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=V0$@jjō$<šņ~¶Ė~u²p$ō$E%0u%|$xO)'O)ō$=~~jjjjŁStatistics: Who Cares?
-Lets try and identify and fixable problems on rez or in American society if you want to think more generally.
-Grants provide the money to study or fix these problems. But dont get handed out for good ideas, but only for good research designs.
-Good research almost always involves a careful consideration of sampling and statistical analyses. By the end of this class, if you do the work, hopefully you will have a good enough knowledge of basic statistical principals to design your own basic analyses or even write a simple grant proposal.
-Archaeology disclaimer: I am an archaeologist so I learned statistics using archaeological examples.
-Almost every single thing starts out as a count of something (for me it might be something like three orange pieces of broken pottery versus 18 purple ones, four arrowheads, three scrapers). So we also will start with counts of things:
-Criminology: how many people get arrested a month for violent crime in this neighborhood?
-Sociology: what was the suicide rate in one city vs. another city or community?
-Social Work: what was the rate of relapse for alcoholics who attended AA meetings vs. those who dont?
-Census (Demography): 18 people live in this trailer, 5 in that one, and 12 in the one over the hill.
-You do not need to be mathematically inclined to do well in this course. If you are, this course might move a little slow at points for you. If you not, than youll be ok. But this course will occasionally be a LOT of work. If you have no time for any work outside of class time, you will fail. As we already discussed your homework projects will make up the majority of your grade so if you dont do your homework there is no way for your to pass.
How this class will be different than typical statistical courses:
-Most other stats classes, like those offered in the math department, have hard rules that must be followed regardless of the situation, this class is designed to give you tools that work better or worse depending on the specific situation. We will not memorize very many mathematical laws. In fact you wont have to ever memorize any mathematical formulas, you will use them but I will always provide you with a sheet of formulas on your tests.
-You wont hear too much about things like a null hypothesis or calling something significant versus not significant (thats why we dont have a textbook). Such terms/techniques often dont work too well in the social sciences.
-As you will see, this is because social scientists often have to work with small samples. If a chemist doesnt see a pattern in a small set of chemical reactions, she simply creates a larger set of the same chemical reactions in the lab. This will cost more $$ and time, but otherwise is no problem.
-If a social scientist doesnt like working with census data from 1985 on Pine Ridge, theres no going back in time to increase the sample. You often have to work with what you get, which is often small, not they way youd like it, and generally pretty complicated.
-Also will be working with techniques that my colleagues and I have found particularly useful in common research situations, some of these techniques are not all that conventional and wont be found in most stats books, but they are very useful in social science research.
-There are, however, a whole bunch of complicated techniques that are useful that we will not be able to get to in this class. If you want to learn these for whatever reason, you have to ace this class, invest in more expensive software and sign up for an independent study with me.
-Sampling: This is one of the most important aspects of social science research because we cant study everything because ultimately there just is not enough time and money. We have to choose a smaller more manageable part of a population, or sample, to study, but ultimately we want to say something about a larger population (voting trends example).
-1st part of this class deals with exploring bunches of numbers, especially when these are just a part of a larger population.
-2nd part considers how samples of numbers are related to larger populations- what we can say, what we cant say.
-3rd part- tests of strength, significance.
COIN FLIPPING EXERCISE:
-You already intuitively know some of the basic statistic principles and I am going to demonstrate with this coin flipping demonstration.
-After each coin flip I want you to write down what you are thinking, try not to yell anything out.
-So at what point did you start to think that something was up? Why did you think something was wrong? Why didnt you start thinking something was up after 2 or 3 flips?
-All of this was an excellent example of probability. You had a 50% or one in two chance of predicting one coin flip correct. After that the probability of guessing all the flips correctly goes down with each additional coin flip.
