Math150 S-PLUS> bdtest() in 10 random samples of 1800 birthdays, the maximum number of matching birthdays were: ************************************************************** [1] 12 [1] 12 [1] 11 [1] 11 [1] 12 [1] 13 [1] 12 [1] 12 [1] 12 [1] 13 ************************************************************** In the real OXY sample: max number of MATCHing birthdays: 14 after the 0-values are removed, here is the distribution of the MATCH numbers (from 1 to max) [see crosstabulation for real zeros] 19 35 54 55 60 51 34 33 8 8 4 1 1 1 [1] "with a value of day+31*month= 289" day/month:10/9 DAY MO YEAR STATE 75 10 9 1980 CA 136 10 9 1985 CA 325 10 9 1986 CA 326 10 9 1986 CA 519 10 9 1987 CA 520 10 9 1987 CA 521 10 9 1987 CA 725 10 9 1988 CA 903 10 9 1989 CA 904 10 9 1989 CA 905 10 9 1989 CA 1122 10 9 1986 IL 1285 10 9 1985 MO 1733 10 9 1987 WA [1] "BTW, here is the crosstabulated sample of 1814 students:" Call: crosstabs(formula = ~ DAY + MO, data = birthdays.S08) 1814 cases in table +----------+ |N | |N/RowTotal| |N/ColTotal| |N/Total | +----------+ DAY |MO |1 |2 |3 |4 |5 |6 |7 |8 |9 |10 |11 |12 |RwTtl| ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 1 | 2 | 3 | 9 | 6 | 7 | 2 | 5 | 6 | 3 | 8 | 5 | 4 |60 | |0.033 |0.05 |0.15 |0.1 |0.12 |0.033 |0.083 |0.1 |0.05 |0.13 |0.083 |0.067 |0.033| |0.014 |0.022 |0.054 |0.046 |0.038 |0.013 |0.036 |0.039 |0.018 |0.05 |0.035 |0.027 | | |0.0011|0.0017|0.005 |0.0033|0.0039|0.0011|0.0028|0.0033|0.0017|0.0044|0.0028|0.0022| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 2 | 5 | 8 | 1 | 3 | 6 | 6 | 2 | 1 | 5 | 5 | 8 | 5 |55 | |0.091 |0.15 |0.018 |0.055 |0.11 |0.11 |0.036 |0.018 |0.091 |0.091 |0.15 |0.091 |0.03 | |0.035 |0.059 |0.006 |0.023 |0.033 |0.04 |0.014 |0.0065|0.03 |0.031 |0.057 |0.034 | | |0.0028|0.0044|5.5e-4|0.0017|0.0033|0.0033|0.0011|5.5e-4|0.0028|0.0028|0.0044|0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 3 | 4 | 6 | 6 | 5 | 7 |11 | 2 | 4 | 8 | 3 | 3 | 8 |67 | |0.06 |0.09 |0.09 |0.075 |0.1 |0.16 |0.03 |0.06 |0.12 |0.045 |0.045 |0.12 |0.037| |0.028 |0.044 |0.036 |0.038 |0.038 |0.073 |0.014 |0.026 |0.048 |0.019 |0.021 |0.055 | | |0.0022|0.0033|0.0033|0.0028|0.0039|0.0061|0.0011|0.0022|0.0044|0.0017|0.0017|0.0044| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 4 | 8 | 2 | 4 | 3 | 2 | 7 | 1 | 7 | 5 | 8 | 2 | 5 |54 | |0.15 |0.037 |0.074 |0.056 |0.037 |0.13 |0.019 |0.13 |0.093 |0.15 |0.037 |0.093 |0.03 | |0.056 |0.015 |0.024 |0.023 |0.011 |0.046 |0.0072|0.045 |0.03 |0.05 |0.014 |0.034 | | |0.0044|0.0011|0.0022|0.0017|0.0011|0.0039|5.5e-4|0.0039|0.0028|0.0044|0.0011|0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 