Power
Randomization-Based Inference
The Null Hypothesis
From data to schedule
| My Data | ||
| i | d_i | y_i |
|---|---|---|
| 1 | 1 | 0.90 |
| 2 | 0 | -0.50 |
| 3 | 1 | 2.20 |
| 4 | 0 | -1.40 |
| 5 | 0 | 0.10 |
| 6 | 0 | -1.00 |
| 7 | 0 | 1.10 |
| 8 | 1 | 1.00 |
| 9 | 1 | 1.02 |
| 10 | 1 | 1.50 |
| My Observed Schedule | ||
| i | Y_0 | Y_1 |
|---|---|---|
| 1 | NA | 0.90 |
| 2 | -0.5 | NA |
| 3 | NA | 2.20 |
| 4 | -1.4 | NA |
| 5 | 0.1 | NA |
| 6 | -1.0 | NA |
| 7 | 1.1 | NA |
| 8 | NA | 1.00 |
| 9 | NA | 1.02 |
| 10 | NA | 1.50 |
From data to schedule
| My Observed Schedule | ||
| i | Y_0 | Y_1 |
|---|---|---|
| 1 | NA | 0.90 |
| 2 | -0.5 | NA |
| 3 | NA | 2.20 |
| 4 | -1.4 | NA |
| 5 | 0.1 | NA |
| 6 | -1.0 | NA |
| 7 | 1.1 | NA |
| 8 | NA | 1.00 |
| 9 | NA | 1.02 |
| 10 | NA | 1.50 |
| My Null Schedule | ||
| i | Y_0 | Y_1 |
|---|---|---|
| 1 | 0.90 | 0.90 |
| 2 | -0.50 | -0.50 |
| 3 | 2.20 | 2.20 |
| 4 | -1.40 | -1.40 |
| 5 | 0.10 | 0.10 |
| 6 | -1.00 | -1.00 |
| 7 | 1.10 | 1.10 |
| 8 | 1.00 | 1.00 |
| 9 | 1.02 | 1.02 |
| 10 | 1.50 | 1.50 |
Estimate Dist under H0
rand_stats <- function(schedule, d_i, stat = "diff in means", reps = 1000) {
# store treatment vector separately
d_i_vec <- d_i
# replicate the schedule reps times and stack them on top of one another
randomized_exp_df <- map_dfr(1:reps, ~ schedule, .id = "experiment") |>
mutate(experiment = factor(experiment, levels = as.character(1:reps), ordered = TRUE),
d_i = c(replicate(n = reps, sample(d_i_vec))), # create random assignments
y_i = Y_1 * d_i + Y_0 * (1 - d_i)) |> # find observed responses
arrange(experiment)
# calculate test statistic for every random assignment
if (stat == "diff in means") {
stats <- randomized_exp_df |>
group_by(experiment, d_i) |>
summarize(ybar = mean(y_i), # average within each group within each experiment
.groups = "drop_last") |>
summarize(ATE_hat = diff(ybar),
.groups = "drop") |> # take the difference between the two groups mean
pull()
} else {
stop("Statistic not implemented")
}
return(stats)
}Estimate Dist under H0
[1] 0.024 0.584 0.664 -0.616 -0.584 0.344 1.136 0.896 1.304 -1.504
[11] 0.136 0.264 0.304 -0.544 0.776 -1.144 -0.864 1.144 0.496 0.256
[21] -0.496 1.104 -1.144 -0.696 1.184 -0.864 -0.376 0.664 -1.224 1.304
[31] 0.096 -0.336 -0.264 -1.744 0.704 0.416 -0.096 0.224 -0.336 -0.544
[41] -0.336 -0.064 0.584 -0.296 0.376 -1.344 0.896 -0.504 0.584 -0.704
[51] -0.096 -0.416 -1.224 0.216 -0.864 -0.304 -1.344 1.384 -0.544 0.416
[61] 0.336 -0.336 0.864 0.776 -0.584 0.904 0.744 0.136 0.536 -1.504
[71] -0.536 0.224 0.376 -0.704 -0.576 -0.584 0.664 0.224 0.776 0.144
[81] 0.064 0.776 -0.144 -0.856 -1.136 -0.104 1.104 0.224 -0.496 -0.504
[91] -0.264 -0.296 -0.016 -0.096 0.296 -0.144 -0.904 -1.144 -0.104 0.304
[101] -0.496 0.504 -0.184 -1.744 -1.224 0.096 1.504 0.864 -0.064 -0.096
[111] 0.856 0.056 0.296 -1.384 -1.344 -0.256 -1.104 -0.296 -0.536 0.104
[121] 0.664 -1.744 -0.256 -1.144 0.904 -0.176 -0.064 -0.304 0.304 0.944
[131] 0.296 0.584 0.544 -0.664 0.496 0.576 0.584 -1.696 -0.096 -0.344
[141] -0.104 0.384 -0.584 -0.696 0.056 0.376 0.576 -0.696 -1.184 -0.776
[151] -0.736 1.504 0.424 -0.384 0.256 -1.664 -0.504 0.664 -0.536 -0.096
[161] -0.096 0.704 0.856 0.336 0.136 0.096 -1.224 -0.536 0.424 -0.536
[171] -0.544 0.616 0.856 -1.096 0.376 -0.536 0.224 -1.136 0.904 -0.416
[181] -1.384 -0.616 0.024 0.744 0.424 1.664 -1.296 -0.144 -0.536 0.824
[191] -0.704 -1.744 0.224 -0.864 0.424 0.584 -1.504 -0.096 -1.224 0.376
[201] -0.864 -1.136 0.024 1.144 -1.376 0.104 -0.536 0.056 0.136 0.536
[211] -0.136 1.384 -0.096 0.384 0.904 0.256 -0.384 -0.256 0.176 0.224
[221] -0.176 -0.344 -0.784 -1.104 -1.104 0.264 -0.736 -0.104 0.176 0.864
[231] -0.504 -0.576 0.696 -1.064 0.264 -1.376 0.304 -0.704 -0.704 -0.864
[241] 0.616 -0.336 -0.944 -0.864 1.664 0.904 -0.536 0.664 0.696 0.376
[251] -0.496 0.376 0.144 -0.336 0.536 -0.064 -0.664 -1.384 0.056 0.136
[261] -1.336 -1.664 0.696 -0.104 0.304 0.104 -0.696 0.144 0.824 0.736
[271] 0.864 -1.184 0.064 0.744 -0.016 0.584 0.576 0.104 0.064 -0.704
[281] 0.856 0.104 -0.944 0.576 -1.296 0.696 0.784 0.136 0.104 -0.096
[291] -0.536 -0.224 0.056 0.896 -0.584 0.576 -0.016 0.296 -0.744 0.664
[301] -1.184 -1.296 0.264 -0.224 0.896 -0.704 0.384 0.304 0.144 -1.696
[311] 0.216 -0.904 0.144 -0.784 -0.064 0.064 0.856 0.864 -0.296 -0.224
[321] 0.544 0.664 1.744 -0.744 -0.024 1.104 -0.784 0.704 -0.296 -0.424
[331] -0.144 -0.424 -0.664 0.496 0.056 -0.136 0.536 -0.696 -0.176 -0.376
[341] -0.744 -0.896 -0.096 0.104 0.384 -0.944 0.096 1.056 -0.584 0.824
[351] -0.744 0.776 -0.904 0.896 0.576 0.224 -0.896 0.376 0.344 -0.664
[361] 0.856 -0.864 0.776 0.864 0.024 0.944 -0.256 0.544 -0.544 0.296
[371] -0.736 -1.224 0.056 -0.536 -1.104 -0.104 1.064 0.256 0.896 1.696
[381] -0.144 -0.624 0.144 -0.224 -0.696 0.504 -0.304 0.536 0.864 -1.144
[391] -1.104 -0.416 0.056 0.544 -0.744 0.304 -0.336 0.256 0.224 -0.176
[401] 0.744 -0.296 -0.576 -0.104 0.936 0.096 0.104 -1.096 0.336 -0.064
[411] -0.144 -0.544 0.696 -0.336 -0.144 -0.464 -0.736 0.304 0.384 -0.384
[421] 1.696 1.696 0.496 -0.584 -0.544 0.904 -0.864 -1.336 -0.344 0.256
[431] 1.224 -0.336 -0.296 -0.336 0.056 0.904 0.496 -0.496 -0.064 0.424
[441] -0.384 -0.296 0.696 1.336 -0.576 -0.864 0.224 0.136 0.096 1.136
[451] 0.664 0.304 0.576 0.064 1.504 0.696 0.304 -0.016 0.536 0.664
[461] 0.376 0.864 -0.584 0.144 0.664 -0.144 0.904 1.104 0.056 1.136
[471] -0.784 -0.296 1.296 0.224 0.784 0.896 0.584 0.544 0.224 -0.224
[481] -1.336 -0.944 0.296 -0.584 1.184 0.224 -0.336 1.504 -0.944 -0.744
[491] 0.064 -0.536 0.224 1.744 -0.696 -0.144 0.056 -0.376 0.576 0.904
[501] -0.896 -1.136 -0.304 0.576 -0.696 -1.136 -0.224 0.696 0.024 1.144
[511] -1.296 0.896 0.696 1.704 1.344 -0.424 1.224 -0.104 -0.496 -0.576
[521] 0.136 -0.256 0.144 1.336 0.904 -0.136 0.544 0.544 0.376 -0.064
[531] -1.104 -0.544 0.704 -1.104 -0.136 -1.704 -0.384 0.864 -0.576 -1.664
[541] -0.304 -0.416 -0.024 -0.016 0.224 -1.704 0.664 -0.136 0.304 0.584
[551] -0.584 0.224 -0.264 -1.136 -1.136 0.336 0.584 0.264 0.104 -0.784
[561] 0.296 -0.296 0.864 0.256 -0.224 1.096 0.056 -0.224 1.056 0.216
[571] 0.104 -1.336 -0.304 0.664 -0.296 1.304 0.056 0.584 0.064 0.376
[581] -1.296 -0.736 1.296 0.416 -0.296 -1.504 0.024 0.896 -0.304 1.704
[591] -0.896 0.584 0.824 -0.096 -0.544 -0.536 -0.624 -0.184 -0.896 0.864
[601] 0.304 -0.416 -1.136 -0.256 -0.144 1.136 -0.216 0.056 -0.736 1.144
[611] 0.696 -0.104 -0.584 0.904 0.256 1.336 -0.576 -0.056 -0.704 -0.224
[621] -0.104 0.096 1.384 -1.224 0.544 -0.136 -1.064 0.664 0.776 -0.856
[631] 0.144 1.184 -0.104 1.344 0.536 -0.344 -0.744 -0.384 -1.136 1.504
[641] 0.224 -0.776 -0.216 0.584 0.496 0.256 -1.504 1.104 0.544 0.144
[651] -0.064 -0.544 -1.104 0.024 0.904 0.824 -0.704 -1.336 -1.136 0.704
[661] 0.744 0.304 0.016 0.224 0.256 1.296 -0.224 0.296 -0.264 1.056
[671] -0.336 1.104 -0.424 1.064 0.256 0.904 -0.496 0.904 -0.096 -0.416
[681] 0.776 -0.096 -0.616 -0.736 0.736 -0.264 -1.184 -0.216 -0.296 -0.576
[691] -0.576 -0.216 -0.176 0.776 0.504 -0.576 -0.696 -0.824 1.184 -0.224
[701] -0.904 1.136 0.704 -0.064 -0.336 -1.104 0.896 -1.704 -0.744 0.896
[711] -0.304 -0.496 0.304 0.944 -0.544 1.056 0.024 -0.384 0.216 0.336
[721] 0.384 -1.224 0.104 1.504 1.336 0.216 -0.536 0.376 -0.464 0.896
[731] 0.264 0.024 0.224 1.384 -0.824 1.376 0.224 0.104 0.056 -0.296
[741] -0.096 -0.056 0.024 0.176 -0.744 1.136 -0.584 1.096 0.664 0.224
[751] 0.584 -1.096 -0.624 0.944 0.096 0.256 -0.504 0.024 0.056 1.304
[761] -0.744 1.104 -1.056 0.376 0.696 0.344 0.904 0.664 0.024 -0.904
[771] 0.584 0.664 -0.496 -0.304 -0.536 1.104 0.016 0.304 0.256 -0.864
[781] 1.064 -0.504 -1.376 -0.384 -1.336 -0.384 0.216 -0.064 -1.744 -0.736
[791] 0.904 0.136 -1.696 0.584 0.744 0.064 1.344 -0.304 -0.256 -0.024
[801] 0.744 -0.904 1.504 -0.384 0.664 1.744 0.904 0.064 -0.624 0.224
[811] -0.744 -0.704 -0.616 -1.136 0.904 -1.376 -1.744 -0.056 1.304 -1.296
[821] 0.536 -0.704 -0.424 -0.304 0.856 1.144 0.896 0.216 0.904 -0.224
[831] -0.064 -0.176 1.136 -1.144 0.464 0.944 -0.064 0.776 -0.664 1.344
[841] 0.016 0.096 0.736 1.696 0.416 1.376 0.304 0.264 0.264 -0.296
[851] -0.256 0.256 0.864 -0.056 0.064 -0.744 1.144 0.296 0.336 -0.904
[861] 0.216 0.544 0.096 -0.104 0.896 0.256 0.536 0.544 1.504 -0.224
[871] 0.144 0.056 -1.136 0.664 -1.136 0.176 -0.616 0.256 1.184 0.856
[881] 1.144 0.424 0.024 -1.744 -0.264 0.464 0.384 -1.744 -0.136 0.264
[891] -0.056 1.696 -0.376 -0.544 -0.216 0.264 0.704 -0.544 -0.304 -0.384
[901] 0.856 -0.576 -0.176 0.056 -0.376 0.224 -0.224 -0.776 -1.296 -0.336
