People are an uncontrollable source of variation – common cause.
Have the people in the modern method group been assigned using any special classification methods? If so, these inputs could be used to design factors to partition the SS.
If the people in the two groups have been chosen as random and the desired outcome of the experiment will be to compare the one factor, with two levels e.g. two teaching methods only – with a one variable response e.g. score on a standardized English test, you could use the single factor analysis of variance method to draw your conclusions.
You would have to ensure that the appropriate number of people have been tested to ensure that you have a statistically valid test – e.g. controlled Type II error.
If you have historical testing scores available this can be used as an estimate of the standard deviation for the nominal group. e.g. http://nces.ed.gov/dasol/
With the estimate of standard deviation you can be used to develop the appropriate OC curve for your chosen alpha. Jurans Quality Handbook has some good information on the subject Determining sample sizes for Testing a Hypothesis.
Another approach might be to conduct a before and after treatment analysis e.g. administer the standardized test to each group before and after testing in essence blocking the people out of the analysis. This provides an estimate of each teams ability before and after. Then you can test the hypothesis that difference in the over all groups average increase is significant.
.