5 | 3 | 1 | 2 | 4 | 6 | 3 | 7 | 4 | 5 | 7 | 3 | 4 |49 | |0.061 |0.02 |0.041 |0.082 |0.12 |0.061 |0.14 |0.082 |0.1 |0.14 |0.061 |0.082 |0.027| |0.021 |0.0074|0.012 |0.031 |0.033 |0.02 |0.05 |0.026 |0.03 |0.043 |0.021 |0.027 | | |0.0017|5.5e-4|0.0011|0.0022|0.0033|0.0017|0.0039|0.0022|0.0028|0.0039|0.0017|0.0022| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 6 | 3 | 2 | 7 | 3 | 4 | 2 |10 | 3 | 6 | 2 | 7 | 5 |54 | |0.056 |0.037 |0.13 |0.056 |0.074 |0.037 |0.19 |0.056 |0.11 |0.037 |0.13 |0.093 |0.03 | |0.021 |0.015 |0.042 |0.023 |0.022 |0.013 |0.072 |0.019 |0.036 |0.012 |0.05 |0.034 | | |0.0017|0.0011|0.0039|0.0017|0.0022|0.0011|0.0055|0.0017|0.0033|0.0011|0.0039|0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 7 | 7 | 3 | 9 | 2 | 3 | 5 | 6 | 3 | 6 | 7 | 8 | 5 |64 | |0.11 |0.047 |0.14 |0.031 |0.047 |0.078 |0.094 |0.047 |0.094 |0.11 |0.12 |0.078 |0.035| |0.049 |0.022 |0.054 |0.015 |0.016 |0.033 |0.043 |0.019 |0.036 |0.043 |0.057 |0.034 | | |0.0039|0.0017|0.005 |0.0011|0.0017|0.0028|0.0033|0.0017|0.0033|0.0039|0.0044|0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 8 | 1 | 6 | 3 | 7 | 9 | 4 | 4 | 5 | 3 | 6 | 6 | 6 |60 | |0.017 |0.1 |0.05 |0.12 |0.15 |0.067 |0.067 |0.083 |0.05 |0.1 |0.1 |0.1 |0.033| |0.007 |0.044 |0.018 |0.054 |0.049 |0.026 |0.029 |0.032 |0.018 |0.037 |0.043 |0.041 | | |5.5e-4|0.0033|0.0017|0.0039|0.005 |0.0022|0.0022|0.0028|0.0017|0.0033|0.0033|0.0033| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 9 | 1 | 5 | 4 | 8 | 3 | 8 | 1 | 1 | 6 |10 | 6 | 6 |59 | |0.017 |0.085 |0.068 |0.14 |0.051 |0.14 |0.017 |0.017 |0.1 |0.17 |0.1 |0.1 |0.033| |0.007 |0.037 |0.024 |0.062 |0.016 |0.053 |0.0072|0.0065|0.036 |0.062 |0.043 |0.041 | | |5.5e-4|0.0028|0.0022|0.0044|0.0017|0.0044|5.5e-4|5.5e-4|0.0033|0.0055|0.0033|0.0033| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 10 | 8 | 5 | 4 | 3 | 6 | 7 | 9 | 3 |14 | 5 | 7 | 5 |76 | |0.11 |0.066 |0.053 |0.039 |0.079 |0.092 |0.12 |0.039 |0.18 |0.066 |0.092 |0.066 |0.042| |0.056 |0.037 |0.024 |0.023 |0.033 |0.046 |0.065 |0.019 |0.085 |0.031 |0.05 |0.034 | | |0.0044|0.0028|0.0022|0.0017|0.0033|0.0039|0.005 |0.0017|0.0077|0.0028|0.0039|0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 11 | 1 | 4 | 3 | 2 | 6 | 5 | 1 | 3 | 2 | 3 | 4 | 4 |38 | |0.026 |0.11 |0.079 |0.053 |0.16 |0.13 |0.026 |0.079 |0.053 |0.079 |0.11 |0.11 |0.021| |0.007 |0.029 |0.018 |0.015 |0.033 |0.033 |0.0072|0.019 |0.012 |0.019 |0.028 |0.027 | | |5.5e-4|0.0022|0.0017|0.0011|0.0033|0.0028|5.5e-4|0.0017|0.0011|0.0017|0.0022|0.0022| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 