[911] 0.064 0.376 0.376 0.496 -1.696 0.056 1.064 -1.296 0.296 -0.224
[921] 1.376 -1.664 -0.176 0.016 0.696 -0.136 0.744 -0.424 -0.504 0.864
[931] -0.464 0.304 -0.584 -0.024 -0.744 0.064 -0.576 -0.336 -0.056 -0.064
[941] -0.064 1.136 -0.016 1.096 -0.864 0.704 -0.584 1.224 0.224 -0.064
[951] 1.304 -0.896 0.136 0.416 0.224 -0.776 0.904 -0.856 0.144 -0.224
[961] 0.104 0.736 1.664 -0.744 -1.384 0.736 -0.704 -0.896 -0.096 -1.664
[971] 0.856 -1.064 0.376 0.384 0.224 -0.704 -0.056 -0.064 -0.744 -0.224
[981] -1.104 -0.576 0.696 0.744 0.896 -1.184 -0.944 1.504 0.424 0.736
[991] 0.056 -0.504 0.024 0.336 -0.424 -0.384 0.776 -0.936 0.536 -0.304
[1001] 0.256 -0.504 -0.544 -0.576 -0.736 0.424 0.696 -0.304 -0.224 -0.856
[1011] 1.504 0.176 -0.496 -0.216 0.544 0.424 0.336 0.384 0.936 1.704
[1021] -0.944 -0.944 0.704 0.224 -1.376 -0.224 -0.096 0.336 0.144 0.704
[1031] -0.704 -0.056 0.056 -0.264 0.016 -0.584 -1.504 -0.856 -1.344 -1.504
[1041] 0.704 -0.104 -0.536 0.296 -0.576 0.104 0.904 0.184 -0.216 1.184
[1051] -1.664 0.856 0.824 -0.496 1.704 0.144 1.184 0.704 1.136 -1.744
[1061] 1.096 1.344 1.104 0.424 0.216 1.144 -0.696 -0.376 -1.136 0.376
[1071] -1.144 -1.504 -0.864 -0.664 -0.296 -0.744 0.416 0.264 -0.296 0.496
[1081] 1.224 -0.864 0.224 -0.704 0.096 0.336 -0.336 1.344 -1.344 -0.736
[1091] -0.176 0.144 -0.864 0.024 0.864 1.104 1.384 0.304 0.584 -1.344
[1101] 0.776 -0.136 0.056 -0.424 -1.336 -0.664 -0.336 0.104 0.096 0.336
[1111] -1.104 -0.176 -0.496 0.864 0.744 1.104 -0.336 0.056 1.184 -1.384
[1121] 0.664 0.696 -0.104 1.296 0.864 0.784 -0.176 -1.344 -0.736 -1.344
[1131] -0.744 0.064 0.056 0.536 1.184 0.864 -1.696 0.176 -0.944 -0.896
[1141] -0.064 0.544 1.376 0.544 -0.224 -0.304 0.696 -0.624 0.336 0.496
[1151] 0.144 1.304 -0.096 0.496 -0.664 1.056 -0.056 0.064 -0.024 0.696
[1161] -0.224 -0.376 1.664 -0.296 -0.424 -0.304 0.584 -0.104 -0.136 0.056
[1171] 0.544 0.264 0.304 0.776 -0.744 -0.536 -0.296 0.536 -0.304 0.264
[1181] -0.296 0.264 -0.104 0.344 0.856 -0.704 -0.536 -0.376 -0.536 0.424
[1191] -0.296 -0.264 0.096 0.064 0.904 -0.896 -0.336 -0.336 0.736 -0.224
[1201] 0.136 -0.704 1.744 -0.384 0.664 1.184 -0.904 0.064 -0.464 -0.104
[1211] -1.504 -1.296 0.224 -1.136 -0.696 0.384 -0.104 -0.584 0.544 -1.376
[1221] 1.696 -0.664 0.544 0.144 -0.104 0.896 0.384 -0.744 -0.864 0.536
[1231] -0.424 0.544 0.144 0.216 -0.176 0.064 0.544 -1.056 -0.056 0.864
[1241] -1.064 0.856 -0.944 -1.136 1.064 0.544 0.904 0.944 0.016 -0.664
[1251] 0.864 -0.344 0.304 0.056 -0.696 -0.224 -0.136 -0.416 -0.776 -0.136
[1261] -0.776 0.544 0.144 -0.296 0.256 0.944 -0.744 -0.224 -0.136 -0.896
[1271] -0.696 -0.256 -1.296 -0.744 0.584 -0.336 -0.576 0.224 0.504 -0.536
[1281] -0.184 -0.376 -0.704 -0.936 -1.136 -0.304 0.864 0.624 -0.264 -1.336
[1291] -0.376 -0.064 -0.224 0.704 -0.896 0.096 0.136 0.744 0.176 -0.576
[1301] -0.064 -0.704 0.584 0.856 -1.144 -0.304 1.104 -0.744 0.856 0.304
[1311] -1.104 0.496 0.536 -0.056 0.896 0.384 -0.744 -1.104 -0.264 -0.416
[1321] 0.744 0.424 -0.376 1.136 0.304 -0.784 0.184 -0.496 1.504 -0.104
[1331] -0.176 0.616 0.056 -0.896 1.336 -0.464 0.424 -1.104 0.776 -0.584
[1341] -0.664 0.496 -0.344 -0.136 0.144 0.144 1.344 0.544 0.376 -0.264
[1351] -0.944 -0.904 0.104 0.384 -1.136 -0.104 0.864 -0.304 -0.024 -1.144
[1361] -0.336 -0.544 -0.296 -0.464 0.904 -0.384 0.536 0.176 0.184 0.304
[1371] -0.064 0.136 0.104 0.376 -0.304 0.384 0.704 1.384 0.064 -0.536
[1381] 0.264 -1.664 -0.536 -1.136 -1.056 0.104 0.264 0.376 0.896 -0.024
[1391] -0.264 -1.224 -0.176 0.704 0.944 -0.016 0.216 -0.544 -0.104 0.864
[1401] 0.696 -0.424 -0.536 -0.536 -0.144 -0.304 1.144 -0.224 -0.856 0.744
[1411] -1.304 -0.496 1.224 0.056 0.536 -0.336 -0.104 0.376 -0.576 1.384
[1421] -0.104 0.376 -0.216 -1.224 -0.696 -0.376 0.384 -0.144 -0.576 -0.136
[1431] -0.544 0.936 0.064 1.384 -0.136 0.576 1.696 0.064 -0.736 -0.944
[1441] 1.664 0.504 -0.856 -0.904 -1.664 0.744 -0.256 1.104 -0.344 0.784
[1451] 0.664 1.344 -0.944 -1.344 0.856 0.424 -1.056 0.864 0.024 -0.424
[1461] 0.416 0.504 -1.096 -0.024 -1.136 -0.624 -0.464 0.056 -1.144 0.744
[1471] 1.296 -0.376 -0.296 1.704 -0.856 1.184 -0.144 0.864 -0.336 -0.864
[1481] 0.736 -0.424 -0.224 -0.056 0.024 -0.424 -0.904 -0.576 1.384 -0.144
[1491] -1.104 0.144 -0.136 -0.104 0.664 -0.904 -0.584 0.216 -0.896 0.696
[1501] -0.464 -0.744 -1.144 -0.384 -0.216 -0.864 1.144 -0.664 -1.304 0.184
[1511] 0.176 1.504 0.384 -0.064 0.264 -0.304 -0.296 -0.664 0.424 -0.144
[1521] -0.216 -0.256 0.024 -0.504 1.664 -0.304 -0.616 1.504 0.056 0.424
[1531] 0.336 -0.376 -1.104 -0.824 0.296 0.056 -0.304 -1.224 -0.104 1.696
[1541] 0.944 -0.176 1.104 0.744 1.064 0.384 -0.584 0.856 -1.136 -0.304
[1551] -0.224 0.064 -0.384 -0.304 0.496 0.056 -0.104 0.144 0.856 0.744
[1561] -0.056 -0.264 0.304 0.744 0.496 -0.304 1.336 -0.024 0.536 -0.776
[1571] -0.424 -1.184 0.544 -0.104 -0.736 0.016 0.504 0.496 1.344 0.784
[1581] -0.304 1.384 -0.504 -0.864 -0.336 1.136 0.096 0.376 -0.936 -0.704
[1591] -0.136 0.616 0.904 -1.336 -0.144 -0.824 0.904 0.616 0.144 0.424
[1601] 0.576 -0.776 -0.584 -0.944 0.544 1.144 1.136 0.176 -1.104 0.896
[1611] 0.224 -0.256 0.544 -0.224 -1.744 0.904 1.136 -0.144 -0.216 0.376
[1621] -0.136 -0.584 -0.176 -0.504 1.664 0.664 -1.184 -0.056 1.304 0.256
[1631] -0.744 -0.736 0.896 -0.384 0.504 0.664 -1.224 -0.864 0.824 -1.704
[1641] -0.824 -0.696 -0.744 -0.416 -0.224 0.544 -1.064 -0.256 0.744 0.496
[1651] 1.184 -0.896 0.296 0.744 -0.256 -0.264 0.384 -0.216 -0.264 -0.904
[1661] 0.624 -0.056 0.856 0.256 0.104 -0.376 -0.056 -0.064 -0.704 -0.584
[1671] -1.296 -0.536 0.576 -0.304 -0.264 1.304 -1.144 -0.616 -0.544 0.064
[1681] 0.176 0.024 0.696 -0.144 -1.504 0.696 -1.744 0.576 0.304 0.376
[1691] 0.416 0.536 1.704 -0.136 -0.664 0.024 -0.384 -0.944 0.536 -0.864
[1701] -0.416 -0.336 0.336 -0.064 1.064 -0.704 0.824 0.504 0.584 -0.736
[1711] -0.784 0.416 0.264 -1.096 -0.744 -0.856 0.336 -0.864 0.576 0.704
[1721] 0.504 -0.944 0.744 -0.304 -0.304 -1.104 0.064 0.256 0.776 0.904
[1731] 0.856 1.376 0.336 -0.184 0.464 -0.856 0.096 0.256 -0.216 -0.176
[1741] 0.856 -0.784 0.144 0.744 0.864 0.096 -0.576 -0.864 -0.384 -0.016
[1751] 0.384 0.304 -0.384 0.664 -0.224 -0.104 -0.384 -0.944 -1.304 -0.696
[1761] -0.584 0.304 -0.264 1.384 0.384 0.384 -0.776 0.536 0.736 1.224
[1771] -1.384 0.664 -0.136 0.664 -0.536 0.016 0.944 0.416 -0.416 0.264
[1781] 0.184 0.704 1.296 1.096 0.504 -0.296 0.784 -0.216 -0.176 -0.256
[1791] 1.104 0.896 0.664 0.776 -1.136 -0.056 -0.056 -0.536 0.856 -0.296
[1801] 0.744 -0.096 0.144 -0.616 -0.136 0.144 0.096 0.224 -0.064 0.416
[1811] 0.584 0.424 -0.776 0.576 0.176 -0.744 0.696 -0.216 0.104 0.904
[1821] 0.744 1.096 1.336 -0.464 0.576 -0.336 0.864 -0.336 0.064 -0.584
[1831] -1.104 -0.544 0.944 -1.744 0.904 -0.744 -0.304 -0.136 -0.136 -1.104
[1841] -0.144 -0.416 0.544 -1.104 -0.376 -0.144 0.864 0.024 0.064 0.224
[1851] -0.776 -0.944 -0.584 -0.904 0.904 0.664 -1.344 -0.696 0.696 -0.384
[1861] 0.176 -0.224 -1.136 0.696 -0.536 -1.296 0.016 -0.416 -1.064 0.096
[1871] -1.296 -0.176 -0.024 0.336 0.384 1.384 1.504 -0.736 0.384 -0.056
[1881] 0.104 -0.064 0.904 -1.344 -0.504 1.104 0.544 -0.264 0.736 0.384
[1891] 1.096 -0.384 0.536 0.256 0.104 -0.064 0.136 0.584 0.696 -0.056
[1901] 0.344 -0.744 -0.504 -0.776 -0.264 -0.584 -0.224 -0.136 0.864 -0.064
[1911] -0.216 -0.224 -0.144 1.144 0.176 -1.384 -0.584 -0.376 0.576 -0.056
[1921] 0.576 -0.736 1.504 -0.224 0.344 -0.864 0.896 0.304 0.584 -1.664
[1931] 0.144 -0.936 -1.056 -0.416 -1.144 -0.056 -0.064 -0.864 -0.224 -0.224
[1941] -0.776 -0.504 0.584 -0.864 -0.224 -0.384 1.664 0.776 -0.536 0.584
[1951] -0.664 -0.064 -0.064 -0.256 -0.496 0.024 0.496 1.384 -0.936 0.736
[1961] -0.536 1.184 -0.056 0.904 -0.256 0.224 0.664 -0.256 0.256 -1.504
[1971] 0.056 -0.496 -1.704 0.584 -1.384 0.896 0.064 -0.896 -0.304 -0.064
[1981] -0.256 -0.376 1.096 0.136 -0.784 0.296 -0.856 0.696 -0.736 -0.904
[1991] -0.216 1.064 0.384 0.136 0.144 -0.504 0.304 1.144 0.904 -0.664
[2001] 0.944 0.416 1.304 -0.136 0.416 -0.384 -1.704 -1.384 0.664 1.104
[2011] 0.544 -0.216 0.256 0.584 0.664 -0.136 -0.744 0.856 -0.376 0.896
[2021] 0.944 0.576 -0.504 -0.416 -0.216 0.064 0.136 0.744 -0.296 -0.064
[2031] -0.944 0.256 0.064 0.616 -1.664 0.104 -0.504 0.016 -1.344 -1.744
[2041] 1.504 0.416 0.744 1.104 0.064 -0.696 0.904 0.144 -1.744 -0.016
[2051] 0.576 0.896 0.896 0.584 -0.384 0.384 -1.384 -0.496 -0.784 -0.224
[2061] -0.944 0.776 -0.056 -0.384 -0.584 0.904 -0.224 -1.744 0.264 -0.024
[2071] 0.536 -1.184 -0.424 -1.096 -1.376 -0.864 -0.704 0.424 0.224 0.096
[2081] 0.536 -0.776 0.224 1.136 0.424 0.216 0.776 -0.304 0.416 0.776
