UNDERSTANDING EQUATIONS-A NEW LANGUAGE

UNDERSTANDING EQUATIONS IS NOT ABOUT BEING "SMART"- IT'S JUST A NEW WAY OF CONVEYING SOMETHING

Often I see students when they first see a new equation in a statistics class, and they panic! When this happens to you, delay hitting the "panic" button-you can do this!

Years ago when internet usage was first becoming widespread, I saw a bunch of new ways of communicating that were meaningless to me: ROTFLOL, YMMV, TTYL, IMHO and so on...I was terrified! Who had created this complex new way of quickly conveying ideas? PEOPLE WHO ARE PROBABLY A LOT LIKE YOU! "Average" older teens and young adults!

You created a language that baffled the older generation (some of the older generation are still baffled). You have the full capacity to communicate using symbols that shorten your meaning. 

Think of "YMMV": 

It conveys something that would take me a couple of sentences to explain: "This is how things turned out for me based on my situation, but you may or may not have the same experience depending on your situation." But people just like you seized upon this little four letter expression to convey it all. See also ROTFLOL, TTYL and so on...

So, we have the same thing in stats. 

You probably know how to calculate the mean of a set of numbers: add them all together and divide by the total number of observations in the set. Well, statisticians who use means for a lot of different things, and as part of other equations don't want to go around saying or writing "add up all of the observations in a set and divide by the total number of observations in the set"! So they use this: 

That probably looks terrible to you, but if it does, just think of YMMV! ROTFLOL! The next time you see it, it means-"the mean" (of Y in this case...) Just like you memorized YMMV or ROTFLOL. You may say that you can easily remember ROTFLOL or YMMV because each letter represents a word. That is the case in statistics as well...you just don't know the letters yet. 

Here is a "dictionary" to help you learn what all the parts of any equation means:

(Click here for a printable version).

So, the equation for the mean: 

                                       

Can be translated like this by using the dictionary: "sum (add up)" "all of the Ys" and divide by the "total number"! 

Now you try. Use the "equation dictionary" below to interpret the equations. Try to get them all right on the first try!

EQUATION DICTIONARY:

EQUATION QUIZ:

Try to "translate" each equation from the picture above into English.

        Equation #1:

The sum of all Xs minus the mean of X. Then multiply by all Ys minus the mean of Y
The sum of: all Xs minus the mean of each X, times all Ys minus the mean of each Y
The sum of: all Xs minus the mean of X, times all Ys minus the mean of Y
The sum of X minus the mean of X, times the sum of Y times the mean of Y
None of these

Equation #2:

The sum of all Xs, squared
The population standard deviation for X, squared
The X sum to the second power
The sample standard deviation for X, squared

Equation #3:

The sum of X over the total sample size
The sum of: Each X divided by its population size
The sum of all Xs, divided by population size
The population standard deviation for X, divided by population size
None of these

Equation #4:

Predicted Y equals: "a", plus, slope # 1 times X #1
Y equals the acceptable probability of false rejection plus, slope # 1 times X #1
Y equals "a" plus, slope # 1 times X #1
Predicted Y equals: the acceptable probability of false rejection, plus, slope # 1 times X #1
None of these

Equation #5:

The sum of all Ys, minus predicted Y squared
The sum of: Y minus predicted Y, squared
The population standard deviation of all Ys minus predicted Y, squared
The sum of: all Ys minus all predicted Ys, squared
None of these

How do you think you did?


Good work! You are now ready to see and understand more equations with confidence!