.50 x .50 = 0.25 (one quarter 1/4)
.50 x .50 x .50 = 0.125 (one eighth 1/8)
.50 x .50 x .50 x .50 = 0.0625 (one sixteenth 1/16)
.50 x .50 x .50 x .50 x .50 = 0.03125 (one thirty second 1/32)
.50 x .50 x .50 x .50 x .50 x .50 = 0.015625 (one sixty fourth 1/64)
.50 x .50 x .50 x .50 x .50 x .50 x .50 = 0.0078125 (one one hundred and twenty eighth 1/128)
.508 = 0.00390625 (one two hundred and fifty sixth 1/256)
.509 = 0.001953125 (one five hundred and twelfth 1/512)
.5010 = 0.0009765625 (one one thousand and twenty fourth 1/1024)
-Whether it lands heads or tails is hard to predict, we take its odds at landing one way or the other as 50/50. An earlier flip does not influence how I flip it the next time. There is a random chance it lands one way or the other on any given flip
-The number of times I flipped the coin is called sample size.
-You wouldnt call me a liar unless you were pretty sure I was a liar, when you know, we called that statistical confidence.
-So when you have random chance built into statistical observations (like a coin lip), every time we increase the sample size, you gain more and more statistical confidence. You can therefore have more faith that the patterns you are observing are real, or not real.
-This is the core principal behind all statistical analysis
-Now imagine a bunch of different coins being flipped at once, some have two sides, some have three sides, some have four sides.. etc. Gets hard to manage all those observations on a whiteboard or with a handheld calculator, today we have computerized statistical programs to help us with this.
-Basic Algebra (Order of Operations):
-One of the prerequisites for this class was that you are supposed to have taken and passed basic algebra. Some of the things you learned in that class will be useful to you here when performing statistical calculations.
-One of the most basic math skills that you will need in order to understand the equations we will be suing throughout this course is called the Order of Operations.
-This is a set of rules that mathematicians have come up with so that everyone will calculate equations in the same way or same order so that everyone gets the same answers.
-So when we see a complicated equation such as: 8 x 22 + 7 x (4 + 1) = we know what to do first by following the rules of Order of Operations.
-There is a simple reminder that can help you remember what to do first:
-P.E.M.D.A.S. (Please Excuse My Dear Aunt Sally)
-This means:
Do all operations inside parentheses.
Do any work with exponents or radicals (so the small numbers above other numbers).
Working from left to right do all multiplication and division.
Working from left to right do all addition and subtraction.
-So that is the basics of order of operations. Having a good grip on this concept will help you solving the statistical equations we will be using this semester.
-Even though this may be review for many of you lets practice doing some equations on the board. After that I will hand out an order of operations worksheet that you can work on in groups and if you dont finish it you will take it home for homework that is due next week.
-Using Microsoft Excel
-Excel is a spreadsheet program that can be used for a variety of data management and analysis purposes. It is set up so that data can be entered into a variety of cells. The cells have letters on the X-axis (horizontally) and are numbered on the Y-axis (vertically). Each cell can be identified by a letter-number combination; so for example the first cell on the sheet is cell A1.
-Other than simply entering numbers one of the most important things you will have to know how to do is enter formulas into cells.
-Click on a cell
-Enter an equal sign (=); all formulas start with an equal sign
-Now you can begin your formula
-Important symbols within formulas include:
+ (plus): this will add two values
- (minus): this will subtract two values
/ (slash): this will divide two values
* (asterisk): this will multiply two values
^ (caret): this will multiply a value to the power of
-Excel has many formulas that are ready made for you to use and they are called functions. If you click on the formulas tab on the top of your screen you will be able to enter many kinds of functions.
-For this class most of the functions we will use are found under the More Functions button and then under Statistical in the drop down menu. Dont worry about what all these functions mean at this point, as we need to use them I will teach you about them.
-To use a function, such as AVERAGE, you simply click on that function and then in the dialog box tell Excel what numbers you cells you want it to look at to calculate the average. If for example we have twenty number going from cells A1 to A20 you would just input the value A1:A20 into the dialog box. Alternatively you could drag the mouse over the cells you want to use for this function.
-Another important tool that you can find in Excel is called the Analysis ToolPak. We will probably have to install this on each of your computers but it is easy to do.
-To see if this tool is installed on your computer click on the Data tab on the top of your screen. If on the far right there is no tab for Data Analysis then you will need to install this tool. If it is there you are set to go.
-To install the ToolPak click on the Microsoft Office button on the far left top of your screen and then click options.
-Click Add-Inns, and then in the Manage box, select Excel Add-Inns.
-Click Go
-In the Add-Inns available box, select the Analysis ToolPak check box and then click OK.
Week 1 Introduction to Stats & Basic Algebra
PAGE 5
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