[2091] 1.056 0.584 -0.024 1.104 -0.336 0.064 0.824 0.864 -0.944 -0.664
[2101] -0.536 0.376 -0.264 0.504 0.136 0.136 0.416 0.696 -1.104 1.704
[2111] 0.304 -1.504 -0.056 0.176 -0.864 -0.056 0.664 -0.136 -0.664 0.744
[2121] -0.416 1.744 -0.264 0.216 0.904 -0.584 0.896 0.704 -1.096 0.864
[2131] -0.384 -0.696 -1.104 -0.344 -0.056 -0.336 -0.336 -0.504 1.384 0.696
[2141] -0.504 -0.224 -0.576 0.776 -0.544 1.744 -0.496 -0.376 0.504 -0.064
[2151] 0.616 -0.576 -0.064 -1.136 -0.216 -0.424 0.624 0.176 -0.064 0.704
[2161] -0.336 0.664 1.144 -1.064 0.224 0.256 -0.744 0.576 -0.424 0.304
[2171] 1.664 -1.336 -0.536 -1.184 -0.504 -0.704 0.224 -0.504 -0.176 1.664
[2181] 0.376 0.104 0.904 1.296 -0.496 -0.144 0.944 0.544 0.136 -0.224
[2191] 1.696 0.464 0.424 0.776 0.016 -0.384 -0.344 1.144 0.696 0.616
[2201] 0.144 1.376 0.904 -0.864 0.144 0.336 0.256 0.576 0.056 -0.256
[2211] -1.704 -0.176 -0.776 0.344 -1.136 1.336 0.416 0.336 -0.784 0.936
[2221] 0.536 0.136 0.736 -0.024 0.696 0.936 -0.944 -1.104 -0.856 0.024
[2231] -0.296 -1.384 -0.304 -0.256 -0.664 -0.776 -0.736 0.096 -0.544 -0.384
[2241] -0.384 1.376 0.064 -0.936 0.336 0.304 0.136 -0.176 -1.184 0.216
[2251] 0.224 0.864 0.104 -0.536 -0.176 0.936 -0.416 1.744 -0.504 1.096
[2261] -0.304 -0.016 -1.136 1.704 -0.416 0.064 -0.304 -0.144 -0.096 0.104
[2271] -0.664 -0.144 0.736 -0.704 -1.056 0.296 -0.336 0.544 0.584 -0.256
[2281] 0.776 -1.224 0.264 -0.224 0.856 0.216 0.904 -0.936 -0.064 0.104
[2291] 0.944 1.344 0.336 0.336 0.696 0.016 -0.936 -0.264 -0.136 -0.384
[2301] 0.544 -0.096 -0.144 1.744 -0.856 0.256 0.056 0.864 0.536 1.344
[2311] -0.304 0.664 -0.904 -0.064 -0.856 1.136 0.296 -1.144 -0.136 1.336
[2321] 0.264 -0.136 1.224 0.504 1.336 1.384 -0.696 0.304 1.144 0.584
[2331] -1.664 -0.424 -0.776 0.304 -0.696 -0.376 1.056 0.784 0.424 -0.336
[2341] -1.296 -0.136 -0.736 1.336 0.296 -0.096 0.024 1.744 0.176 0.136
[2351] 0.584 0.336 0.136 0.344 -0.496 1.064 -0.216 0.096 -0.336 -1.296
[2361] 0.064 -0.296 -0.296 -0.024 1.696 0.896 -0.736 1.296 1.664 -0.264
[2371] 1.064 -0.264 0.544 -0.536 1.376 0.104 -0.576 -1.304 -0.336 0.104
[2381] -0.144 0.064 1.064 0.904 0.576 -0.304 -0.904 0.584 0.496 0.536
[2391] -0.304 -0.216 -0.464 0.136 0.096 -0.104 0.136 0.744 0.904 -0.296
[2401] 0.224 -1.144 0.904 0.896 0.536 -0.416 -1.704 -0.096 -0.856 -0.304
[2411] -0.664 -0.256 0.536 -0.504 0.176 1.096 0.016 -0.016 -0.096 0.264
[2421] 0.064 -1.344 -0.184 -0.904 -1.136 -0.504 0.544 -0.336 -0.264 -0.224
[2431] -0.464 -0.544 -0.264 0.096 0.904 0.416 -1.744 -0.384 0.864 1.384
[2441] 0.184 -0.584 1.664 0.424 1.136 -1.104 0.784 -0.936 0.896 0.424
[2451] -1.384 0.904 -0.024 -0.384 -0.576 0.744 -0.824 -0.856 -0.216 1.336
[2461] -0.256 1.336 -1.504 -1.064 -0.176 0.064 -0.664 1.136 0.424 0.776
[2471] -0.664 0.496 -0.864 1.064 1.336 0.176 -1.056 -0.104 0.224 -1.184
[2481] -0.224 0.904 0.696 0.536 0.536 0.136 -0.384 -0.016 -0.864 -0.784
[2491] 0.064 0.696 -0.176 1.296 0.256 -0.424 -0.056 -0.504 0.336 -0.224
[2501] -0.864 0.544 0.056 -0.744 -0.856 -0.064 -0.144 -0.624 -0.136 -0.496
[2511] -0.336 -0.856 0.904 0.824 0.536 -0.496 -0.776 -0.016 -0.784 -1.104
[2521] -0.376 -0.664 0.896 -0.784 -0.064 0.704 1.064 -0.744 -0.376 -1.744
[2531] 1.344 0.856 0.864 0.256 1.224 -0.384 -0.296 0.024 -0.384 -0.096
[2541] 0.016 -1.136 -0.864 0.224 -0.856 -0.344 -0.536 -0.144 0.544 0.616
[2551] 0.064 -0.264 -0.224 -0.104 0.504 0.944 0.224 -1.136 1.696 -0.936
[2561] 0.496 1.696 0.136 1.704 -0.384 -0.944 0.584 0.336 0.584 -1.744
[2571] 0.264 -0.376 -0.104 -0.296 0.504 -1.064 -0.176 -0.336 0.736 -1.096
[2581] -0.856 0.424 -0.144 -0.664 -0.096 -1.056 -0.304 0.384 0.904 0.096
[2591] -0.336 -0.304 -0.584 -0.864 -0.584 0.704 -0.376 0.176 -0.296 0.416
[2601] -0.264 0.624 -0.136 0.224 1.744 0.864 -0.136 -0.576 0.376 -0.064
[2611] -0.864 0.904 -1.296 -0.144 0.056 1.136 -0.824 -0.424 -0.864 -0.064
[2621] -0.864 0.256 -0.696 -1.144 1.104 0.224 0.384 -0.944 0.664 0.096
[2631] 0.904 1.376 -0.896 0.096 1.184 0.544 -0.576 -0.096 -0.704 -0.504
[2641] -0.776 1.376 -0.424 0.176 -0.216 -0.264 -0.384 -0.264 1.376 -1.144
[2651] -1.304 1.064 -0.744 0.584 -1.184 0.464 -0.096 -0.264 0.496 0.176
[2661] 0.544 -0.096 -1.096 -0.736 -0.376 0.696 -0.224 -0.736 0.536 -0.824
[2671] 0.736 0.904 0.576 -0.736 0.104 0.296 0.256 -1.744 -0.536 -0.384
[2681] 0.296 0.464 0.576 0.696 0.736 0.896 0.144 0.016 -0.944 -0.224
[2691] -1.224 -0.696 -0.704 -0.216 -0.096 -1.056 1.056 0.144 -0.256 -0.544
[2701] -0.496 0.224 0.696 -0.544 0.224 0.544 -0.144 1.384 0.496 0.064
[2711] 0.544 0.576 -0.376 -0.136 -0.144 -1.136 0.104 0.304 1.344 0.056
[2721] -0.304 0.904 0.736 -0.424 0.704 -0.304 0.576 -1.144 -1.376 -0.376
[2731] -0.256 0.384 0.256 0.016 0.696 -0.936 0.264 0.136 -0.416 -1.744
[2741] -0.064 -0.384 -0.376 0.144 -0.216 1.384 1.224 0.904 0.176 0.136
[2751] -0.824 -0.376 1.384 -1.344 0.216 0.056 0.864 -0.664 -0.096 -0.416
[2761] -0.016 -0.776 -0.256 1.104 -0.416 -0.224 -0.504 1.104 -0.176 -0.896
[2771] 0.016 -0.696 -0.504 0.384 0.136 -0.944 -0.936 -1.224 0.664 -1.304
[2781] 0.704 -0.904 -0.496 -0.096 0.224 0.896 0.776 -0.776 0.216 1.144
[2791] -1.096 0.544 -0.544 0.496 -0.576 -0.216 -0.336 0.696 -1.224 0.176
[2801] 0.064 0.696 -1.336 -0.696 0.464 0.544 1.224 -0.024 0.544 0.736
[2811] -0.016 0.864 -0.536 -0.184 -0.136 0.096 -1.336 -0.824 0.736 -0.664
[2821] -1.384 0.944 0.936 0.776 1.344 -0.024 -0.896 -1.336 1.744 -0.096
[2831] 0.336 -0.664 -0.256 -0.584 -0.744 -1.504 0.176 0.736 0.416 -0.064
[2841] -0.504 0.264 0.096 -0.664 0.504 -0.664 0.896 -0.544 0.096 -0.304
[2851] 0.424 -0.296 0.744 0.736 -1.664 0.056 0.496 0.896 1.704 -0.344
[2861] -0.664 -0.376 1.664 -0.256 -1.296 0.856 -0.664 0.056 1.344 0.584
[2871] 0.864 1.184 -1.704 0.224 0.064 -0.496 -0.744 -0.536 0.624 -0.144
[2881] 1.304 -0.864 0.704 -0.464 0.296 0.944 -0.664 -0.056 -0.744 -0.616
[2891] -0.296 -0.824 -0.536 -1.696 -0.296 0.904 -0.296 0.704 -1.104 0.704
[2901] 0.024 -0.776 -0.144 -0.856 -0.056 0.016 0.224 0.024 -1.144 0.664
[2911] 0.384 1.096 1.104 0.296 -0.144 0.376 1.504 0.416 -0.544 -0.944
[2921] -0.336 0.384 0.584 1.136 0.664 -0.904 -0.224 -0.224 -0.584 1.144
[2931] 0.696 0.224 -0.864 0.864 1.064 0.496 0.536 -0.096 -0.064 0.904
[2941] -0.384 -0.544 0.464 0.216 0.176 0.096 0.264 -0.904 -0.304 0.096
[2951] -0.224 1.696 0.616 -0.744 0.096 1.296 0.336 1.744 -1.144 0.064
[2961] 0.064 0.864 1.504 0.256 0.144 -0.464 -0.016 0.056 0.096 0.224
[2971] -0.264 0.104 1.064 -1.224 0.504 -0.136 -0.256 -1.696 -0.864 1.136
[2981] -0.944 -0.096 -0.104 0.344 0.664 0.304 0.664 -0.864 0.784 -0.696
[2991] -0.536 0.664 1.064 -0.864 0.896 0.296 -1.336 0.256 -0.496 -1.336
[3001] -0.016 0.664 0.296 -0.416 -0.424 0.336 0.176 0.664 1.096 0.416
[3011] -0.176 -0.424 0.256 1.224 -0.944 -0.464 -1.504 -0.736 0.296 0.864
[3021] 0.664 1.056 -0.864 -1.664 -0.296 0.704 -1.304 -0.304 0.536 1.304
[3031] -0.336 -0.584 1.664 -0.024 -0.664 0.744 -0.224 0.856 -1.056 -0.536
[3041] 0.216 1.384 -1.104 0.336 -0.304 -0.904 -0.296 1.144 -0.904 -0.144
[3051] 0.224 -0.336 -0.136 0.096 -0.664 0.464 0.584 1.744 -0.384 0.536
[3061] 0.504 0.864 0.576 0.296 0.856 0.704 -0.096 0.344 -0.904 -1.064
[3071] -0.056 1.304 -1.376 -0.664 -0.064 1.704 -0.416 -0.664 0.416 0.304
[3081] 1.136 -0.136 0.096 0.864 0.904 0.696 0.264 -1.104 -0.944 -0.864
[3091] -0.384 -0.016 -0.696 -0.864 0.744 0.536 0.064 1.056 -0.216 0.016
[3101] -1.064 0.864 0.304 -1.704 0.704 -0.856 -0.224 -0.136 -0.424 0.904
[3111] -0.024 -0.904 0.864 -0.256 0.056 -0.296 0.584 -0.136 0.096 -0.096
[3121] 0.184 0.576 -0.264 -0.776 0.336 -1.704 0.536 0.344 -0.864 -0.736
[3131] -0.424 -0.296 -1.144 -0.864 0.384 -0.064 0.416 1.344 0.096 0.136
[3141] 0.016 0.744 0.256 0.544 -0.144 -0.544 -0.256 0.624 -0.896 0.264
[3151] -0.704 -0.216 0.384 0.136 -0.744 0.096 -0.864 -0.736 -0.136 -1.664
[3161] 0.744 -0.776 -0.904 -0.144 -0.056 0.064 1.304 0.064 -0.784 -0.936
[3171] 0.896 -0.224 0.776 1.144 0.104 -0.856 0.376 1.384 -0.616 -1.504
[3181] -0.056 -0.256 1.064 0.904 -1.096 -0.096 -0.496 -0.064 0.736 -1.344
[3191] -0.736 0.544 0.144 0.784 0.624 -1.136 -0.424 -0.016 -0.256 -0.584
[3201] -0.136 -0.176 -0.536 0.536 -0.776 -0.544 -0.696 -0.064 -0.144 0.224
[3211] -0.344 0.336 1.144 0.696 -0.104 0.184 0.256 0.336 -0.896 -0.664
[3221] -0.744 0.704 -0.096 -1.104 -0.344 0.256 -1.296 1.136 0.416 -0.424
[3231] 0.096 0.496 0.056 -0.184 0.064 -1.144 -0.176 -0.424 0.024 0.616
[3241] -1.384 1.144 -0.064 0.296 -0.496 0.064 0.584 0.056 0.144 -0.216
[3251] 0.744 -0.736 -0.224 0.104 -1.144 0.144 0.144 0.224 -0.136 0.096
[3261] -0.576 -1.056 0.336 -0.064 -1.056 -0.184 0.296 -0.704 -0.096 1.344
