Linganisha mbinu

	Jaribio la Migongano la Wald-Wolfowitz	Jaribio la Ljung-Box Q la Uunganishaji Kiotomatiki
Nyanja	Takwimu	Ekonometriki
Familia	Hypothesis test	Hypothesis test
Mwaka wa asili	1940	1978
Mwanzilishi	Abraham Wald & Jacob Wolfowitz	Greta Ljung & George Box
Aina	Nonparametric randomness test	Portmanteau goodness-of-fit test
Chanzo asilia	Wald, A. & Wolfowitz, J. (1940). On a test whether two samples are from the same population. Annals of Mathematical Statistics, 11(2), 147–162.	Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303.
Majina mbadala	Wald-Wolfowitz test, runs test for randomness, Runs Testi (Wald-Wolfowitz)	Ljung-Box Q Test, Modified Box-Pierce Test, Portmanteau Test for Autocorrelation, Otokorelasyon Portmanteau Testi
Zinazohusiana	5	3
Muhtasari	The Wald-Wolfowitz runs test is a nonparametric hypothesis test that determines whether a sequence of observations — coded as a series of binary symbols — follows a random pattern or contains systematic structure. Introduced by Abraham Wald and Jacob Wolfowitz in 1940, the test counts the number of uninterrupted runs of identical symbols and asks whether that count is consistent with random arrangement.	The Ljung-Box Q test is a diagnostic portmanteau test proposed by Ljung and Box (1978) to assess whether a group of autocorrelations in a time series residual sequence is jointly zero. It is widely used to evaluate the adequacy of fitted time series models — especially ARIMA models — by testing whether remaining residuals exhibit any systematic pattern. The test is applicable in econometrics, finance, and any field that relies on temporal data modeling.