Repeated Measures

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Tricks and Hints for Doing Calculations with Complicated Formulas

The key to all of this is:

1. break the formula down into its component parts 2. set up a chart for calculations 3. plug the results into the original formula 4. use the order of operations to solve the formula 5. interpret the resulting calculation

For example, when calculating a formula like standard deviation, the formula is as follows: s = ∑x2 - (∑x)2 Note: The square root goes over the whole formula. n

n – 1

Step 1. The component parts are ∑x2 (which means you square each x and then add all of the x2’s) and (∑x)2 (which means you add each x first and then square the sum). Actually the most basic parts are x2 and x. n will be the number of people in the study.

Step 2. Set up a chart for calculations. You will need a column for each of the two parts above.

Data is made up below to illustrate the process. x x2 1 1 5 25 6 36 3 9 4 16 2 4 __

∑x = 21 ∑x2 = 91 Add both columns to the left, this will add all the x’s in the first column and add all of the x2’s in the second column (later you will plug these into the formula).

(∑x)2 = 441 After adding all the x’s in the first column, then square the sum of all of the x’s. That gives you the (∑x)2.

n = Finally “n” in the formula is the number of people in the research study (i.e. the number of x’s).

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Step 3. Plugging the results of your chart above into the original formula, you have:

s = ∑x2 - (∑x)2 = 91 - 441 n 6

n – 1 6 – 1

Step 4. Use the order of operations to solve the formula (see symbols handout) s = 91 – 73.5 multiply/divide before add/subtract 5 = 17.5 add/subtract before divide the whole fraction 5 = 3.5 multiply/divide the whole fraction = 1.87 Step 5. Now what does a standard deviation of 1.87 for the sample mean?