Bell Ringer 1. Which countries compose a greater percentage of the world’s population? 2. Developed countries are more likely to damage the ecosystem by [overpopulation, overconsumption].

Statistics and Models So, how can we interpret our data?

Statistics  Statistics is the collection and organization of numerical data.  Statistics is very useful for interpreting our data, and for finding important trends.  Example: Sports statistics, such as YPA (yards per attempt), ERA (earned run avg.)  Example: Climate statistics, such as temperature, humidity.

Statistics  Each statistic must describe a statistical population, or a group that we are interested in studying.  Each member of a statistical population must be similar. However, this does NOT mean that every member of that population is perfectly alike.  Example: Temperature measures how warm each day is.  Our statistical population is days. Every member of our population is a day, but not every day is alike!

Statistics  This graph shows the size of dwarf wedge mussels.  What is the statistical population?  Is every member of this group 100% alike?

Statistics  As shown in this graph, the dwarf mussels have different sizes.  We can calculate the average size of the mussels. This is also known as the mean.

Statistics  Also note the distinctive pattern that the bar graph has. We call this pattern a distribution.  This particular distribution or pattern has a distinctive bell shape. This bell shape is also called normal distribution.

Statistics  In a normal distribution, the data appears symmetric, with the mean value as the apex of the curve.  What is the relative mean for this graph?

Statistics  The probability is the chance that a particular outcome will occur.  For instance, the probability that flipping a coin will cause it to come out heads is 50%. This means that half the time, we will get heads…eventually.  Is it possible to flip 6 heads in a row?  If we do, what is the chance that our next coin flip will produce a heads outcome?

Statistics  Each outcome happens independently…so no matter how many heads or tails we flip, the next flip always has a 50% chance of producing a heads or tails outcome.  We can say that each individual outcome is independent.  That said, what is the probability that we will get 6 heads in a row, anyway?

Statistics  Well, to get the overall possibility, we have to multiply each individual possibility against each other.  Since the odds of one coin flip resulting in a heads is 50%...  To see what the odds of six heads outcomes are, we have to multiply 50% six times.  So, (½)^6 = 1/64 ≈ 1.6%!

Statistics  Recall that I said that each coin flip has a 50% chance of producing a heads outcome.  This does NOT mean that exactly 50% of our flips will produce heads!

Statistics  It turns out that it is very possible to flip 10 coins, and NOT get 5 heads and 5 tails outcomes.  This is because we had a very small sample size – or, the size of our statistical population.

Statistics  The bigger our sample size, the greater the odds of us getting close to the expected probability.  If our sample size is too small, our results will NOT be reliable!

Statistics  Statistically, risk is the numerical probability of an undesirable outcome.  So, if we guess on a true/false question, our risk is 50% (the odds we are wrong).  But, if we guess on a multiple-choice question with four possibilities, our risk is instead 75%!

Statistics  Do you remember risk assessment?  Risk assessment is the act of calculating the risk of each of our possible actions.  So, we are evaluating our possible actions based on how likely they will backfire!

Exit Ticket 1. What is distribution? 2. Describe normal distribution. What should it look like? 3. We roll two six-sided dice. If we rolled a “4” on one die, what is the probability of rolling a “4” on the other die? 4. Which sample size is most likely to give us results closest to the expected probability? a. 20 flips b. 200 flips c flips

Bell Ringer 1. Why is a control group so important for experiments? 2. Statistically, what is risk? 3. You hear the following on TV: “We surveyed several pet owners, and found three of five own dogs, and two of five own cats.” Does this statement prove anything? Why or why not?

Models  Models are representations of objects or systems. We use them to describe concepts, places or phenomena in our world.  What are some examples of models that you are familiar with?  There are four basic types of models we use in environmental science.

Models  There are physical models, which are 3-D representations of other objects.  As such, they must closely resemble the object or system they represent.

Models  Graphical models are visual models.  They show routes and positions of various objects.  Includes maps and charts.

Models  A conceptual model is a verbal or visual explanation of how something works.  Includes flow charts and diagrams.

Models  A mathematical model is one or more equations that represents how something works.  For instance, the exponential function describes exponential growth.

Models  Note that models do not always fall into just one category.  Some models have characteristics of several different classes.  Atomic model: works as a conceptual and a physical model  A physical map of the U.S.: works as a graphical and a physical model

Exit Ticket 1. What is a model? 2. Name an example of each model type: a. Physical b. Graphical c. Conceptual d. Mathematical