Understanding Experimental Design

Statistical analysis begins with a solid experimental design. It includes control groups, randomization, and replication to ensure data quality and meaningful analysis. Well-planned designs prevent biases and allow for accurate statistical inference.

Significance levels (alpha) define the threshold for accepting a hypothesis. Commonly set at 0.05, it means there's a 5% chance of rejecting a true null hypothesis. It's a balance between sensitivity and the risk of false positives.

Power analysis determines sample size needed to detect an effect. It considers the significance level, effect size, and desired power, typically 80%. This helps avoid Type II errors, where true effects go undetected.

P-values don't measure the probability that the hypothesis is true. They indicate the probability of observing data at least as extreme as the sample, under the null hypothesis. Misinterpreting p-values can lead to incorrect conclusions.

Confidence intervals provide a range of values for an estimate. A 95% confidence interval means if the experiment were repeated many times, 95% of the intervals would contain the true value. It's a measure of precision, not probability.

Conducting multiple hypothesis tests increases the likelihood of a Type I error. Techniques like the Bonferroni correction adjust significance levels to mitigate this problem, controlling the familywise error rate.

Bayesian statistics calculate the probability of a hypothesis being true, incorporating prior knowledge. They're gaining popularity in experimental analysis for their flexibility and ability to update beliefs with new evidence.