F-test and One-way ANOVA (in R)?

[x^2]

I have five groupings of data measurements, each group with a different quantity of measurements. I want to see if one grouping has higher measurements than the rest, but was told that using multiple t-tests was incorrect and that I should use ANOVA.

I'm using R for the analysis. Exactly how might I go about this? I've looked at a couple tutorials, but the examples are too complex for me to understand.

Using the formulas http://en.wikipedia.org/wiki/F-test#One-way_ANOVA_example" I tried an F-test, but got an F-value of on the order of 10^16 as my "within-group" sum of squares value is on the order of 10^-13.

Could someone show me how I'd run a simple ANOVA test in R given a few columns of data and how to interpret the results to test whether one grouping has statistically higher values?

Thank you,
x^2

 

[Redbelly98]

I can't help with doing the analysis in R, but I would be able to do it in Excel. I would run the ANOVA calculations just like the example shown in the Wikipedia article.

Did you use the mean-square values, not the sum-of-squares, to compute the F-value? Have you considered the possibility that your F-value really is of order 10¹⁶?

If you really have doubts, perhaps you could post your data here. How many total measurements do you have?

EDIT:
As a test, you could try a t-test between just the groups with the highest and lowest average. You seem confident in your ability to do a t-test; see if you get a t-value that is outrageously large like your F-value was.

 

[statdad]

Don't use Excel, for a variety of reasons.
"“Meanwhile, researchers should continue to avoid using the statistical functions in Excel 2007 for any scientific purpose.”
- Yalta (2008), ref 1 below

“... it is not safe to assume that Microsoft Excel’s statistical procedures give the correct answer. Persons who wish to conduct statistical analyses should use some other package.”
- McCullough and Heiser (2008), ref 2 below

"If you need to perform analysis of variance, avoid using Excel, unless you are dealing with extremely simple problems."
- Statistical Services Centre, Univ. of Reading, U.K. (at A, below)

"Excel is of very limited use in the formal statistical analysis of data unless your experimental design is very simple. . . . the "Data Analysis Toolpack" provided with Excel is no easier to use than most statistics packages, has very limited capability, has known bugs and so, on the whole, is not worth bothering with. "
-Neil Cox, ref 7 below

"Enterprises should advise their scientists and professional statisticians not to use Microsoft Excel for substantive statistical analysis. Instead, enterprises should look for professional statistical analysis software certified to pass the (NIST) Statistical Reference Datasets tests to their users' required level of accuracy."

Problems have existed in Excel's statistical analysis from the earliest years, and most (if not all) have not been addressed.

In R: I don't know what you've named your variables, so I'll use these names.
MyNumericalData - this is the vector that contains the measured values
MyCategories - this is the variable that contains the names of the factors (note: it has to be the same length as MyNumericalData)

If you do this:

myfit<-lm(MyNumericalData~MyCategories)

and then do

anova(myfit)

you have your ANOVA table.

If you have the pdf manuals for R installed, look at
"An Introduction to R"
The section on Statistical Models in R, subsection Linear Models