DevSq is the Word

Problem Set 5, originally uploaded by Mathew Mitchell.

Several of you have been posting questions about small rounding off errors. There are a few ways to handle this including: (1) willing to live with small rounding off errors when hand calculating, (2) using Raylene's super-smooth calculation trick (email/phone her), or (3) using your new found spreadsheet skills.

In the end, the real direction you want to go is to become comfortable enough with spreadsheets that you use them for all your basic calculation needs. (The notable exception is that you'll want to use dedicated statistical analysis software for big and complicated analyses.)

1. Spreadsheet Setup
You can easily calculate all of the homework Problem Set 5 answers using your current spreadsheet skills. However, I'm going to make it even easier! First, set up your spreadsheet for the calculations. You should have something like what you see at the top of this post. Note that I've filled in some cells, but left others empty for you to figure out. (All the shown calculations you've already calculated in previous problem sets.)

2. New Spreadsheet Command
The new spreadsheet command that makes life easier for you: DEVSQ. This is a command to figure out the Sum of Squares (or deviations squared) for a specified array of numbers. With this command you do not need to create Deviation and Deviation Squared columns.

Notice that you have three possible DEVSQ commands you'd want to use with the data presented above: SS for the female group, SS for the male group, and SS for the total sample.

3. Calculate
All that is left is to do the calculations. SS Total is very simple since it treats all the data as belonging to one group. SS Within is also straightforward since it's the same thing as adding up the SS for each of your groups. So the one place where you'll really be practicing your formula-creation-chops is figuring out SS Between. That said the formula for this is much simpler than the one used for s_pooled. Finally, eta^2 is easy to calculate once you have SS Between.

4. Spreadsheet Concepts Revisited
There's a conceptual difference between what you do by hand, and how a spreadsheet operates. When you round off then you end up using those rounded-off-numbers in subsequent calculations. In this way it's easy for hand calculations (even if done correctly) to vary a small amount from the actual correct answer. (Of course if your calculations vary a large amount then something went askew!) However, spreadsheets work differently. In essence, spreadsheets always use the full number in all calculations. However, with a spreadsheet you can choose to have only part of the full number (e.g. two decimal places) displayed on the screen. So with spreadsheets you get the best of both worlds: all calculations done with the full number, but your eyes only need to look at the nicely formatted two-decimal-place rounded off number.