Hypothesis Testing

Service Description

Definition Hypothesis testing is a formal statistical process used to make decisions or inferences about a population based on a sample of data. It helps determine whether an observed effect, difference, or relationship is real (statistically significant) or merely the result of random variation (chance). In simple terms, it answers the question: “Is what we’re seeing in our sample strong enough evidence to believe it’s true for the whole population?” ________________________________________ Purpose • To validate or reject assumptions about data. • To support data-driven decision-making rather than relying on opinions. • To determine if changes in a process, product, or system lead to a meaningful improvement. ________________________________________ Key Concepts 1. Null Hypothesis (H₀): o The default assumption that there is no effect, difference, or relationship. o Example: “The new process does not reduce defects.” 2. Alternative Hypothesis (H₁ or Ha): o The statement that there is an effect, difference, or relationship. o Example: “The new process reduces defects compared to the old one.” 3. Significance Level (α): o The threshold for deciding whether to reject the null hypothesis. o Commonly α = 0.05, meaning a 5% risk of wrongly concluding that a difference exists when it doesn’t (Type I error). 4. p-value: o The probability of observing the data—or something more extreme—if the null hypothesis were true. o If p < α, the result is statistically significant, and we reject H₀. 5. Type I and Type II Errors: o Type I Error (α): Rejecting H₀ when it is true (false positive). o Type II Error (β): Failing to reject H₀ when it is false (false negative). 6. Test Statistic: o A calculated value (such as t, z, F, or χ²) used to compare the sample result to a theoretical distribution and determine the p-value.