12 | 4 | 3 | 6 | 2 | 7 | 4 | 4 | 6 |11 | 6 | 5 | 4 |62 | |0.065 |0.048 |0.097 |0.032 |0.11 |0.065 |0.065 |0.097 |0.18 |0.097 |0.081 |0.065 |0.034| |0.028 |0.022 |0.036 |0.015 |0.038 |0.026 |0.029 |0.039 |0.067 |0.037 |0.035 |0.027 | | |0.0022|0.0017|0.0033|0.0011|0.0039|0.0022|0.0022|0.0033|0.0061|0.0033|0.0028|0.0022| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 13 | 5 | 8 | 4 | 3 | 8 | 7 | 3 | 3 | 2 | 6 | 1 | 5 |55 | |0.091 |0.15 |0.073 |0.055 |0.15 |0.13 |0.055 |0.055 |0.036 |0.11 |0.018 |0.091 |0.03 | |0.035 |0.059 |0.024 |0.023 |0.044 |0.046 |0.022 |0.019 |0.012 |0.037 |0.0071|0.034 | | |0.0028|0.0044|0.0022|0.0017|0.0044|0.0039|0.0017|0.0017|0.0011|0.0033|5.5e-4|0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 14 | 8 | 8 | 5 | 5 | 8 | 2 | 5 | 5 | 6 | 5 | 0 | 5 |62 | |0.13 |0.13 |0.081 |0.081 |0.13 |0.032 |0.081 |0.081 |0.097 |0.081 |0 |0.081 |0.034| |0.056 |0.059 |0.03 |0.038 |0.044 |0.013 |0.036 |0.032 |0.036 |0.031 |0 |0.034 | | |0.0044|0.0044|0.0028|0.0028|0.0044|0.0011|0.0028|0.0028|0.0033|0.0028|0 |0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 15 | 2 | 5 | 5 | 4 | 5 | 6 | 5 | 8 | 7 | 3 | 5 | 3 |58 | |0.034 |0.086 |0.086 |0.069 |0.086 |0.1 |0.086 |0.14 |0.12 |0.052 |0.086 |0.052 |0.032| |0.014 |0.037 |0.03 |0.031 |0.027 |0.04 |0.036 |0.052 |0.042 |0.019 |0.035 |0.021 | | |0.0011|0.0028|0.0028|0.0022|0.0028|0.0033|0.0028|0.0044|0.0039|0.0017|0.0028|0.0017| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 16 | 3 | 1 | 7 | 6 | 9 | 8 | 2 | 9 | 4 | 4 | 3 |10 |66 | |0.045 |0.015 |0.11 |0.091 |0.14 |0.12 |0.03 |0.14 |0.061 |0.061 |0.045 |0.15 |0.036| |0.021 |0.0074|0.042 |0.046 |0.049 |0.053 |0.014 |0.058 |0.024 |0.025 |0.021 |0.068 | | |0.0017|5.5e-4|0.0039|0.0033|0.005 |0.0044|0.0011|0.005 |0.0022|0.0022|0.0017|0.0055| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 17 | 3 | 5 | 3 | 6 | 2 | 5 | 5 | 2 | 3 | 5 | 3 | 5 |47 | |0.064 |0.11 |0.064 |0.13 |0.043 |0.11 |0.11 |0.043 |0.064 |0.11 |0.064 |0.11 |0.026| |0.021 |0.037 |0.018 |0.046 |0.011 |0.033 |0.036 |0.013 |0.018 |0.031 |0.021 |0.034 | | |0.0017|0.0028|0.0017|0.0033|0.0011|0.0028|0.0028|0.0011|0.0017|0.0028|0.0017|0.0028| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 18 | 2 | 8 | 4 | 4 | 8 | 3 | 9 | 5 | 4 | 6 | 4 | 6 |63 | |0.032 |0.13 |0.063 |0.063 |0.13 |0.048 |0.14 |0.079 |0.063 |0.095 |0.063 |0.095 |0.035| |0.014 |0.059 |0.024 |0.031 |0.044 |0.02 |0.065 |0.032 |0.024 |0.037 |0.028 |0.041 | | |0.0011|0.0044|0.0022|0.0022|0.0044|0.0017|0.005 |0.0028|0.0022|0.0033|0.0022|0.0033| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 