[3271] -1.344 -0.264 0.216 0.304 0.416 -0.304 -0.336 -0.664 -1.136 -0.536
[3281] -0.296 -0.104 -0.944 0.096 0.384 0.024 0.904 -1.704 0.944 0.944
[3291] -1.064 0.256 0.336 -1.744 -0.624 -0.696 0.536 -0.136 -1.104 -0.096
[3301] -0.864 -0.296 -0.096 -0.496 -0.416 0.424 0.544 1.056 0.056 0.584
[3311] -1.096 1.304 0.224 0.744 -0.056 -0.024 0.904 0.416 0.496 -0.544
[3321] -0.304 -1.696 1.104 0.304 -0.504 0.344 0.064 -0.496 1.664 -0.944
[3331] 0.664 -0.496 0.784 0.136 0.224 0.024 0.784 0.064 0.176 -0.616
[3341] -1.144 0.896 0.904 1.696 -0.776 0.504 0.224 0.664 -0.064 0.544
[3351] -0.904 0.696 -1.704 0.216 -0.496 -0.384 -0.104 -0.864 -0.104 1.096
[3361] -0.064 -0.704 0.184 -0.496 -1.696 0.384 -0.104 0.344 -1.064 0.184
[3371] -0.336 0.304 0.104 -0.104 0.944 -0.224 -0.784 -0.496 -1.704 1.504
[3381] 0.664 0.496 -0.896 0.904 -0.376 -0.576 0.856 0.336 -0.584 0.504
[3391] -0.856 0.384 -0.864 1.296 -1.664 0.384 0.216 -0.736 0.056 1.384
[3401] 0.384 -0.096 -0.664 0.536 0.736 0.664 -0.144 0.416 0.304 0.536
[3411] 0.096 0.136 -0.224 0.416 -0.344 1.136 -0.536 -1.504 -0.904 -0.296
[3421] -0.296 -0.936 -0.056 -0.256 -0.296 -1.344 0.104 -0.104 0.224 0.136
[3431] -0.064 -0.104 -0.904 1.056 0.104 0.704 -1.096 0.864 0.696 -0.536
[3441] -1.376 -0.864 1.136 0.424 1.664 0.784 -0.936 -0.776 0.584 1.704
[3451] -0.016 0.536 -0.304 0.496 0.064 0.944 0.856 0.776 -0.064 -1.336
[3461] -1.296 -1.184 1.104 -0.616 0.224 1.336 0.096 0.864 -0.744 0.904
[3471] -0.424 0.144 -1.184 -0.584 -0.104 -0.776 0.704 0.336 0.344 -0.896
[3481] 1.504 -0.536 -0.336 0.416 -0.224 0.744 0.336 0.224 -0.136 -0.464
[3491] 0.896 1.304 0.216 -0.336 0.256 -0.744 0.096 0.384 -1.144 -0.224
[3501] 0.376 0.304 0.896 -0.584 0.336 0.176 -0.304 -0.536 0.384 1.144
[3511] 0.576 0.504 0.384 1.296 -0.104 0.216 0.104 0.104 -1.744 -0.544
[3521] 0.376 -0.544 -0.504 -0.896 -0.704 -0.824 -0.744 -0.336 0.696 0.856
[3531] -1.104 -0.376 0.104 0.064 0.664 -0.304 0.064 -1.184 0.184 0.064
[3541] -0.296 -0.016 -0.576 0.016 0.696 0.744 1.344 -0.144 0.576 0.064
[3551] 0.864 -0.536 0.024 -0.064 -0.536 -0.664 -0.376 0.144 0.064 0.904
[3561] -0.416 -1.184 0.744 0.544 -0.384 0.624 -0.856 -0.304 -1.104 -0.864
[3571] 0.544 0.104 0.256 -0.096 -0.904 -0.416 0.496 -0.696 1.376 -0.896
[3581] -1.344 -0.936 0.064 -0.736 -0.864 0.856 -0.064 0.696 -0.136 1.296
[3591] 1.336 0.944 -1.664 -1.224 -0.336 -0.264 0.296 0.056 1.296 0.056
[3601] 0.544 0.064 0.936 1.384 0.864 0.864 0.384 -0.064 -0.416 -0.584
[3611] -0.304 0.264 0.064 -0.584 -0.464 -0.336 0.024 0.696 1.304 0.744
[3621] -0.696 -0.064 -0.776 -0.664 -0.744 -0.864 0.736 1.064 -0.144 1.336
[3631] 0.176 0.104 0.144 -0.664 0.704 -0.664 1.136 0.776 -0.384 0.304
[3641] -0.496 1.064 0.336 -0.576 -0.536 0.944 0.864 0.544 -1.296 0.584
[3651] -0.384 -0.304 0.104 0.104 -0.296 0.664 -0.616 0.904 0.736 0.136
[3661] 0.096 -0.024 -0.096 0.256 0.416 0.176 1.136 -0.024 -1.384 0.704
[3671] -0.136 0.696 0.296 1.744 0.936 0.784 -0.544 0.776 0.944 -0.264
[3681] -0.024 0.256 -0.424 1.056 1.144 -0.416 -0.384 0.224 -0.936 1.384
[3691] 0.416 -0.864 -0.944 1.376 0.296 0.104 0.736 -0.896 0.856 -0.336
[3701] 1.064 -0.856 0.944 0.376 0.136 -0.864 -0.536 0.416 0.064 1.384
[3711] 0.664 -0.224 0.136 0.176 -0.696 0.936 0.536 -0.216 -0.664 1.224
[3721] -0.664 -0.296 -0.224 0.224 0.096 -0.264 0.936 0.704 0.704 0.584
[3731] 1.136 -0.304 -0.616 0.384 -1.744 0.584 -0.296 0.664 -0.464 -0.384
[3741] 0.744 0.576 1.104 -0.584 -1.696 -0.096 0.824 1.344 0.296 -0.216
[3751] -0.696 -0.216 -0.024 -0.256 0.544 -0.616 0.544 -0.264 -1.104 -0.096
[3761] -0.624 -0.696 0.176 -0.496 -0.304 -1.504 -0.464 -0.176 -0.384 -0.144
[3771] -0.224 0.944 0.256 0.576 -0.136 0.536 -0.336 -0.016 -0.064 0.376
[3781] 0.144 1.296 0.384 1.096 0.584 -1.104 -0.264 -0.496 1.144 -0.104
[3791] 0.216 0.544 -0.064 -0.304 0.296 0.504 -0.424 -1.104 -0.856 0.336
[3801] 0.256 -0.704 -0.416 -1.504 -0.264 0.104 -0.064 0.664 -0.264 -0.336
[3811] 0.504 0.224 -0.544 0.016 1.136 -0.384 0.696 -1.136 0.416 -0.136
[3821] -0.664 0.304 0.104 0.104 1.144 -0.744 -1.184 0.624 -0.224 -1.696
[3831] -1.344 1.096 -0.144 0.864 -0.096 -0.256 -0.696 0.224 -0.256 -0.096
[3841] -0.224 1.296 0.904 -0.464 -0.784 0.616 -0.296 0.296 -0.104 -0.144
[3851] -0.416 -0.584 -0.064 0.536 -0.904 0.096 -1.344 1.384 1.144 -0.304
[3861] 0.936 -0.144 -0.264 0.224 0.696 0.024 -0.424 -0.224 0.864 -1.096
[3871] -0.544 0.944 1.144 -0.536 -0.824 0.704 -0.056 -1.096 0.704 -0.904
[3881] 0.696 1.376 -0.344 1.744 0.296 -1.096 -0.224 -0.096 1.664 1.344
[3891] -0.176 0.744 0.624 -0.296 -0.136 1.384 -0.544 -0.016 -0.464 0.304
[3901] -0.496 1.136 -0.744 -0.904 0.696 0.384 0.696 0.144 -0.896 1.336
[3911] 0.336 0.424 1.104 0.176 0.056 1.096 0.504 -0.024 1.744 0.096
[3921] 0.296 0.904 -0.384 0.304 0.856 -0.024 -0.104 -1.744 -0.024 1.104
[3931] 0.264 -0.584 -0.296 0.256 0.104 -0.784 -0.824 -0.904 -1.296 -0.584
[3941] -0.576 -1.704 0.104 -1.096 -0.696 -0.296 -0.424 0.904 -0.896 0.224
[3951] 0.864 -1.104 0.384 0.664 1.144 -0.624 -0.576 -1.064 -0.056 -1.096
[3961] -0.464 0.104 1.096 -0.096 0.224 0.384 -0.704 -0.864 -0.264 -0.064
[3971] 1.136 0.904 -1.224 -0.096 1.136 0.736 1.376 0.336 -0.496 0.544
[3981] 0.336 1.136 0.544 0.864 -0.864 -0.344 -0.704 0.896 0.304 -0.256
[3991] -0.896 -0.744 -1.336 -0.896 -0.856 0.336 1.144 -0.096 -0.144 0.144
[4001] 0.824 0.504 -0.224 -0.536 -0.296 -1.504 0.736 -0.296 1.144 -1.096
[4011] -1.064 0.536 0.376 -0.344 -0.304 -0.776 0.304 -0.176 0.704 0.296
[4021] -0.856 0.424 -0.624 0.064 0.064 -0.376 -0.336 1.064 -0.144 -0.944
[4031] 1.104 -0.744 0.496 -0.024 -1.056 0.616 -0.056 0.864 1.064 0.104
[4041] 0.136 0.664 -0.136 0.096 0.384 0.384 -0.584 0.056 0.856 -0.576
[4051] -0.176 0.896 -0.904 0.304 -0.944 1.344 -0.256 -0.864 -0.296 -1.184
[4061] 0.576 -0.664 0.936 0.744 0.896 -0.536 -0.744 -0.416 0.696 0.544
[4071] 0.584 0.664 -0.304 -0.376 -0.096 -0.056 -0.696 1.304 -0.304 -0.664
[4081] 0.176 0.736 -0.464 0.584 0.744 0.616 -1.144 -1.744 -0.144 0.576
[4091] 0.376 -0.064 -1.064 -1.136 -0.864 -0.144 0.096 -0.216 -0.824 -0.584
[4101] -1.664 0.776 -0.664 0.664 -0.056 -1.144 -1.744 0.264 -0.264 0.064
[4111] -0.664 -0.944 -0.224 -0.296 0.864 -0.504 -0.096 0.904 -0.864 0.296
[4121] 0.064 -0.864 0.496 0.336 -1.696 -0.144 1.056 1.304 1.184 -1.744
[4131] 0.696 0.056 0.496 1.184 0.096 0.416 -0.784 -1.296 0.096 0.424
[4141] 0.224 -1.744 0.576 0.824 -0.384 -1.664 0.904 -0.704 0.336 0.104
[4151] 1.344 0.864 -0.384 -0.024 -0.224 0.144 0.864 0.944 -0.136 -1.144
[4161] 0.144 -0.584 -0.776 0.536 1.384 -0.376 1.064 1.144 -0.536 -0.064
[4171] 1.384 0.144 0.536 0.064 -1.144 0.584 -0.336 0.584 -0.104 -1.224
[4181] -0.576 0.544 0.544 -0.304 -0.664 -0.304 0.864 0.904 0.744 -1.096
[4191] 0.896 -1.144 -0.336 -0.264 -0.296 0.416 0.264 1.504 1.704 -0.224
[4201] -0.096 -1.744 0.224 -0.384 0.016 0.536 -0.776 -0.336 0.624 0.144
[4211] 0.536 -0.376 -0.216 -1.096 0.696 -0.056 0.664 -1.064 -0.224 1.504
[4221] -0.096 0.416 -0.224 -0.384 -1.064 -1.224 0.584 -0.464 0.304 1.144
[4231] -0.896 -0.944 0.704 0.136 -0.256 -0.544 0.856 0.136 -0.056 1.376
[4241] 1.344 -1.184 0.136 0.584 -0.904 0.376 -0.024 0.296 -0.216 0.584
[4251] 1.704 -0.224 -1.056 0.224 -0.376 0.064 -0.216 -1.336 1.144 -0.256
[4261] 0.584 0.696 0.664 -0.904 -1.376 0.064 0.896 0.856 0.376 -0.216
[4271] -0.336 -1.064 -1.096 0.376 0.416 0.304 0.384 0.144 0.216 -0.776
[4281] -0.136 -0.136 -1.296 -0.256 -0.536 -0.824 -0.224 0.056 0.944 -0.784
[4291] 0.864 -0.664 -0.064 -0.584 -0.744 0.504 -0.776 0.896 -0.896 0.624
[4301] -0.336 0.384 1.296 -0.776 -1.704 -0.704 -0.296 -0.544 -1.096 -0.384
[4311] -0.296 -0.104 -0.304 -0.704 0.304 0.344 0.544 -0.696 0.336 0.584
[4321] 0.064 -0.416 0.344 0.024 1.696 0.504 0.704 -0.104 0.304 -0.104
[4331] -0.416 0.144 -1.104 0.624 -0.224 0.064 -1.296 0.304 0.224 0.696
[4341] -0.696 -0.664 -1.136 0.216 -0.664 -0.496 -0.904 0.104 1.376 -0.744
[4351] 1.104 0.056 0.584 -0.576 0.384 0.336 -0.096 1.296 -1.744 -0.424
[4361] -1.144 1.136 1.304 1.304 0.064 -0.736 1.304 -0.424 0.536 0.416
[4371] -0.904 -0.264 0.904 1.504 0.576 1.104 0.696 0.536 -0.224 -0.896
[4381] 0.744 0.144 -0.336 -0.064 -0.024 -1.144 -0.064 -0.264 -0.616 0.384
[4391] 1.136 -1.664 0.224 -0.736 -0.136 -0.136 0.744 0.104 -0.536 1.344
[4401] 0.144 -0.384 -1.376 -0.176 -0.104 0.024 -0.096 0.024 0.744 -0.024
[4411] -0.384 -0.824 0.384 -0.064 0.616 1.376 -1.184 0.704 0.176 -0.664
[4421] -0.576 -1.096 0.496 -0.064 -0.216 -0.064 1.136 -0.576 0.384 -0.736
[4431] -0.336 0.144 -0.664 0.304 0.296 0.536 -0.176 0.296 0.064 0.144
