Testing diagnostics of nuclear activity and star formation in galaxies at z > 1

We present some of the first science data with the new Keck/MOSFIRE instrument to test the effectiveness of different AGN/SF diagnostics at z ~ 1.5. MOSFIRE spectra were obtained in three H-band multi-slit masks in the GOODS-S field, resulting in 2 hr exposures of 36 emission-line galaxies. We compare X-ray data with the traditional emission-line ratio diagnostics and the alternative mass-excitation and color-excitation diagrams, combining new MOSFIRE infrared data with previous HST/WFC3 infrared spectra (from the 3D-HST survey) and multiwavelength photometry. We demonstrate that a high [O III]/Hβ ratio is insufficient as an active galactic nucleus (AGN) indicator at z > 1. For the four X-ray-detected galaxies, the classic diagnostics ([O III]/Hβ versus [N II]/Hα and [S II]/Hα) remain consistent with X-ray AGN/SF classification. The X-ray data also suggest that "composite" galaxies (with intermediate AGN/SF classification) host bona fide AGNs. Nearly ~2/3 of the z ~ 1.5 emission-line galaxies have nuclear activity detected by either X-rays or the classic diagnostics. Compared to the X-ray and line ratio classifications, the mass-excitation method remains effective at z > 1, but we show that the color-excitation method requires a new calibration to successfully identify AGNs at these redshifts.

Analysis of residuals in contingency tables: another nail in the coffin of conditional approaches to significance testing.

Omnibus tests of significance in contingency tables use statistics of the chi-square type. When the null is rejected, residual analyses are conducted to identify cells in which observed frequencies differ significantly from expected frequencies. Residual analyses are thus conditioned on a significant omnibus test. Conditional approaches have been shown to substantially alter type I error rates in cases involving t tests conditional on the results of a test of equality of variances, or tests of regression coefficients conditional on the results of tests of heteroscedasticity. We show that residual analyses conditional on a significant omnibus test are also affected by this problem, yielding type I error rates that can be up to 6 times larger than nominal rates, depending on the size of the table and the form of the marginal distributions. We explored several unconditional approaches in search for a method that maintains the nominal type I error rate and found out that a bootstrap correction for multiple testing achieved this goal. The validity of this approach is documented for two-way contingency tables in the contexts of tests of independence, tests of homogeneity, and fitting psychometric functions. Computer code in MATLAB and R to conduct these analyses is provided as Supplementary Material.