• • • We do not use the following data for averages, fits, limits, etc. • • • 
$0.84$ $\pm0.12$ 
^{ 1} 

MINS 
$0.72$ $\pm0.026$ $\pm0.13$ 
^{ 2} 

MCRO 
$0.57$ $\pm0.05$ $\pm0.15$ 
^{ 3} 

MCRO 
$0.71$ $\pm0.05$ $\pm0.19$ 
^{ 4} 

MCRO 
$0.74$ $\pm0.036$ $\pm0.046$ 
^{ 5} 

MCRO 

^{ 6} 

IMB 

^{ 7} 

NUSX 
$0.95$ $\pm0.22$ 
^{ 8} 


$0.62$ $\pm0.17$ 



^{1}
ADAMSON 2006 uses a measurement of 107 total neutrinos compared to an expected rate of $127$ $\pm13$ without oscillations.

^{2}
AMBROSIO 2001 result is based on the upward throughgoing muon tracks with $\mathit E_{{{\mathit \mu}}}>1$ GeV. The data came from three different detector configurations, but the statistics is largely dominated by the full detector run, from May 1994 to December 2000. The total live time, normalized to the full detector configuration, is $6.17$ years. The first error is the statistical error, the second is the systematic error, dominated by the theoretical error in the predicted flux.

^{3}
AMBROSIO 2000 result is based on the upgoing partially contained event sample. It came from 4.1 live years of data taking with the full detector, from April 1994 to February 1999. The average energy of atmospheric muon neutrinos corresponding to this sample is 4$~$GeV. The first error is statistical, the second is the systematic error, dominated by the 25$\%$ theoretical error in the rate (20$\%$ in the flux and 15$\%$ in the cross section, added in quadrature). Within statistics, the observed deficit is uniform over the zenith angle.

^{4}
AMBROSIO 2000 result is based on the combined samples of downgoing partially contained events and upgoing stopping events. These two subsamples could not be distinguished due to the lack of timing information. The result came from 4.1 live years of data taking with the full detector, from April 1994 to February 1999. The average energy of atmospheric muon neutrinos corresponding to this sample is 4$~$GeV. The first error is statistical, the second is the systematic error, dominated by the 25$\%$ theoretical error in the rate (20$\%$ in the flux and 15$\%$ in the cross section, added in quadrature). Within statistics, the observed deficit is uniform over the zenith angle.

^{5}
AMBROSIO 1998 result is for all nadir angles and updates AHLEN 1995 result. The lower cutoff on the muon energy is 1$~$GeV. In addition to the statistical and systematic errors, there is a Monte Carlo flux error (theoretical error) of $\pm0.13$. With a neutrino oscillation hypothesis, the fit either to the flux or zenith distribution independently yields sin$^22\theta =1.0$ and $\Delta \mathit m{}^{2}\sim{}$ a few times $10^{3}$ eV${}^{2}$. However, the fit to the observed zenith distribution gives a maximum probability for $\chi {}^{2}$ of only 5$\%$ for the best oscillation hypothesis.

^{6}
CASPER 1991 correlates showering/nonshowering signature of singlering events with parent atmosphericneutrino flavor. They find nonshowering ($\approx{}{{\mathit \nu}_{{\mu}}}$ induced) fraction is $0.41$ $\pm0.03$ $\pm0.02$, as compared with expected $0.51$ $\pm0.05$ (syst).

^{7}
AGLIETTA 1989 finds no evidence for any anomaly in the neutrino flux. They define $\rho $ = (measured number of ${{\mathit \nu}_{{e}}}$'s)/(measured number of ${{\mathit \nu}_{{\mu}}}$'s). They report $\rho $(measured)=$\rho $(expected) = $0.96$ ${}^{+0.32}_{0.28}$.

^{8}
From this data BOLIEV 1981 obtain the limit $\Delta \mathit m{}^{2}{}\leq{}$ $6 \times 10^{3}$ eV${}^{2}$ for maximal mixing, ${{\mathit \nu}_{{\mu}}}$ $\nrightarrow$ ${{\mathit \nu}_{{\mu}}}$ type oscillation.