[4441] -0.224 -0.216 0.104 1.136 0.904 -0.776 0.664 0.136 -0.744 -0.696
[4451] -0.304 -0.904 0.696 -0.496 0.664 -0.096 0.224 -0.224 -0.584 -0.936
[4461] -0.136 0.144 -0.544 -0.904 0.856 -1.056 -0.736 -0.576 -0.064 0.864
[4471] 1.144 0.744 0.584 0.296 0.176 0.544 0.664 0.576 1.144 0.864
[4481] 0.584 -0.896 -0.584 1.184 -0.864 -0.384 0.096 -0.904 -0.536 -0.136
[4491] -1.704 -0.864 0.224 0.896 1.144 -0.416 0.176 0.776 -0.944 -0.304
[4501] -0.536 0.296 0.296 -1.096 -1.304 -0.256 -0.624 -0.784 0.376 -0.256
[4511] -1.096 -1.144 -0.424 0.264 -0.104 0.256 0.584 -0.056 0.296 0.016
[4521] -1.504 -0.464 -1.104 -1.336 0.384 -1.504 1.384 1.336 -0.504 0.096
[4531] 0.136 1.064 0.064 0.736 -0.104 -0.296 -0.056 0.824 -1.704 -0.224
[4541] 0.744 0.104 0.664 -0.864 0.024 -0.384 -1.504 -1.056 0.576 0.864
[4551] 1.136 -0.064 -1.104 -1.096 -0.536 -0.376 -0.944 -0.344 0.704 0.536
[4561] -0.096 0.464 0.384 0.704 -0.136 -0.016 0.544 -0.384 0.496 -1.184
[4571] -0.064 0.824 0.144 0.384 -0.544 0.944 -0.336 0.944 0.216 0.176
[4581] -0.384 0.936 -0.104 0.576 -0.936 0.536 -1.344 0.416 -1.664 0.424
[4591] 0.744 0.384 -0.584 -0.744 0.304 -0.664 -0.024 0.616 -1.064 -0.024
[4601] -1.664 -1.144 0.136 -0.104 0.936 -0.424 1.144 -1.664 0.704 -0.256
[4611] 0.264 0.544 0.136 1.664 -0.536 0.336 1.696 -0.504 -1.304 1.696
[4621] -1.304 0.256 -0.064 0.896 -0.384 -0.224 -1.664 0.104 1.056 -0.536
[4631] -0.336 0.064 -0.584 0.136 -1.376 -0.176 1.336 0.704 0.664 0.336
[4641] -0.704 1.096 1.096 0.864 -0.024 -0.096 0.024 -0.064 0.064 -1.136
[4651] 0.824 0.424 -1.504 -0.256 0.184 0.504 -1.384 -0.504 1.296 1.144
[4661] 0.736 -0.384 0.864 -0.856 -0.096 -1.136 1.504 0.016 -0.624 -0.336
[4671] -1.696 0.136 1.304 -0.584 0.304 -1.336 -0.096 -0.496 -0.544 -0.736
[4681] 1.344 -0.864 1.504 -0.376 0.176 -0.304 -0.584 -0.576 -0.056 -0.584
[4691] -0.544 -1.136 0.304 0.376 -0.864 0.864 -0.584 0.584 0.104 1.056
[4701] 0.696 0.256 0.736 1.304 0.136 0.824 0.544 -1.104 1.504 1.136
[4711] -0.536 0.096 0.336 0.944 -0.136 1.064 0.576 1.664 0.136 -1.136
[4721] -0.224 -0.904 0.696 -0.576 -0.584 -0.336 0.104 0.544 0.704 0.496
[4731] -0.584 -0.264 0.424 0.096 -0.056 0.896 0.544 -0.544 -0.256 0.696
[4741] -0.696 0.736 0.424 0.336 -0.224 1.376 -0.896 0.576 -0.464 -0.104
[4751] 0.544 0.664 -0.576 -0.064 -0.896 0.104 0.824 0.624 -0.416 -0.024
[4761] -1.104 0.176 0.416 -0.016 0.064 0.864 0.256 -0.176 0.624 -0.296
[4771] -1.056 0.504 0.336 -0.584 -1.104 0.504 0.056 -0.104 -1.664 0.664
[4781] 0.736 -0.536 0.224 0.104 -0.416 0.896 -0.864 -0.064 0.864 0.096
[4791] -0.224 -0.176 0.096 -0.064 0.664 -1.664 1.144 0.536 0.056 0.096
[4801] -0.824 0.704 0.096 -0.464 -0.824 0.256 0.216 0.464 0.776 0.744
[4811] 0.016 -0.416 0.576 1.376 0.424 -0.696 0.944 -0.736 -0.704 -0.064
[4821] 0.536 1.504 -0.904 -1.184 0.264 -0.176 -0.144 -0.056 0.224 -0.336
[4831] 1.336 0.144 1.376 1.704 0.856 -0.256 -0.224 0.944 0.944 -0.424
[4841] -0.584 -0.824 0.056 0.744 0.064 -1.696 1.696 0.096 -0.304 -0.904
[4851] 0.224 -1.504 -0.896 -0.024 0.504 -0.576 1.344 0.224 0.384 0.336
[4861] 0.584 0.416 0.136 -0.856 -0.296 0.696 0.704 1.096 -1.104 -0.264
[4871] -0.944 -0.896 -0.536 0.336 -0.064 0.496 1.704 0.536 -0.504 0.944
[4881] 0.256 0.144 0.944 0.136 -0.664 0.664 0.616 0.376 -1.376 0.616
[4891] -0.736 -0.136 0.336 0.304 0.384 1.144 0.064 0.904 -1.376 -0.736
[4901] 1.104 0.304 -0.136 -1.344 -0.536 -0.496 0.176 -1.344 -0.904 1.104
[4911] 0.584 0.944 0.416 -0.944 0.064 -0.896 0.336 -0.384 -0.216 0.104
[4921] 0.776 -0.384 -0.064 1.224 0.616 0.384 0.624 -0.376 0.384 -0.544
[4931] 0.024 0.496 0.696 -1.744 0.904 -0.376 -1.104 0.304 1.104 1.336
[4941] -1.304 0.704 -0.096 0.704 -0.344 1.296 -0.936 -0.304 0.744 1.136
[4951] 0.856 0.696 1.504 0.216 0.544 0.936 -0.744 -0.744 0.744 -0.584
[4961] 0.136 -0.896 0.864 -0.904 0.104 0.904 0.896 0.544 -0.064 0.664
[4971] 0.696 0.704 -0.296 0.584 -0.224 -0.344 0.544 1.704 1.136 0.064
[4981] -0.096 -0.216 -0.104 0.224 -0.264 -0.944 -1.664 -0.576 -0.584 0.496
[4991] 0.544 0.104 0.296 -0.296 -0.336 0.304 -0.944 -0.176 0.704 -0.536Estimate Dist under H0
Find Reject Region
Estimate Dist under H0
An Alternative Hypothesis
An Alternative Hypothesis
Consider a constant shift of 1 for all units.
From data to schedule
| My Observed Schedule | ||
| i | Y_0 | Y_1 |
|---|---|---|
| 1 | NA | 0.90 |
| 2 | -0.5 | NA |
| 3 | NA | 2.20 |
| 4 | -1.4 | NA |
| 5 | 0.1 | NA |
| 6 | -1.0 | NA |
| 7 | 1.1 | NA |
| 8 | NA | 1.00 |
| 9 | NA | 1.02 |
| 10 | NA | 1.50 |
| My Alt Schedule | ||
| i | Y_0 | Y_1 |
|---|---|---|
| 1 | -0.10 | 0.90 |
| 2 | -0.50 | 0.50 |
| 3 | 1.20 | 2.20 |
| 4 | -1.40 | -0.40 |
| 5 | 0.10 | 1.10 |
| 6 | -1.00 | 0.00 |
| 7 | 1.10 | 2.10 |
| 8 | 0.00 | 1.00 |
| 9 | 0.02 | 1.02 |
| 10 | 0.50 | 1.50 |
Estimate Dist under HA
[1] 0.736 1.624 1.376 1.776 0.536 1.096 1.264 1.664 0.896 1.744
[11] 1.216 0.984 0.696 1.104 1.304 0.544 0.456 1.696 2.096 0.944
[21] 1.296 0.944 0.944 1.304 0.896 0.504 0.784 0.744 1.264 1.424
[31] 0.856 1.496 1.904 1.096 0.864 0.976 1.424 0.856 1.704 1.464
[41] 0.984 0.616 0.584 0.896 1.464 0.664 0.536 0.944 0.896 0.536
[51] 0.496 0.224 0.056 1.376 1.744 0.864 1.184 1.784 1.064 0.784
[61] 1.584 1.384 0.064 1.024 0.544 1.224 1.064 0.696 0.656 0.816
[71] 1.336 1.144 1.456 0.456 1.544 1.224 0.064 0.224 1.256 1.224
[81] 1.056 1.136 1.744 2.136 1.104 0.424 1.504 1.304 0.736 0.896
[91] 0.944 1.304 1.464 1.064 0.776 0.664 1.376 0.936 0.224 1.576
[101] 0.936 1.184 0.456 1.704 0.624 0.584 0.904 0.864 0.984 1.504
[111] 0.816 2.096 1.416 1.944 0.264 0.936 1.056 0.216 1.056 0.624
[121] 0.424 2.096 1.184 1.296 0.336 0.496 0.856 0.456 0.896 0.936
[131] 1.144 1.976 1.696 1.064 1.656 2.136 2.176 0.864 1.264 1.896
[141] 0.944 0.824 1.664 0.304 1.064 0.064 0.336 2.096 0.656 1.544
[151] 1.504 0.224 0.504 0.656 -0.144 0.696 0.776 0.816 0.936 0.856
[161] 1.304 1.584 0.704 1.496 1.016 1.744 0.104 1.024 1.696 0.824
[171] 1.576 1.256 0.616 0.344 1.104 0.984 2.144 0.656 0.944 0.936
[181] 0.856 0.976 0.464 0.504 0.656 0.816 0.304 0.224 0.336 1.136
[191] 1.776 1.304 0.704 1.496 1.184 0.304 1.904 0.776 0.656 1.344
[201] 1.256 1.104 1.344 0.216 1.976 1.224 0.584 1.624 0.984 0.936
[211] 0.496 1.336 1.376 1.376 1.176 1.056 1.576 0.336 1.536 0.944
[221] 0.416 1.616 0.464 1.096 0.936 1.504 1.696 0.856 1.016 0.104
[231] 1.264 0.544 1.304 0.944 1.576 0.024 1.104 1.096 0.384 0.656
[241] 0.416 0.896 0.656 1.536 0.096 0.224 0.984 1.336 1.224 0.424
[251] 1.136 0.736 1.096 1.016 0.456 1.136 0.624 0.704 0.864 0.256
[261] 1.704 0.784 0.664 0.936 1.296 1.256 0.056 1.096 1.104 1.944
[271] 0.384 1.104 0.464 1.096 0.296 1.576 -0.136 0.744 0.744 0.336
[281] 0.944 1.664 0.016 0.464 1.464 0.896 0.784 0.504 0.856 1.424
[291] 0.904 0.464 1.304 1.264 1.064 1.304 0.536 0.864 0.984 1.024
[301] 0.384 1.056 1.944 1.096 1.664 1.016 0.904 1.024 1.784 1.576
[311] 1.096 1.144 0.296 0.264 0.984 1.424 0.944 0.936 1.176 0.384
[321] 0.344 1.384 1.944 1.896 0.576 0.696 0.896 1.496 0.864 1.304
[331] 0.904 1.504 0.624 1.176 1.624 1.264 0.704 1.224 1.184 0.016
[341] 0.104 1.104 0.936 0.824 1.576 1.256 1.144 1.776 0.024 0.824
[351] 0.936 0.544 0.096 1.624 1.464 1.616 1.056 2.104 0.984 1.064
[361] 1.544 1.224 1.344 0.664 1.144 1.304 0.704 0.456 0.744 1.136
[371] 0.336 0.744 0.696 0.776 0.536 1.104 1.944 1.664 0.856 1.104
[381] 0.704 0.904 1.256 1.704 1.336 1.064 1.936 0.664 0.256 0.944
[391] 1.504 1.304 0.936 1.104 0.936 0.504 0.864 0.624 0.464 2.104
[401] 1.184 0.944 1.136 2.096 0.776 1.584 1.704 1.296 1.264 0.296
[411] 1.184 0.384 0.376 1.264 0.496 0.896 1.264 0.704 0.656 0.584
[421] 0.824 0.704 0.536 0.504 2.176 1.376 0.704 1.544 1.344 1.496
[431] -0.104 0.504 0.464 1.016 0.656 0.416 0.296 0.496 0.624 0.944
[441] 1.544 2.144 0.904 0.896 1.016 1.264 0.464 0.416 0.656 0.456
[451] 0.464 0.944 1.344 1.136 1.376 1.296 -0.096 0.696 1.336 0.504
[461] 0.856 1.704 -0.096 1.064 0.224 0.024 1.176 1.944 1.904 -0.136
[471] 0.536 1.016 1.056 1.016 0.744 1.176 1.344 0.824 1.944 1.256
[481] 1.696 0.464 1.336 2.144 2.144 1.064 1.016 1.216 0.696 1.584
[491] 0.864 0.496 0.704 1.304 2.176 0.664 1.376 1.704 1.096 1.064
[501] 1.896 1.304 1.696 1.496 0.864 0.056 1.064 0.624 1.016 0.664
[511] 1.216 0.816 1.024 1.344 0.224 1.056 1.696 0.616 0.056 1.264
[521] 1.304 0.944 0.496 1.456 1.344 0.904 1.056 0.704 0.416 1.536
[531] 0.456 0.256 1.424 0.416 0.904 1.544 0.896 -0.176 0.936 1.056
[541] 1.216 0.944 0.056 1.536 1.536 0.056 1.584 -0.184 0.456 1.696
[551] 1.224 1.416 1.416 0.496 0.696 2.136 0.744 0.896 1.016 0.784
[561] 1.056 1.384 0.264 0.896 0.496 0.464 1.056 1.544 1.376 1.456
