Statistics - ANOVA table calculation

[XodoX]

Homework Statement

http://studyterps.com/files/STAT401-FE-SP09-CREMINS.pdf

#5

Homework Equations

The Attempt at a Solution

How did they get the MSTr and MSE form that table? I'm aware of the formulas such as MSE= SSE/(N-k) and so on, but usually you have some values given. Do I first claculate SST using the table, then use SST to get MSE?

SST would be: Sum of (Y_ibar - Ybar)²

What's Yi and Y here? I suppose Yi is each separate value for a specific row andYbar is the average for the entire table.

 

[SMA_01]

First, the total=the sum of all the data=216.
The correction factor for the mean (CM)= 216^2/12 (note the total of all values=n=12)

To get MSTr, you first need the SSTr. Get the three totals from each distinct hormone. So, here are the totals:
T1=59, T2=79, T3=78
Then SSTr= (T1^2/n1+T2^2/n2+T3^3/n3)-CM=(59^2/4+79^2/4+78^2/4)-(216^2/12)=63.5
Next, you need the degrees of freedom (d.f.) for the "treatment", i.e. type of hormone=3-1=2
Finally,
MSTr=SStr/d.f.=63.5/2=31.75

For MSE, it's a similar process, but you need to find SSE, and then divide it by the degrees of freedom for error.

Note: The total degrees of freedom=n-1=12-1=11, and the d.f. for treatment=2, so the d.f. for error=11-2=7

 

[SMA_01]

Also,the formula for SSTr you mentioned you need to multiply by ni which equals the number of values per row (in your specific example=4) and if you compute SSTr using the formula you mentioned, Yi is the average of a specific row, and Ybar is the total average (216/12). So you compute (Yi-Ybar)^2 for each row and sum them up then multiply by 4.

 

[XodoX]

First, the total=the sum of all the data=216.
The correction factor for the mean (CM)= 216^2/12 (note the total of all values=n=12)

To get MSTr, you first need the SSTr. Get the three totals from each distinct hormone. So, here are the totals:
T1=59, T2=79, T3=78
Then SSTr= (T1^2/n1+T2^2/n2+T3^3/n3)-CM=(59^2/4+79^2/4+78^2/4)-(216^2/12)=63.5
Next, you need the degrees of freedom (d.f.) for the "treatment", i.e. type of hormone=3-1=2
Finally,
MSTr=SStr/d.f.=63.5/2=31.75

For MSE, it's a similar process, but you need to find SSE, and then divide it by the degrees of freedom for error.

Note: The total degrees of freedom=n-1=12-1=11, and the d.f. for treatment=2, so the d.f. for error=11-2=7

Thank you. Is this not overly complicated for SSTr? How about SST= ni(Xibar-Xbar)^2 ? I don't think I've seen your way of doing it before.

BTW. I'm doing this to get F, which I need for other things. Don't know if there's a faster way to get F.

 

[SMA_01]

Basically, you're filling out the ANOVA table, you can do this easily buy running a test through a statistics package like Minitab. The formula you mentioned for SST is the one that you use for SSTr, I just figured Yi and Yi bar were dummy variables and the meaning was the same. But that does not look like the formula used for SST, are you sure about it?
For SST, I have Ʃ(Xibar-Xbar)^2

You can just compute using the formulas, the way I did it was the way we were taught, but it's the same answer.

And yes, you do it to get F, that way you can use the F distribution to conclude whether to accept or reject your hypothesis.

The easiest way is to run it through a stats package, that way you get the p-value as well.