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Table 8:

Simulation results for the partly periodic cases (S=1 / 3) for the rounded data, otherwise as in Table 4.
  ``Real'' ``False'' ``Real'' ``False'' ``Real'' ``False'' ``Real'' ``False''
  Case 8A
  ti simulations with $F_{{{\rm AP}}}(t,S=1/3,\sigma_{{P}}=0.05)$ rounded to multiples of $(3/\pi)\sigma_{{P}}$
n H1 rejected with $\gamma =0.01$ H0 rejected with $\gamma =0.01$ H1 rejected with $\gamma =0.001$ H0 rejected with $\gamma =0.001$
10 0.20 0.01 0.20 0.01 0.101 0.002 0.029 0.000
25 0.79 0.01 0.85 0.01 0.599 0.002 0.659 0.004
50 0.99 0.00 1.00 0.00 0.977 0.000 0.992 0.000 $\downarrow$
75 1.00 0.00 1.00 0.00 1.000 0.000 1.000 0.000 $\downarrow$
100 1.00 0 1.00 0 1.000 0 1.000 0 $\downarrow$
200 1.00 0 1.00 0 1.000 0 1.000 0 $\downarrow$
  Case 8B
  ti simulations with $F_{{{\rm AP}}}(t,S=1/3,\sigma_{{P}}=0.1)$ rounded to multiples of $(3/\pi)\sigma_{{P}}$
n H2 rejected with $\gamma =0.01$ H0 rejected with $\gamma =0.01$ H2 rejected with $\gamma =0.001$ H0 rejected with $\gamma =0.001$
10 0.10 0.01 0.09 0.01 0.023 0.001 0.002 0.000
25 0.56 0.01 0.66 0.02 0.319 0.002 0.385 0.005
50 0.96 0.00 0.98 0.00 $\downarrow$ 0.876 0.001 $\downarrow$ 0.941 0.002 $\downarrow$
75 1.00 0.00 1.00 0.00 $\downarrow$ 0.991 0.000 $\downarrow$ 0.998 0.000 $\downarrow$
100 1.00 0.00 1.00 0.00 $\downarrow$ 1.000 0.000 $\downarrow$ 1.000 0.000 $\downarrow$
200 1.00 0 1.00 0 $\downarrow$ 1.000 0 $\downarrow$ 1.000 0 $\downarrow$
  Case 8C
  ti simulations with $F_{{{\rm AP}}}(t,S=1/3,\sigma_{{P}}=0.2)$ rounded to multiples of $(3/\pi)\sigma_{{P}}$
n H3 rejected with $\gamma =0.01$ H0 rejected with $\gamma =0.01$ H3 rejected with $\gamma =0.001$ H0 rejected with $\gamma =0.001$
10 0.01 0.01 0.01 0.01 0.001 0.001 0.000 0.000
25 0.04 0.01 0.07 0.03 0.010 0.002 0.015 0.003
50 0.18 0.02 0.31 0.05 0.064 0.003 0.123 0.009
75 0.38 0.02 0.56 0.04 $\downarrow$ 0.189 0.004 0.318 0.011
100 0.59 0.01 $\downarrow$ 0.76 0.03 $\downarrow$ 0.342 0.004 0.539 0.011
200 0.97 0.00 $\downarrow$ 0.99 0.00 $\downarrow$ 0.889 0.002 $\downarrow$ 0.966 0.003 $\downarrow$
  Case 8D
  ti simulations with $F_{{{\rm AP}}}(t,S=1/3,\sigma_{{P}}=0.3)$ rounded to multiples of $(3/\pi)\sigma_{{P}}$
n H4 rejected with $\gamma =0.01$ H0 rejected with $\gamma =0.01$ H4 rejected with $\gamma =0.001$ H0 rejected with $\gamma =0.001$
10 0.00 0.01 0.00 0.01 0.000 0.003 0.000 0.002
25 0.00 0.01 0.01 0.03 0.000 0.002 0.001 0.004
50 0.00 0.02 0.01 0.04 0.001 0.002 0.002 0.006
75 0.01 0.02 0.02 0.05 0.001 0.002 0.004 0.008
100 0.01 0.02 0.03 0.06 0.002 0.002 0.007 0.010
200 0.04 0.02 0.10 0.08 0.009 0.003 0.029 0.016

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