[571] 1.056 1.896 0.896 0.944 0.696 0.264 0.536 0.904 0.776 0.896
[581] 1.536 0.584 1.616 1.704 0.296 0.896 0.936 1.336 1.984 1.104
[591] 1.096 1.296 1.136 1.096 0.376 0.896 1.336 0.736 1.096 0.544
[601] 1.936 1.136 0.656 1.544 1.936 0.376 1.264 0.816 0.464 1.344
[611] 0.896 0.656 1.936 1.496 1.976 0.384 1.496 0.576 1.584 1.936
[621] 1.624 0.776 1.016 0.456 0.296 1.184 1.496 0.904 0.776 0.904
[631] 1.104 1.536 1.096 0.736 0.576 0.064 0.976 1.336 1.344 1.376
[641] 1.784 0.656 1.216 0.096 0.776 0.336 1.376 0.984 1.944 0.304
[651] 0.656 0.776 -0.184 1.696 1.016 1.184 0.816 0.664 1.704 1.336
[661] 0.744 0.056 0.656 0.864 0.496 1.184 1.336 1.016 1.304 1.056
[671] 0.504 0.864 1.224 1.136 1.904 1.344 0.544 0.864 0.896 1.736
[681] 0.416 0.496 1.456 1.536 0.704 0.416 -0.144 1.904 0.576 1.336
[691] 0.104 1.656 0.744 0.224 0.664 1.016 1.976 1.416 1.944 0.344
[701] 1.144 1.024 1.184 0.736 1.016 0.496 1.136 0.704 1.216 2.176
[711] 1.056 -0.176 0.864 0.656 0.496 1.096 0.696 0.656 1.944 1.304
[721] 0.024 0.776 1.736 1.504 1.064 1.264 0.864 0.824 -0.184 0.976
[731] 1.144 1.344 1.256 0.056 0.656 1.224 1.584 -0.144 0.024 0.936
[741] 1.224 1.664 1.176 1.376 1.744 1.736 0.504 0.984 1.184 0.504
[751] 1.344 2.184 1.696 1.304 0.304 0.704 0.904 0.776 0.464 1.104
[761] 0.224 1.096 1.456 0.856 1.576 0.936 0.344 1.136 0.504 0.984
[771] 1.096 0.456 0.696 1.096 0.416 1.024 0.944 1.504 1.096 1.304
[781] 1.616 0.936 1.424 1.104 0.344 0.656 1.304 0.464 0.536 0.776
[791] 1.504 0.456 1.136 1.704 1.096 1.696 1.016 0.896 1.064 1.296
[801] 0.784 0.496 0.224 1.096 1.744 0.776 0.616 0.856 2.136 1.096
[811] 1.056 0.784 0.624 2.176 0.584 0.816 1.504 1.616 0.304 0.536
[821] 0.424 1.784 0.304 1.696 1.576 0.936 1.984 1.024 1.304 1.144
[831] 0.976 0.784 0.696 0.464 1.544 1.984 1.504 0.504 1.024 0.576
[841] 0.776 1.704 1.504 0.744 1.336 0.976 0.224 1.144 0.784 0.416
[851] 1.104 0.464 0.496 0.104 2.144 0.264 2.176 0.056 0.656 2.144
[861] 0.536 0.336 1.944 0.376 0.744 0.624 0.704 0.824 1.304 1.304
[871] 0.664 0.784 0.304 1.624 1.384 1.976 1.056 1.296 1.536 1.264
[881] 0.504 1.096 0.264 1.784 0.504 0.896 1.504 1.496 0.704 0.336
[891] 1.096 1.784 0.296 1.704 1.536 0.944 1.784 1.104 0.656 0.104
[901] 0.464 0.256 1.456 0.696 1.496 1.096 1.456 1.336 0.304 0.584
[911] 1.224 0.656 1.064 1.264 2.096 1.264 0.576 0.656 0.696 1.984
[921] 1.384 0.656 1.144 1.744 0.864 1.136 1.776 0.784 1.616 0.296
[931] 0.656 1.344 0.096 2.136 0.656 1.104 1.224 -0.136 1.264 -0.136
[941] 1.776 1.496 1.664 1.136 0.464 1.104 0.864 0.304 1.136 1.096
[951] 0.816 1.664 -0.144 1.904 1.496 1.344 1.096 1.536 0.264 0.576
[961] 0.704 1.504 0.864 0.256 1.016 1.056 0.664 0.536 1.696 1.696
[971] 0.904 0.616 0.424 1.736 0.624 0.704 0.936 1.136 1.104 1.456
[981] 0.464 1.704 0.864 0.336 1.304 1.224 1.656 0.864 0.896 0.936
[991] 1.016 0.736 1.024 1.224 1.264 1.256 0.736 0.736 0.104 0.944
[1001] 1.696 0.816 0.464 0.256 0.856 0.624 0.456 0.704 0.464 1.584
[1011] 0.304 0.784 1.704 0.696 0.816 1.224 0.936 1.504 1.096 0.536
[1021] 1.584 0.696 1.784 0.896 1.776 2.184 1.664 0.544 1.256 1.104
[1031] 1.544 1.136 0.064 1.296 0.904 0.936 1.224 0.496 0.816 1.016
[1041] 0.496 0.064 1.304 1.504 0.104 0.056 0.256 1.576 0.336 1.464
[1051] 1.944 0.936 0.696 0.896 0.696 0.344 1.136 0.864 2.144 0.984
[1061] 1.216 0.616 1.144 1.504 1.104 0.696 1.536 0.544 1.536 1.016
[1071] 2.136 1.736 0.984 1.344 0.376 0.624 1.784 0.536 1.584 1.056
[1081] 0.096 1.544 0.384 0.464 0.624 0.936 1.736 0.296 0.976 0.256
[1091] 1.136 0.464 0.256 0.464 0.864 0.696 0.936 1.464 0.424 0.784
[1101] 1.304 1.144 1.624 0.624 1.344 1.736 1.424 1.616 0.456 0.056
[1111] 1.936 0.904 1.544 0.744 0.496 1.744 0.944 1.216 1.424 -0.136
[1121] 0.496 0.936 1.176 1.464 0.576 0.304 1.336 1.616 0.856 1.056
[1131] 1.736 1.176 0.736 1.776 1.704 1.544 0.664 0.464 0.936 0.264
[1141] 1.704 1.176 1.504 0.904 1.176 1.024 1.296 0.936 0.936 1.104
[1151] 0.416 0.584 2.144 0.824 0.544 0.584 1.136 1.184 1.136 0.576
[1161] 0.056 1.496 0.464 1.696 1.256 0.736 1.696 0.656 1.296 1.096
[1171] 1.464 1.584 0.896 0.816 0.304 0.264 1.736 0.456 1.144 -0.096
[1181] 0.704 1.504 1.704 1.376 0.664 0.776 0.824 1.176 1.496 1.744
[1191] 1.456 1.024 0.976 1.064 0.784 1.184 1.136 0.736 1.744 0.944
[1201] 0.496 1.376 0.264 0.664 1.544 0.456 0.104 0.864 0.296 0.016
[1211] -0.176 1.104 1.144 0.824 0.704 0.656 0.256 0.664 0.424 1.264
[1221] 0.984 2.104 0.544 1.064 0.544 0.576 0.064 0.736 0.656 0.384
[1231] 1.096 1.296 0.264 0.944 1.704 0.664 0.744 0.816 0.096 1.664
[1241] 0.976 1.176 1.704 1.064 0.536 0.016 1.216 0.424 0.664 0.424
[1251] 1.696 1.344 1.744 0.376 0.744 -0.136 0.344 1.256 0.384 0.976
[1261] 1.696 1.064 0.864 1.056 1.976 -0.144 1.144 1.896 1.584 0.056
[1271] 0.944 1.496 0.896 0.104 1.336 0.464 0.944 1.984 0.776 0.304
[1281] 0.864 1.376 1.096 1.584 0.816 0.896 0.296 0.736 1.736 1.344
[1291] 0.936 0.904 0.704 0.936 0.496 0.776 0.784 1.016 0.944 0.704
[1301] 0.976 1.336 0.216 1.144 1.416 0.856 0.744 1.696 0.616 0.456
[1311] 1.944 1.664 1.536 1.296 1.264 0.776 0.336 -0.144 0.336 0.904
[1321] 1.536 1.584 1.264 0.424 0.544 1.696 1.304 0.504 0.536 1.696
[1331] 2.144 1.696 1.184 1.136 0.696 0.024 0.736 0.536 1.224 0.704
[1341] 0.944 0.864 1.256 0.864 1.256 1.264 0.984 0.216 0.696 1.144
[1351] 1.544 0.224 1.416 1.264 1.224 0.496 1.664 1.224 1.056 1.304
[1361] 0.624 1.944 0.024 0.704 -0.104 1.216 1.304 0.936 1.664 1.544
[1371] 1.704 1.136 1.304 0.744 0.056 0.496 2.096 0.744 0.656 1.944
[1381] 0.904 1.744 1.064 0.984 0.264 0.256 2.184 0.696 0.376 1.424
[1391] 0.216 0.504 1.336 0.696 1.784 0.904 0.824 0.536 0.056 0.304
[1401] 1.096 0.544 0.536 0.976 2.176 1.216 -0.104 0.104 1.504 1.456
[1411] 1.296 1.704 1.464 2.104 0.656 1.384 1.976 1.584 1.936 1.984
[1421] 0.624 0.656 0.816 1.104 0.216 1.776 0.464 1.296 1.224 1.696
[1431] 1.264 0.696 -0.184 0.456 0.264 1.384 0.584 0.496 1.544 0.904
[1441] 1.304 0.936 1.096 0.224 1.624 1.064 2.176 1.496 1.944 2.184
[1451] 0.296 0.584 0.464 0.056 1.536 1.384 1.464 1.296 1.096 0.496
[1461] 0.064 1.336 0.744 -0.144 0.616 0.864 1.064 0.944 1.056 0.544
[1471] 1.056 0.424 1.056 1.216 0.656 0.736 0.864 1.456 0.936 0.104
[1481] 0.256 1.184 0.944 1.296 0.424 0.344 0.104 0.336 1.504 1.304
[1491] 0.416 1.896 0.944 0.664 1.544 0.944 -0.096 0.256 1.136 0.056
[1501] 1.184 1.576 1.536 1.424 1.736 0.544 0.256 1.456 0.376 0.624
[1511] 2.096 2.184 0.704 1.136 0.464 1.664 0.816 1.704 1.736 1.104
[1521] 1.176 0.944 1.504 0.776 1.216 0.904 1.304 0.896 1.064 0.576
[1531] 0.936 1.064 1.176 0.536 0.536 1.464 0.064 0.576 0.744 0.264
[1541] 0.256 0.424 0.904 1.584 2.096 0.776 1.504 1.224 0.544 1.424
[1551] 1.744 0.576 1.424 0.016 1.344 1.224 0.656 0.536 0.704 0.784
[1561] 1.224 1.016 -0.144 0.304 0.904 1.056 0.464 0.056 1.104 0.864
[1571] 0.496 1.344 1.696 0.376 1.376 0.856 1.256 0.776 1.144 1.064
[1581] 0.736 1.464 0.256 1.064 0.936 -0.184 0.776 0.336 0.856 1.224
[1591] 0.016 2.136 2.176 0.904 0.496 0.296 0.544 1.144 0.984 1.264
[1601] 0.664 0.056 0.704 1.496 1.744 0.496 0.224 1.256 1.136 1.344
[1611] 0.264 0.416 0.304 0.104 1.544 1.256 2.184 1.744 1.696 1.176
[1621] 1.704 0.896 1.664 0.624 0.824 0.656 0.504 0.736 0.264 1.744
[1631] 1.904 0.856 0.896 1.496 1.064 1.944 0.736 1.744 0.976 0.704
[1641] 0.944 1.576 1.616 0.104 0.744 0.864 0.936 0.864 0.296 1.216
[1651] 0.024 1.704 1.304 0.784 0.944 0.696 0.296 0.824 0.664 1.696
[1661] 0.904 1.064 0.056 1.304 1.944 1.216 1.344 1.904 1.144 1.704
[1671] 1.304 0.216 0.616 0.664 0.696 1.904 0.576 1.456 0.664 1.464
[1681] 0.424 1.104 0.656 1.496 2.176 0.696 1.096 1.264 0.304 0.496
[1691] 0.824 -0.096 1.656 1.264 2.184 0.536 1.344 0.224 0.896 0.696
[1701] 0.896 0.896 0.616 0.456 0.464 1.544 0.504 1.056 1.096 0.056
[1711] 0.904 0.096 0.864 0.936 0.304 1.064 1.176 1.776 0.744 1.416
[1721] 1.456 0.624 0.704 0.464 1.016 1.744 -0.104 1.424 1.944 1.096
[1731] 1.104 1.224 1.544 1.504 1.104 1.744 1.984 1.144 1.936 0.256
[1741] 1.656 0.776 2.144 0.256 0.744 1.976 1.304 0.304 0.504 0.104
[1751] 0.336 1.016 1.496 1.184 1.064 1.496 0.784 1.304 0.936 0.064
[1761] 0.496 0.896 2.096 1.016 0.856 0.864 1.704 1.056 1.056 0.864
[1771] 1.536 1.344 -0.136 0.296 1.536 0.904 0.624 0.856 0.624 1.224
[1781] 0.224 1.944 1.944 0.696 0.256 0.536 0.064 0.936 0.256 -0.176
[1791] 0.944 1.976 0.856 1.536 1.064 0.696 0.256 0.056 1.184 1.024
[1801] -0.144 0.536 1.336 0.976 1.104 0.656 1.224 1.496 1.656 -0.184
[1811] 0.664 0.736 0.296 0.296 0.296 1.456 0.896 1.424 0.696 1.344
[1821] 1.296 1.056 0.984 1.416 1.576 1.544 1.296 0.576 1.424 0.744
[1831] 0.336 1.224 0.256 0.256 1.696 1.304 1.496 2.104 1.136 0.816
