Experimental Design

Statistics · Axiom Academy

REAL WORLD Experimental Design How scientists and engineers use ANOVA to design powerful experiments that reveal the truth In the 1920s, British statistician Ronald Fisher was working at an agricultural research station. Farmers needed to know: Which fertilizer produces the best crop yield? But there was a problem... Fields aren't uniform. Some plots have better soil, more sunlight, or better drainage. If you just test fertilizers in different locations, how do you know whether differences in yield are due to the fertilizer or the location? Fisher's brilliant solution: Randomized experimental designs combined with Analysis of Variance (ANOVA). This revolutionized not just agriculture, but all of science and industry. Factorial Experiments: Testing Multiple Factors Modern experiments often need to test multiple factors simultaneously. A factorial design tests all combinations of factors. Example: Industrial Process Optimization A chemical engineer wants to maximize the yield of a manufacturing process. Two factors might matter: Temperature: Low (150°C) vs. High (200°C) Pressure: Low (2 atm) vs. High (4 atm) Click each combination to see the experimental runs: What can we learn from this design? Factorial designs let us detect: Main effects: Does temperature matter? Does pressure matter? Interaction effects: Does the effect of temperature depend on pressure level?

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