PSY 394U Do It Yourself Statistics Chapter 1 A sample MATLAB session This tutorial assumes that you have purchased and installed the student version of MATLAB on your computer The student version is currently cheaper than most college textbooks and is well worth the investment It is available directly from the Mathworks and at most university computer or bookstores As we go through this tutorial please try everything yourself typing each command and seeing what it does Remember however that we are mainly getting used to the look and feel of a MATLAB session and seeing what kinds of things MATLAB can do Some of the commands I ll ask you to input will seem a little mysterious at present relax don t worry enjoy the test drive Start MATLAB on your computer You should see a window something like this Yours will look slightly different but there should be a large command window on the right and this is the window in which we will working in for this tutorial Note that the flashing cursor is next to a This is called a command prompt In this document I will proceed all commands you should actually enter with this prompt For example let s start out by using MATLAB as a calculator 1 1 always hit return or enter at the end of the line 1 of 7 PSY 394U Do It Yourself Statistics MATLAB should respond with the hopefully correct answer ans 2 An important aspect of programming languages is the ability to store values in variables which are containers for data similar to cells rows or columns in Excel SPSS etc The ans in the output above is actually a special variable that MATLAB creates when you don t specify one Store something into a variable called x x 1 1 x 2 Note that the resulted is output back to the console You can suppress this by ending the line with a semicolon x 1 1 This is very handy when the output of a calculation is large or later when you write programs that do lots of calculations To see the value of a variable just type the variable name x x 2 Variable names can be more than just a single letter so they can be a little more descriptive nqp 22 7 You can also make them really descriptive but they get cumbersome to type not quite pi 22 7 Notice I was able to use underscores to make the variable name more readable You can use numbers too but avoid using anything else Also variable names must begin with a letter and they are case sensitive as is everything else in MATLAB So X is not the same variable as x 2 of 7 PSY 394U Do It Yourself Statistics We can test the equality or inequality of variables The variable pi is built into MATLAB so nqp pi Note the double equals which means are these equal Let s see how bad the approximation is pi nqp Okay then perhaps you can guess what this returns nqp pi Note that command prompt is special and not part of the command per se but the you type is interpreted as greater than You can see what variables you have created by listing them who or you can get a little more detail with whos whos And you can remove a variable like this clear nqp Whoops maybe we didn t want to do that To re do a command you can hit the up arrow on your keyboard to go back through previously entered commands When you see the one you want just hit return If you overshoot it hit the down arrow Let s clean up by removing all the variables clear Don t worry if this command or others below seem mysterious to you we re just taking MATLAB for a test drive Variables can hold more than one number note a variable that holds a single value is often called a scalar and one that holds multiple values is often called a vector x 1 5 You can also enter numbers into a variable by hand y 2 3 5 8 10 3 of 7 PSY 394U Do It Yourself Statistics which means concatenate the numbers 2 3 5 8 10 and assign them to y When working with these kinds of variables MATLAB behaves in a convenient fashion x 5 No need to add 5 to each and every element of x MATLAB automatically interprets the command this way If we add two vectors x y Again the result is sensible MATLAB adds each value of y to the corresponding value of x Comparisons work the same x 3 x y Now we can do some fun stuff scatter x y Looks like x and y are pretty highly correlated Let s see by how much corrcoef x y Note that this returns the entire correlation matrix but only the upper or lower triangle in this case a single point has meaning in this case Some connecting lines might make the form of the relationship a little clearer line x y This looks sigmoidal s shaped to me but I ll bet a straight line still does a pretty good job of describing the data So let s fit a linear model y as a linear function of x and plot it One nice thing about MATLAB is that even though at it s heart it is a programming language you can also do a lot with plots using the GUI graphical user interface From the menubar at the top of the figure select Tools Basic Fitting A new window similar to the one shown here should appear 4 of 7 PSY 394U Do It Yourself Statistics Now check the linear box as well as Show equations and Plot residuals boxes to see the results of the fit on the plot You can also press the large right arrow button at the lower right of the page to see additional fitting information in this window Visually the fit isn t bad but it still looks like the data are departing from a straight line in a systematic fashion If these were real data I d want to see if this was really a sigmoidal shape Let s clean up again clear One of the great things about MATLAB is that it has lots of random number generators and statistical distributions built in Let s get a sample of size 100 from a normally distributed population Here x randn 100 1 And look at them What do you expect the mean and standard deviation to be hist x This looks like a standard normal distribution in that the mean looks to be about zero the s d looks to be about one and most or all of it looks to be between 3 Let s check mean x std x summary dataset x So everything looks consistent with a standard normal mean and median both near zero s d of about 1 etc I realize that the summary dataset command looks a little awkward and mysterious right now but …
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