[1841] 2.136 0.736 1.344 1.264 1.176 0.736 1.664 1.136 1.304 1.944
[1851] 0.504 1.664 0.896 1.424 0.344 1.016 1.256 1.304 1.896 0.736
[1861] 1.104 0.064 1.664 1.504 1.656 1.256 1.336 1.096 1.544 1.416
[1871] 0.416 1.456 1.096 1.496 1.224 0.736 0.416 0.456 0.944 1.264
[1881] 1.256 0.824 0.816 1.536 0.536 0.224 1.304 1.504 0.856 1.216
[1891] 1.296 1.536 0.096 0.864 0.056 0.304 1.096 2.144 1.784 1.144
[1901] 0.016 0.824 0.056 1.416 1.096 1.064 0.664 1.544 0.744 0.624
[1911] 1.136 1.136 0.416 1.376 1.056 1.744 0.576 0.984 0.984 0.744
[1921] 0.976 1.184 2.104 0.016 0.664 1.696 0.864 0.664 0.656 0.976
[1931] 1.056 1.064 1.504 1.464 0.664 0.384 -0.136 0.944 0.016 1.896
[1941] 0.096 1.224 1.144 0.696 0.504 0.976 0.904 1.376 0.656 1.184
[1951] 0.696 1.544 0.824 1.936 0.656 0.296 0.864 1.064 1.504 1.216
[1961] 1.056 0.104 0.736 1.576 0.936 0.944 1.096 1.496 1.936 1.344
[1971] 0.944 0.736 0.416 0.696 0.584 1.464 1.776 1.376 0.704 1.456
[1981] 1.104 0.936 1.096 1.504 0.576 0.744 0.376 0.304 0.856 0.424
[1991] 1.664 0.704 1.536 1.024 1.376 0.936 1.296 0.984 1.464 0.736
[2001] 1.984 1.024 0.856 0.344 0.904 0.424 1.256 0.896 1.584 1.976
[2011] 0.896 0.064 0.896 1.464 1.056 0.704 1.944 0.104 1.696 1.104
[2021] 1.024 0.624 0.456 -0.104 2.096 0.864 1.504 0.824 1.224 0.816
[2031] 1.344 0.416 0.624 0.664 1.576 0.664 0.504 2.136 1.464 0.416
[2041] 0.624 0.304 0.776 0.664 0.296 -0.176 1.184 1.384 0.544 1.696
[2051] 1.136 0.776 2.096 1.984 -0.104 0.936 1.136 0.496 0.504 1.776
[2061] 1.176 1.704 0.944 -0.136 1.944 0.936 1.576 0.616 1.104 1.416
[2071] 0.936 1.304 0.664 1.544 1.344 1.424 0.056 1.736 1.024 1.064
[2081] 1.064 1.344 1.304 1.376 1.256 0.304 1.304 0.536 1.736 1.256
[2091] 0.496 0.296 1.176 0.856 1.664 0.824 0.896 1.464 0.904 1.336
[2101] 1.424 0.904 1.464 1.544 0.584 0.104 1.136 1.696 1.096 0.304
[2111] 1.104 0.256 1.144 0.224 1.776 1.104 1.984 0.656 0.936 1.944
[2121] 0.976 1.496 1.624 2.144 1.744 1.344 1.136 0.296 1.536 0.936
[2131] 1.904 1.376 1.496 1.504 1.064 1.736 0.584 1.064 1.456 0.936
[2141] 0.456 0.104 0.696 1.416 0.704 0.656 0.864 0.776 1.936 1.184
[2151] 0.864 0.496 0.736 1.336 0.856 0.536 0.384 1.104 0.464 0.456
[2161] 0.744 1.024 0.296 1.344 0.856 1.744 0.856 1.376 0.784 1.264
[2171] 1.536 0.296 1.336 1.496 1.096 0.256 1.416 0.536 1.296 1.064
[2181] 1.536 0.424 0.536 1.656 1.264 2.176 0.976 0.536 0.696 0.656
[2191] 0.576 1.376 0.944 1.664 1.024 1.696 1.536 1.504 1.264 1.056
[2201] 0.744 1.776 1.736 1.544 0.504 0.856 0.496 1.336 0.224 1.384
[2211] 1.704 0.896 1.064 1.104 1.736 1.896 0.496 0.504 1.016 1.376
[2221] 0.304 0.984 0.664 1.936 1.024 0.696 0.624 1.576 1.776 1.056
[2231] 1.904 1.344 1.736 1.296 0.736 0.304 1.344 0.744 0.264 1.104
[2241] 0.016 0.664 0.976 0.624 1.496 1.136 0.464 1.696 0.776 1.136
[2251] 1.376 0.664 1.784 1.504 0.856 0.696 0.224 1.456 0.936 1.376
[2261] 1.184 0.664 0.824 1.416 0.464 -0.176 1.216 1.504 1.416 1.136
[2271] 1.264 0.856 1.536 0.696 0.304 1.136 0.904 1.624 0.704 0.544
[2281] 1.024 1.176 1.016 0.064 1.264 1.344 1.184 0.064 0.656 1.944
[2291] 1.096 1.264 1.024 0.896 0.896 0.256 1.776 0.496 0.304 1.064
[2301] 1.944 0.096 1.224 1.304 0.784 1.304 1.064 1.616 0.584 1.536
[2311] 1.056 0.224 0.664 0.984 0.696 0.936 0.856 0.384 1.304 0.424
[2321] 1.224 0.216 1.104 0.224 1.176 0.696 1.064 0.936 0.536 1.344
[2331] 0.216 0.656 0.696 0.624 0.696 0.496 0.736 0.896 0.304 1.176
[2341] 1.704 1.256 2.104 1.096 0.976 1.104 1.024 0.864 1.576 0.256
[2351] 0.056 0.976 0.656 0.936 1.344 1.264 1.616 1.464 0.464 0.624
[2361] 0.704 1.416 1.536 1.696 2.176 1.504 1.184 1.536 0.464 0.984
[2371] 0.064 0.936 0.224 1.976 2.096 0.616 1.016 0.744 1.536 0.936
[2381] 1.504 0.336 1.736 1.656 -0.136 1.136 1.344 1.136 1.296 1.016
[2391] 1.536 0.504 1.296 0.944 0.744 2.144 0.464 0.496 0.736 1.064
[2401] 1.296 0.504 0.984 0.744 -0.136 0.304 0.776 1.344 1.536 0.816
[2411] 1.304 1.496 0.416 0.296 0.944 0.776 0.344 1.504 1.464 1.184
[2421] 1.744 1.696 1.944 0.264 0.856 0.624 1.144 0.656 1.464 2.184
[2431] 1.424 1.544 1.304 0.296 1.304 0.256 1.424 1.264 1.104 1.424
[2441] 1.696 1.064 1.024 0.656 0.096 0.424 0.976 0.896 0.736 1.496
[2451] 1.376 0.056 0.656 1.704 0.104 0.696 0.696 1.464 0.896 0.336
[2461] 1.504 0.784 1.776 1.096 0.736 1.536 0.704 1.264 0.544 0.496
[2471] 1.704 1.104 1.064 1.264 0.544 0.416 1.136 1.344 1.304 0.984
[2481] 0.896 0.824 0.784 0.296 1.416 1.544 0.496 0.984 0.696 1.944
[2491] 0.576 0.336 0.784 0.464 1.664 1.616 1.056 1.104 0.304 0.856
[2501] 0.464 1.104 1.296 0.504 0.856 1.064 0.936 0.464 0.024 1.296
[2511] 0.024 0.936 1.336 0.776 0.464 0.624 1.344 1.216 0.696 0.944
[2521] 1.104 1.176 1.096 2.136 1.104 0.584 0.464 0.976 1.304 2.104
[2531] 2.136 0.904 1.704 0.904 1.976 0.336 0.864 1.224 0.496 1.344
[2541] 1.064 2.104 0.576 0.936 1.704 0.304 0.496 1.344 0.544 0.816
[2551] 0.736 1.344 0.904 1.144 0.656 1.336 0.904 1.376 0.856 1.144
[2561] 0.576 0.856 1.144 -0.136 0.576 -0.136 0.656 0.936 0.336 0.776
[2571] 1.536 0.696 1.224 -0.096 0.456 1.064 1.024 1.936 1.944 -0.184
[2581] 0.264 0.656 1.336 0.824 -0.096 1.336 0.824 0.496 0.736 0.544
[2591] 1.664 1.136 1.256 0.824 1.184 0.424 0.664 0.456 1.056 0.944
[2601] 1.984 0.856 1.096 0.904 1.304 1.936 0.064 0.536 0.896 0.656
[2611] 1.096 1.656 0.704 0.296 1.344 0.896 0.904 1.344 1.736 0.336
[2621] 0.936 1.264 1.416 1.144 0.696 1.896 0.856 1.096 2.176 0.944
[2631] 0.936 0.664 0.576 1.496 0.456 0.336 1.536 1.184 1.216 0.584
[2641] 0.736 1.096 1.624 0.776 1.704 1.416 0.744 0.744 1.936 1.984
[2651] 1.224 0.896 1.064 1.016 1.616 2.104 0.984 0.856 0.304 0.704
[2661] 0.944 0.064 0.736 1.896 1.776 1.224 0.704 0.896 0.704 1.496
[2671] 1.584 0.904 0.744 2.096 0.496 1.936 0.216 0.336 1.576 1.216
[2681] 0.736 0.056 0.656 1.296 1.016 0.984 1.264 0.896 0.256 0.056
[2691] 1.224 1.504 0.424 0.256 1.704 0.936 0.504 1.104 0.504 1.736
[2701] 1.016 0.656 1.456 1.496 0.944 1.136 1.136 1.344 0.816 0.904
[2711] 0.816 1.296 0.856 0.496 0.896 0.984 1.616 0.896 0.024 0.664
[2721] 1.936 0.216 1.056 1.176 0.224 1.144 1.144 1.096 0.936 1.184
[2731] 1.296 1.176 1.104 0.824 1.496 0.864 1.536 0.864 1.344 1.504
[2741] 0.256 1.736 0.944 0.944 0.704 1.256 0.256 1.336 0.816 0.336
[2751] 0.544 0.936 1.336 1.776 1.224 1.336 1.024 1.144 0.704 0.696
[2761] 1.296 0.296 1.144 1.624 0.504 1.224 1.136 1.096 0.896 1.256
[2771] 0.344 1.056 1.256 0.656 1.264 0.696 0.216 1.264 1.264 1.984
[2781] 1.744 1.144 0.984 0.496 1.304 1.304 0.664 2.096 1.504 0.656
[2791] 0.816 0.104 0.824 1.176 0.904 0.544 1.344 1.144 1.304 0.936
[2801] 0.856 1.216 1.336 0.856 1.984 0.504 1.304 0.056 0.904 0.824
[2811] -0.096 0.344 1.416 0.504 0.904 1.416 0.856 1.144 0.776 1.536
[2821] 1.584 1.104 0.256 1.224 0.976 1.264 1.304 0.736 1.296 0.704
[2831] 1.296 1.176 1.744 1.056 0.944 0.456 -0.184 1.504 0.944 0.936
[2841] 0.464 1.904 0.944 0.896 1.704 0.496 1.056 1.424 0.656 0.744
[2851] 2.184 0.024 1.096 1.176 0.704 1.104 1.544 1.104 0.536 1.344
[2861] 0.064 0.096 1.424 1.144 0.864 0.656 1.344 0.704 0.784 0.856
[2871] 1.264 0.856 2.184 0.776 0.696 0.736 0.216 1.704 0.776 0.936
[2881] 1.624 0.416 0.296 1.896 0.416 1.584 2.184 0.624 0.696 1.744
[2891] 1.944 1.096 0.904 1.304 1.744 0.464 0.384 1.616 1.016 1.336
[2901] 0.664 0.304 1.264 0.864 0.336 0.896 1.024 1.104 0.784 0.584
[2911] 0.624 0.664 1.376 0.304 1.176 0.504 0.896 1.064 1.016 0.424
[2921] 0.736 0.696 0.576 0.624 1.344 1.064 0.496 0.624 0.224 2.176
[2931] 1.704 2.176 0.296 1.496 1.176 1.984 0.296 0.304 1.184 1.576
[2941] 0.696 1.024 0.816 0.296 1.224 0.936 1.464 1.416 1.336 1.224
[2951] -0.136 0.376 1.176 0.224 1.304 1.536 1.376 1.296 0.504 1.096
[2961] 0.296 0.216 0.736 0.584 0.656 0.336 0.816 1.064 0.856 0.744
[2971] 0.824 1.064 0.544 0.664 1.304 1.264 1.784 0.816 1.144 -0.176
[2981] 1.016 0.456 1.344 0.824 1.144 0.256 0.224 2.096 0.696 1.344
[2991] 0.864 1.696 0.224 1.296 2.184 1.056 0.504 0.296 0.216 0.704
[3001] 1.144 0.776 1.744 0.936 1.744 0.704 0.416 0.464 0.536 0.936
[3011] 0.336 0.856 0.696 1.144 1.264 1.584 1.384 1.016 1.144 1.416
[3021] 1.656 0.264 0.696 0.664 0.416 0.464 0.304 1.016 0.576 0.304
[3031] 0.984 0.896 1.104 0.264 0.264 1.464 0.904 1.384 0.784 0.904
[3041] 0.984 0.496 0.944 1.224 0.336 1.776 0.704 1.416 1.136 2.184
[3051] 1.024 0.656 0.656 0.304 1.056 0.344 0.776 1.504 1.696 0.744
[3061] 0.216 1.416 1.784 0.504 1.304 0.896 0.456 1.024 0.896 1.376
[3071] -0.096 1.416 1.256 0.256 0.704 1.696 1.896 1.504 0.464 1.104
[3081] 1.464 0.944 0.696 0.256 1.576 0.456 0.464 0.024 1.784 0.024
[3091] 1.184 0.424 1.104 1.064 0.896 0.696 0.864 1.304 -0.096 0.936
[3101] 0.944 1.344 0.984 1.936 1.176 1.336 0.656 1.456 0.496 1.656
