday problem) which asks the question: how many people do you think need to be in a room for there to likely be a shared birthday? (It's likely much fewer than you would expect!)

Today we’re going to talk about ethical data collection. From the Tuskegee syphilis experiments and Henrietta Lacks’ HeLa cells to the horrifying experiments performed at Nazi concentration camps, many strides have been made from Institutional Review Boards (or IRBs) to the Nuremberg Code to guarantee voluntariness, informed consent, and beneficence in modern statistical gathering. But as we’ll discuss, with the complexities of research in the digital age many new ethical questions arise.

Today we're going to begin our three-part unit on p-values. In this episode we'll talk about Null Hypothesis Significance Testing (or NHST) which is a framework for comparing two sets of information. In NHST we assume that there is no difference between the two things we are observing and and use our p-value as a predetermined cutoff for if something seems sufficiently rare or not to allow us to reject that these two observations are the same. This p-value tells us if something is statistically significant, but as you'll see that doesn't necessarily mean the information is significant or meaningful to you.

Today, we're going to begin our discussion of Big Data. Everything from which videos we click (and how long we watch them) on YouTube to our likes on Facebook say a lot about us - and increasingly more and more sophisticated algorithms are being designed to learn about us from our clicks and not-clicks. Today we're going to focus on some ways Big Data impacts on our lives from what liking Hello Kitty says about us to how Netflix chooses just the right thumbnail to encourage us to watch more content. And Big Data is necessarily a good thing, next week we're going to discuss some of the problems that rise from collecting all that data.

Today we’re going to talk about measures of central tendency - those are the numbers that tend to hang out in the middle of our data: the mean, the median, and mode. All of these numbers can be called “averages” and they’re the numbers we tend to see most often - whether it’s in politics when talking about polling or income equality to batting averages in baseball (and cricket) and Amazon reviews. Averages are everywhere so today we’re going to discuss how these measures differ, how their relationship with one another can tell us a lot about the underlying data, and how they are sometimes used to mislead.

Today, we're looking at measures of spread, or dispersion, which we use to understand how well medians and means represent the data, and how reliable our conclusions are. They can help understand test scores, income inequality, spot stock bubbles, and plan gambling junkets. They're pretty useful, and now you're going to know how to calculate them!

Today we're going to talk big picture about what Neural Networks are and how they work. Neural Networks, which are computer models that act like neurons in the human brain, are really popular right now - they're being used in everything from self-driving cars and Snapchat filters to even creating original art! As data gets bigger and bigger neural networks will likely play an increasingly important role in helping us make sense of all that data.

Today is the day we finally talk about the normal distribution! The normal distribution is incredibly important in statistics because distributions of means are normally distributed even if populations aren't. We'll get into why this is so - due to the Central Limit Theorem - but it's useful because it allows us to make comparisons between different groups even if we don't know the underlying distribution of the population being studied.