19 | 6 | 2 | 7 | 4 | 4 | 2 | 5 | 5 | 3 | 6 | 4 | 4 |52 | |0.12 |0.038 |0.13 |0.077 |0.077 |0.038 |0.096 |0.096 |0.058 |0.12 |0.077 |0.077 |0.029| |0.042 |0.015 |0.042 |0.031 |0.022 |0.013 |0.036 |0.032 |0.018 |0.037 |0.028 |0.027 | | |0.0033|0.0011|0.0039|0.0022|0.0022|0.0011|0.0028|0.0028|0.0017|0.0033|0.0022|0.0022| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 20 | 4 | 4 |10 | 3 | 4 | 4 | 7 |10 | 4 | 7 | 5 | 2 |64 | |0.062 |0.062 |0.16 |0.047 |0.062 |0.062 |0.11 |0.16 |0.062 |0.11 |0.078 |0.031 |0.035| |0.028 |0.029 |0.06 |0.023 |0.022 |0.026 |0.05 |0.065 |0.024 |0.043 |0.035 |0.014 | | |0.0022|0.0022|0.0055|0.0017|0.0022|0.0022|0.0039|0.0055|0.0022|0.0039|0.0028|0.0011| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 21 | 4 | 5 | 4 | 5 | 4 | 5 | 4 | 4 | 3 |11 | 7 | 6 |62 | |0.065 |0.081 |0.065 |0.081 |0.065 |0.081 |0.065 |0.065 |0.048 |0.18 |0.11 |0.097 |0.034| |0.028 |0.037 |0.024 |0.038 |0.022 |0.033 |0.029 |0.026 |0.018 |0.068 |0.05 |0.041 | | |0.0022|0.0028|0.0022|0.0028|0.0022|0.0028|0.0022|0.0022|0.0017|0.0061|0.0039|0.0033| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 22 | 2 | 3 | 8 | 7 | 7 | 4 | 4 | 5 | 5 | 2 | 1 | 3 |51 | |0.039 |0.059 |0.16 |0.14 |0.14 |0.078 |0.078 |0.098 |0.098 |0.039 |0.02 |0.059 |0.028| |0.014 |0.022 |0.048 |0.054 |0.038 |0.026 |0.029 |0.032 |0.03 |0.012 |0.0071|0.021 | | |0.0011|0.0017|0.0044|0.0039|0.0039|0.0022|0.0022|0.0028|0.0028|0.0011|5.5e-4|0.0017| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 23 | 7 | 6 | 4 | 1 | 7 | 6 | 7 | 8 | 8 | 1 | 6 | 7 |68 | |0.1 |0.088 |0.059 |0.015 |0.1 |0.088 |0.1 |0.12 |0.12 |0.015 |0.088 |0.1 |0.037| |0.049 |0.044 |0.024 |0.0077|0.038 |0.04 |0.05 |0.052 |0.048 |0.0062|0.043 |0.048 | | |0.0039|0.0033|0.0022|5.5e-4|0.0039|0.0033|0.0039|0.0044|0.0044|5.5e-4|0.0033|0.0039| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 24 | 5 |10 | 7 | 8 | 8 | 3 | 6 | 7 | 1 | 7 | 4 | 1 |67 | |0.075 |0.15 |0.1 |0.12 |0.12 |0.045 |0.09 |0.1 |0.015 |0.1 |0.06 |0.015 |0.037| |0.035 |0.074 |0.042 |0.062 |0.044 |0.02 |0.043 |0.045 |0.0061|0.043 |0.028 |0.0068| | |0.0028|0.0055|0.0039|0.0044|0.0044|0.0017|0.0033|0.0039|5.5e-4|0.0039|0.0022|5.5e-4| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 25 | 6 | 5 | 8 | 1 | 8 | 7 | 3 | 8 | 8 | 5 | 6 | 3 |68 | |0.088 |0.074 |0.12 |0.015 |0.12 |0.1 |0.044 |0.12 |0.12 |0.074 |0.088 |0.044 |0.037| |0.042 |0.037 |0.048 |0.0077|0.044 |0.046 |0.022 |0.052 |0.048 |0.031 |0.043 |0.021 | | |0.0033|0.0028|0.0044|5.5e-4|0.0044|0.0039|0.0017|0.0044|0.0044|0.0028|0.0033|0.0017| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 