Table 4.
The error between simulated coverage probability and nominal coverage probability for the 95% two-sided and 97.5% one-sided confidence intervals when N = 50, 100, and 200
| Exact approach | Chakraborti and Li [24] | Bland and Altman [2] | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| N | p | Upper | Lower | Two-sided | Upper | Lower | Two-sided | Upper | Lower | Two-sided |
| 97.5% CI | 97.5% CI | 95% CI | 97.5% CI | 97.5% CI | 95% CI | 97.5% CI | 97.5% CI | 95% CI | ||
| 50 | 0.025 | −0.0004 | − 0.0022 | −0.0026 | − 0.0188 | 0.0144 | − 0.0044 | −0.0221 | 0.0157 | −0.0064 |
| 0.05 | −0.0002 | −0.0026 | − 0.0028 | −0.0169 | 0.0131 | −0.0038 | − 0.0208 | 0.0145 | − 0.0063 | |
| 0.10 | 0.0007 | −0.0018 | −0.0011 | − 0.0135 | 0.0104 | − 0.0031 | −0.0164 | 0.0120 | −0.0044 | |
| 0.20 | 0.0009 | −0.0020 | −0.0011 | − 0.0083 | 0.0084 | 0.0001 | −0.0105 | 0.0089 | −0.0016 | |
| 0.80 | −0.0001 | −0.0008 | − 0.0009 | 0.0102 | − 0.0114 | −0.0012 | 0.0112 | −0.0132 | − 0.0020 | |
| 0.90 | 0.0020 | −0.0017 | 0.0003 | 0.0138 | −0.0161 | −0.0023 | 0.0146 | −0.0189 | − 0.0043 | |
| 0.95 | 0.0031 | 0.0006 | 0.0037 | 0.0159 | −0.0145 | 0.0014 | 0.0161 | −0.0183 | −0.0022 | |
| 0.975 | 0.0014 | −0.0010 | 0.0004 | 0.0160 | −0.0182 | −0.0022 | 0.0167 | −0.0227 | − 0.0060 | |
| 100 | 0.025 | 0.0015 | −0.0017 | −0.0002 | − 0.0096 | 0.0105 | 0.0009 | −0.0119 | 0.0116 | −0.0003 |
| 0.05 | 0.0007 | −0.0030 | −0.0023 | − 0.0090 | 0.0091 | 0.0001 | −0.0108 | 0.0106 | −0.0002 | |
| 0.10 | 0.0002 | −0.0008 | −0.0006 | − 0.0106 | 0.0095 | − 0.0011 | −0.0128 | 0.0101 | −0.0027 | |
| 0.20 | −0.0002 | 0.0035 | 0.0033 | −0.0090 | 0.0110 | 0.0020 | −0.0104 | 0.0115 | 0.0011 | |
| 0.80 | 0.0014 | 0.0008 | 0.0022 | 0.0088 | −0.0075 | 0.0013 | 0.0092 | −0.0094 | −0.0002 | |
| 0.90 | 0.0005 | 0.0000 | 0.0005 | 0.0111 | −0.0096 | 0.0015 | 0.0121 | −0.0120 | 0.0001 | |
| 0.95 | 0.0013 | −0.0012 | 0.0001 | 0.0115 | −0.0143 | −0.0028 | 0.0117 | −0.0164 | − 0.0047 | |
| 0.975 | 0.0014 | −0.0011 | 0.0003 | 0.0118 | −0.0140 | −0.0022 | 0.0125 | −0.0160 | − 0.0035 | |
| 200 | 0.025 | 0.0006 | −0.0019 | −0.0013 | − 0.0066 | 0.0077 | 0.0011 | −0.0084 | 0.0084 | 0.0000 |
| 0.05 | 0.0021 | −0.0013 | 0.0008 | −0.0056 | 0.0075 | 0.0019 | −0.0077 | 0.0079 | 0.0002 | |
| 0.10 | 0.0005 | 0.0023 | 0.0028 | −0.0068 | 0.0088 | 0.0020 | −0.0079 | 0.0095 | 0.0016 | |
| 0.20 | 0.0012 | −0.0012 | 0.0000 | −0.0042 | 0.0047 | 0.0005 | −0.0052 | 0.0053 | 0.0001 | |
| 0.80 | 0.0029 | −0.0017 | 0.0012 | 0.0077 | −0.0077 | 0.0000 | 0.0080 | −0.0095 | −0.0015 | |
| 0.90 | −0.0015 | −0.0001 | − 0.0016 | 0.0054 | − 0.0070 | −0.0016 | 0.0061 | −0.0085 | − 0.0024 | |
| 0.95 | 0.0020 | −0.0021 | −0.0001 | 0.0100 | −0.0089 | 0.0011 | 0.0104 | −0.0100 | 0.0004 | |
| 0.975 | 0.0016 | 0.0003 | 0.0019 | 0.0093 | −0.0080 | 0.0013 | 0.0103 | −0.0099 | 0.0004 | |