= Test Statistic = A '''test statistic''' is a statistic generated for hypothesis testing in [[Statistics/CausalInference|causal inference]]. <> ---- == Description == A test statistic is compared to a '''critical value'''. ''H,,0,,'' is rejected if: {{attachment:test.svg}} A critical value should reflect a tolerance for Type I error. === P-Values === A '''p-value''' is the probability of achieving a test statistic assuming the null hypothesis is true. This is effectively a reformulation of the above framework: a critical level is selected (commonly 0.05; or conversely a level of significance is selected, like 95%) and ''H,,0,,'' is rejected if the p-value exceeds it. The advantage to formulating inference through p-values is that anyone can formulate their personal tolerance for Type I error, determine the corresponding critical level, and re-evaluate the inference. In contexts where a variety of critical levels ought to be considered (e.g., at 0.1, 0.05, and 0.01 simultaneously), it can also be more succinct to report p-values than annotate each. The disadvantage to this formulation is that p-values are more easily misunderstood (e.g., possible to misinterpret a p-value of 0.02 as meaning there is a 98% probability that the result is correct, when it truly means that there is a 2% probability that the estimate is 0). ---- == Usage == There are a variety of test statistics. Most tests are designed for application in specific contexts, when certain assumptions hold. See the below pages for usage guidance: * [[Statistics/CollinearityTest|Collinearity test]] * [[Statistics/HosmerLemeshowTest|Hosmer-Lemeshow test]] * [[Statistics/KolmogorovSmirnovTest|Kolmogorov-Smirnov test]] * [[Statistics/LagrangeMultiplierTest|Lagrange multiplier test]] * [[Statistics/LikelihoodRatioTest|Likelihood-ratio test]] * [[Statistics/PearsonTest|Pearson test]] * [[Statistics/WaldTest|Wald test]] ---- CategoryRicottone