This study introduces a new analytical procedure based on the chi-square (x²) statistic to evaluate tree- ring weather relationships. An iterative x² method, developed previously for relating annual crop production to daily values of meteorological measurements, is applied to tree-ring data and compared to results obtained from correlation and bootstrapped response function analyses. All three analytical procedures use a southern Arizona chronology (Pinus arizonica Engelm.) and the latter two use monthly average meteorological data. The x² analysis revealed most of the relationships exhibited by the correlation and response function analyses as well as new linear and nonlinear associations. In addition, cardinal values were obtained that define daily thresholds of the meteorological variables at which the limitation to growth becomes significant. Some of the associations are plausible from the physical system but require more study to confirm or refute a real cause and effect. A few associations appear to be too late in the season or too early in the previous year to affect ring width. We recommend that this x² technique be added to the existing dendroclimatic procedures because it reveals many more possible cause and effect relationships.