Cochran's theorem is a fundamental result in statistics that deals with the distribution of sums of squares in analysis of variance (ANOVA). It states that if you have a set of independent random variables, the sum of their squares can be partitioned into components that follow a chi-squared distribution. This is particularly useful for understanding the variability in data and for testing hypotheses about group means. The theorem is named after William G. Cochran, a prominent statistician who contributed significantly to the field of experimental design. Cochran's theorem helps researchers determine how much of the total variability in their data can be attributed to different sources, aiding in the interpretation of experimental results.