1. **Problem Statement:** You want to understand the basic principles of experimental design: Replication, Randomization, and Reduction of Error/Local Control, and their purposes. 2. **Replication:** This means repeating the experiment multiple times. - Purpose: - To estimate the experimental error, which is the natural variation in results. - To increase precision by reducing the standard error of the mean, making results more reliable. - To broaden the base for making inference, meaning conclusions are more general and trustworthy. 3. **Randomization:** This means randomly assigning treatments or conditions. - Purpose: - To get unbiased estimates of parameters, so results are fair and not influenced by outside factors. - To reduce personal bias, ensuring the experimenter’s preferences don’t affect results. - To obtain a valid estimate of experimental error, helping to understand natural variability. 4. **Reduction of Error/Local Control:** This involves controlling or accounting for factors that cause variability. - Purpose: - To reduce the error in the experiment by controlling variables that might affect the outcome. 5. **Summary:** Replication helps confirm results and reduce uncertainty. Randomization ensures fairness and unbiased results. Reduction of error improves accuracy by controlling unwanted variation. Understanding these principles helps design experiments that give trustworthy and precise results.