26 | 4 | 7 | 2 | 6 | 3 | 6 | 3 | 5 | 6 | 0 | 1 | 2 |45 | |0.089 |0.16 |0.044 |0.13 |0.067 |0.13 |0.067 |0.11 |0.13 |0 |0.022 |0.044 |0.025| |0.028 |0.051 |0.012 |0.046 |0.016 |0.04 |0.022 |0.032 |0.036 |0 |0.0071|0.014 | | |0.0022|0.0039|0.0011|0.0033|0.0017|0.0033|0.0017|0.0028|0.0033|0 |5.5e-4|0.0011| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 27 | 5 | 6 | 5 | 3 |13 | 4 | 5 | 6 | 4 |10 | 6 | 4 |71 | |0.07 |0.085 |0.07 |0.042 |0.18 |0.056 |0.07 |0.085 |0.056 |0.14 |0.085 |0.056 |0.039| |0.035 |0.044 |0.03 |0.023 |0.071 |0.026 |0.036 |0.039 |0.024 |0.062 |0.043 |0.027 | | |0.0028|0.0033|0.0028|0.0017|0.0072|0.0022|0.0028|0.0033|0.0022|0.0055|0.0033|0.0022| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 28 |10 | 3 |12 | 6 | 6 | 4 | 4 | 3 | 6 | 2 | 4 | 2 |62 | |0.16 |0.048 |0.19 |0.097 |0.097 |0.065 |0.065 |0.048 |0.097 |0.032 |0.065 |0.032 |0.034| |0.07 |0.022 |0.072 |0.046 |0.033 |0.026 |0.029 |0.019 |0.036 |0.012 |0.028 |0.014 | | |0.0055|0.0017|0.0066|0.0033|0.0033|0.0022|0.0022|0.0017|0.0033|0.0011|0.0022|0.0011| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 29 | 8 | 2 | 2 | 7 | 6 | 3 | 3 | 5 |11 | 4 | 9 | 4 |64 | |0.12 |0.031 |0.031 |0.11 |0.094 |0.047 |0.047 |0.078 |0.17 |0.062 |0.14 |0.062 |0.035| |0.056 |0.015 |0.012 |0.054 |0.033 |0.02 |0.022 |0.032 |0.067 |0.025 |0.064 |0.027 | | |0.0044|0.0011|0.0011|0.0039|0.0033|0.0017|0.0017|0.0028|0.0061|0.0022|0.005 |0.0022| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 30 | 8 | 0 | 5 | 3 | 5 | 8 | 3 | 5 | 6 | 2 | 8 | 7 |60 | |0.13 |0 |0.083 |0.05 |0.083 |0.13 |0.05 |0.083 |0.1 |0.033 |0.13 |0.12 |0.033| |0.056 |0 |0.03 |0.023 |0.027 |0.053 |0.022 |0.032 |0.036 |0.012 |0.057 |0.048 | | |0.0044|0 |0.0028|0.0017|0.0028|0.0044|0.0017|0.0028|0.0033|0.0011|0.0044|0.0039| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ 31 | 3 | 0 | 6 | 0 | 2 | 0 | 4 | 5 | 0 | 5 | 0 | 6 |31 | |0.097 |0 |0.19 |0 |0.065 |0 |0.13 |0.16 |0 |0.16 |0 |0.19 |0.017| |0.021 |0 |0.036 |0 |0.011 |0 |0.029 |0.032 |0 |0.031 |0 |0.041 | | |0.0017|0 |0.0033|0 |0.0011|0 |0.0022|0.0028|0 |0.0028|0 |0.0033| | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ ColTtl|142 |136 |166 |130 |183 |151 |139 |154 |165 |161 |141 |146 |1814 | |0.078 |0.075 |0.092 |0.072 |0.1 |0.083 |0.077 |0.085 |0.091 |0.089 |0.078 |0.08 | | ------+------+------+------+------+------+------+------+------+------+------+------+------+-----+ Test for independence of all factors Chi^2 = 396.9 d.f.= 330 (p=0.006706) Yates' correction was not used Some expected values are less than 5, don't trust stated p-value NULL Math150 S-PLUS>