Handling sets of data can be confusing even to the experienced researcher, which is why statistics -- numbers that describe certain aspects of sets of data -- are so important for understanding the data you collect. The F value is the ratio of variance estimates from the possible underlying distributions from which the data came. The numerator is an estimate of the variance, assuming the data came from the same distribution, and the denominator estimates the variance without that assumption. As a statistic, F allows a student to understand whether a significant difference exists between sets of data. Finding the F value requires no creativity, but calls for a strict step-by-step procedure when working with your data set.
Add the data for each of your two data sets, separately. Record these numbers and label them. Use the labels “X” and “Y,” for convenience.
Add all the data points together, square them and divide by the total number of data points -- “n,” for convenience -- for each set. Call "X" the sum of all the data points from your first set and "Y" the sum of all the data points from the second set. The formula you will use them in is MC = [(X + Y)^2]/(2n). "MC" stands for "mean correction." In performing this calculation, remember that “X” and "Y" are the sums of your data points, and "n" is the number of data points you’ve collected for each set. For example, if you collected 130 samples for each set, “n” equals 130.
Find the sum of squares, or SSB, between your data sets. Square the individual sums X and Y, add them together, and divide this result by n. Subtract MC from this result. The formula is SSB = [(X^2 + Y^2)/n] – MC.
Find the total sum of squares, or SST. Square all the individual data points, from both set X and set Y, and add them all together. For SST, you are squaring every data point before adding them into a single number. Call this number “T,” for convenience. Subtract MC from T to get SST. The formula is SST = T – MC.
Find the sum of squares within groups, or SSW. Subtract SSB from SST. Because SST and SSB are simple numbers, this is only a simple subtraction. Thus, SSW = SST – SSB, yielding a single number.
Find the mean square within groups, or MSW. Divide SSW by 2n-2. Thus, MSW = SSW/(2n-2).
Divide SSB by MSW to find the F value: F = SSB/MSW.
Consider using statistical software, such as SAS, to do this more quickly and with less chance of error.
- University of Florida Department of Statistics: Two-Way ANOVA
- Matt Blackwell: Multiple Hypothesis Testing: The F-Test
- Experimental Designs Using ANOVA; Barbara G. Tabachnick, Linda S. Fidell
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