[3111] 0.704 1.976 1.104 1.536 0.904 0.064 2.144 0.296 1.544 1.424
[3121] 0.704 0.344 0.296 0.984 1.064 1.104 0.584 0.024 1.424 1.344
[3131] 1.296 0.664 0.784 0.696 0.696 0.224 0.496 0.024 1.744 0.704
[3141] 1.496 0.656 0.584 1.904 1.064 0.984 1.136 1.736 0.336 0.544
[3151] 0.696 0.304 0.416 0.456 0.224 0.896 0.816 0.336 0.024 0.824
[3161] 1.504 1.056 0.536 1.104 0.704 1.936 1.504 1.944 0.416 0.696
[3171] 0.304 1.056 0.856 1.136 1.096 -0.136 0.944 0.704 1.736 0.336
[3181] 0.904 1.096 1.576 0.904 0.016 0.744 1.736 0.936 1.264 2.184
[3191] 1.784 0.304 0.496 0.904 1.664 1.224 0.616 1.424 1.416 0.736
[3201] 0.896 0.936 1.296 0.904 1.376 0.336 0.824 0.744 1.336 0.504
[3211] 0.216 1.216 1.176 1.456 1.104 0.936 1.536 0.256 0.816 1.064
[3221] 2.096 1.336 0.904 1.496 1.216 0.944 0.496 0.024 0.064 0.784
[3231] 1.616 0.864 1.576 0.296 0.216 0.576 0.496 1.184 1.464 0.736
[3241] 1.584 0.456 1.776 1.096 1.264 0.264 1.136 0.864 0.616 1.496
[3251] 1.144 0.936 0.984 1.696 0.016 1.584 -0.104 1.264 1.056 0.016
[3261] 1.744 1.536 0.336 1.016 0.944 0.376 1.584 0.296 1.024 0.536
[3271] 1.944 0.936 1.256 1.304 0.504 1.104 1.376 0.576 0.456 0.096
[3281] 1.744 2.096 1.784 1.664 1.344 1.664 1.256 1.144 0.584 0.824
[3291] 2.104 0.944 0.944 0.696 0.944 0.064 1.296 0.896 1.504 0.584
[3301] 1.056 1.944 0.016 1.096 1.536 1.176 1.736 1.504 1.944 1.056
[3311] 0.464 1.064 1.376 0.296 0.784 0.816 0.584 1.064 0.464 1.776
[3321] 1.496 0.496 0.656 0.784 0.584 1.064 1.304 1.344 0.104 1.296
[3331] 0.456 1.296 1.504 0.936 1.536 1.064 0.936 0.096 0.856 0.656
[3341] 0.696 1.624 0.024 0.984 0.984 0.496 0.536 0.296 -0.136 0.304
[3351] 0.816 1.424 0.864 -0.136 0.824 1.496 1.024 0.696 0.224 -0.104
[3361] 0.504 1.064 0.256 0.864 2.136 1.504 -0.184 0.904 0.424 0.536
[3371] 1.304 0.896 1.104 0.024 0.704 1.264 0.936 0.504 1.256 1.144
[3381] 1.296 0.256 1.336 1.256 1.384 1.064 1.224 0.736 0.496 1.336
[3391] 0.936 0.576 1.504 0.736 1.744 1.984 0.936 0.256 1.776 1.144
[3401] 0.976 0.664 1.696 1.624 1.376 1.416 1.544 0.664 1.984 1.984
[3411] 0.536 1.776 1.024 0.904 0.456 0.624 1.704 1.584 0.704 0.056
[3421] 0.704 0.976 0.864 0.656 0.744 0.464 1.224 0.944 0.704 0.536
[3431] 1.136 0.376 1.496 0.984 -0.144 -0.176 1.024 0.016 0.904 1.304
[3441] 0.496 1.504 1.704 0.224 -0.184 0.984 1.144 0.736 0.656 2.104
[3451] 1.264 0.904 1.096 1.536 2.136 0.944 1.496 0.504 0.976 1.544
[3461] 0.944 2.176 1.656 1.256 0.704 0.496 1.616 0.696 0.344 1.736
[3471] 0.656 0.416 1.104 1.376 0.344 0.944 1.464 0.424 0.464 1.264
[3481] 0.256 0.336 0.936 1.264 1.336 0.944 1.104 2.096 1.504 0.904
[3491] 0.576 -0.136 0.064 0.464 0.624 1.104 1.704 0.264 1.776 1.456
[3501] 0.984 1.264 1.144 0.936 0.424 0.664 0.624 1.504 0.856 1.704
[3511] 1.224 1.496 1.656 0.624 1.576 0.664 1.144 1.264 1.576 0.976
[3521] 0.416 1.256 2.136 0.584 0.704 1.424 0.064 0.656 1.176 1.744
[3531] 0.944 1.544 0.064 1.944 0.656 1.104 0.504 1.184 1.496 1.144
[3541] 0.864 1.376 1.984 0.576 -0.104 1.096 1.704 1.024 1.096 1.704
[3551] 0.824 1.136 -0.136 1.056 1.064 1.304 0.936 1.696 1.224 0.664
[3561] 1.304 2.136 1.296 0.336 1.296 1.904 1.096 0.584 -0.136 1.104
[3571] 0.056 0.824 0.664 1.424 0.496 1.056 1.464 1.576 2.096 1.936
[3581] 0.376 1.496 0.864 -0.096 0.936 0.384 0.944 1.344 0.744 1.536
[3591] 1.144 0.416 0.824 0.096 0.904 1.344 1.536 1.224 0.536 1.376
[3601] 0.816 1.464 0.424 1.256 0.496 0.744 0.024 1.944 0.864 0.944
[3611] 0.864 1.336 0.544 0.464 1.776 1.544 0.464 0.096 1.224 -0.136
[3621] 1.056 0.696 1.496 1.096 1.776 1.544 1.976 0.624 1.544 1.064
[3631] 1.704 1.504 0.424 0.936 1.936 0.504 0.464 1.104 -0.144 2.096
[3641] 0.976 1.896 1.656 1.136 0.696 1.456 1.336 1.696 1.304 0.624
[3651] 1.536 1.296 1.504 1.704 0.456 1.496 0.464 1.016 0.904 0.096
[3661] 0.464 0.536 1.104 1.136 0.336 0.384 0.296 0.936 -0.096 0.944
[3671] 0.936 0.416 1.744 0.936 1.096 0.504 0.504 1.376 0.496 1.296
[3681] 1.096 0.944 0.536 0.656 1.224 1.216 0.904 1.096 0.504 0.536
[3691] 1.176 0.864 2.176 1.496 0.696 1.096 1.904 0.464 1.896 1.296
[3701] 0.664 1.504 1.064 2.136 0.464 0.856 1.464 1.456 1.024 0.304
[3711] 0.296 0.864 1.496 0.784 0.464 1.144 1.104 0.384 1.296 1.016
[3721] 0.616 1.424 1.104 1.024 0.696 1.016 0.216 1.584 1.536 0.504
[3731] 1.304 1.064 0.544 1.416 0.504 0.856 1.296 0.896 1.504 1.336
[3741] 0.224 1.776 1.656 1.424 1.216 0.896 1.264 1.656 1.264 0.296
[3751] 1.976 1.744 1.944 0.576 1.296 1.136 0.096 1.376 0.704 1.704
[3761] 0.944 0.864 0.496 1.704 0.704 1.104 2.136 0.304 1.696 0.496
[3771] 0.496 1.496 0.656 0.696 1.344 1.184 0.344 1.336 0.536 2.104
[3781] 1.944 1.536 1.056 1.944 1.096 0.856 1.504 0.664 1.536 0.504
[3791] 0.336 0.864 0.424 1.536 0.904 1.256 0.896 0.536 2.096 1.784
[3801] -0.136 1.104 0.824 1.296 1.056 1.184 1.384 0.464 1.936 0.864
[3811] 1.264 1.064 0.936 1.184 1.304 1.336 0.704 0.904 0.496 0.536
[3821] 0.656 0.696 1.176 0.776 0.936 0.424 0.304 0.824 0.264 0.976
[3831] 0.104 0.936 1.384 1.024 1.136 0.344 0.736 0.936 0.416 2.136
[3841] 0.104 1.296 0.256 1.584 0.936 0.504 2.104 0.424 1.464 0.296
[3851] 0.824 1.376 1.064 1.216 1.656 0.584 0.856 0.296 1.616 1.176
[3861] 0.864 0.824 1.264 1.496 0.936 1.544 1.064 0.496 0.496 1.456
[3871] 1.696 0.944 0.904 0.936 0.096 1.296 0.056 2.144 0.416 1.016
[3881] 1.504 0.704 0.336 0.704 0.936 0.584 1.664 1.536 0.896 0.384
[3891] 0.376 0.304 1.096 0.464 0.656 0.376 0.624 0.896 1.936 1.104
[3901] 1.504 0.416 1.696 1.896 1.976 1.616 1.704 1.336 1.264 1.536
[3911] 0.576 1.376 0.896 0.496 1.216 0.656 0.704 1.136 0.064 1.376
[3921] 1.424 1.136 1.344 0.424 1.344 0.776 1.704 0.856 0.736 0.056
[3931] 0.896 1.704 1.064 0.256 0.104 0.256 0.344 1.496 0.936 1.104
[3941] 0.496 1.056 0.496 1.536 0.264 0.704 0.064 1.464 1.616 1.536
[3951] 0.536 0.856 0.656 1.176 0.536 2.136 -0.104 0.976 0.936 0.104
[3961] 0.896 1.336 0.704 1.016 1.136 0.064 0.696 1.136 0.224 0.256
[3971] 0.904 0.744 0.704 0.656 1.704 1.464 1.144 1.304 0.296 1.264
[3981] 1.504 -0.176 0.464 -0.136 0.744 0.944 1.736 1.664 1.296 1.176
[3991] 1.264 2.096 0.864 0.496 0.984 0.704 1.616 0.624 1.056 0.696
[4001] 1.064 1.304 0.496 1.544 1.016 1.656 1.536 2.136 1.544 1.256
[4011] 1.016 1.344 2.096 1.296 1.096 1.536 1.504 0.224 1.176 0.024
[4021] 0.504 1.016 0.944 0.696 1.456 1.024 1.584 0.736 1.264 1.944
[4031] 2.144 0.296 0.536 0.544 1.104 1.064 0.624 0.256 0.976 1.744
[4041] 1.264 0.296 0.464 1.544 1.616 0.824 1.416 1.376 1.416 1.664
[4051] 1.104 1.984 2.136 0.656 0.744 0.336 1.536 0.944 0.864 0.896
[4061] 1.184 0.896 0.536 0.856 1.776 1.056 1.104 0.264 0.736 1.976
[4071] 1.496 1.264 0.256 0.824 1.696 0.576 0.376 1.776 1.136 1.104
[4081] 0.384 1.576 0.856 0.864 0.864 1.096 1.296 0.696 1.096 1.096
[4091] 1.176 0.976 0.904 0.976 0.216 0.664 2.096 0.464 1.256 0.544
[4101] 1.576 1.296 1.904 0.064 2.136 0.656 1.136 1.584 0.264 1.496
[4111] 1.096 1.016 2.176 1.944 1.296 1.456 0.304 0.296 0.744 1.416
[4121] 0.896 0.064 0.656 0.976 1.056 1.496 -0.176 0.576 0.704 0.584
[4131] 0.744 0.536 1.096 0.736 1.504 1.464 0.904 1.184 0.736 0.656
[4141] 0.864 1.344 1.504 0.744 0.656 1.384 0.696 0.824 1.096 0.264
[4151] 0.736 0.784 1.344 -0.144 0.496 0.744 0.384 0.944 1.304 1.224
[4161] 1.264 1.056 0.664 2.104 0.776 -0.144 1.136 1.016 1.416 1.064
[4171] 1.136 0.864 0.984 1.304 0.256 0.296 1.136 1.336 1.344 1.064
[4181] 0.424 0.536 1.424 1.104 1.264 0.016 1.664 0.704 0.656 0.616
[4191] 0.296 0.896 0.376 1.096 0.056 2.144 1.424 1.696 0.016 1.984
[4201] 1.096 1.496 0.456 0.984 0.864 1.096 1.104 0.704 0.056 0.056
[4211] 0.784 1.224 1.096 1.736 1.544 0.736 1.064 0.784 1.424 0.936
[4221] 1.096 2.096 1.536 1.536 1.064 0.864 1.176 0.864 1.144 0.416
[4231] 1.496 0.256 0.696 1.216 1.344 1.624 0.864 -0.096 1.536 1.304
[4241] 1.144 1.064 0.936 1.904 1.504 1.104 1.064 0.936 1.744 0.736
[4251] 1.256 1.464 1.104 0.104 0.736 0.904 0.744 0.496 1.144 1.456
[4261] 1.584 1.464 0.064 0.304 0.424 0.864 0.856 1.096 0.424 1.496
[4271] 1.064 1.576 1.024 0.544 0.864 1.056 1.344 1.264 0.896 0.696
[4281] 0.256 1.584 2.136 1.376 1.184 1.504 1.696 1.376 1.536 1.304
[4291] 1.336 0.536 1.456 0.864 0.264 2.184 1.144 0.496 1.336 1.264
[4301] 0.984 0.584 0.944 0.624 1.336 0.904 1.744 1.776 0.656 1.224
[4311] 1.104 1.144 1.576 0.656 0.696 1.416 0.656 0.944 -0.136 1.936
[4321] 1.144 0.576 0.216 1.056 2.144 0.904 0.336 1.496 0.656 0.296
[4331] 1.104 1.624 0.256 1.704 0.936 0.944 1.576 0.296 0.824 0.896
[4341] 0.224 2.176 1.304 0.464 1.704 0.904 1.376 0.456 1.144 0.744
[4351] 1.704 1.696 2.144 2.144 2.184 0.736 1.064 1.496 -0.136 1.616
[4361] 2.136 1.056 1.096 0.296 0.656 1.696 1.296 1.464 1.384 0.704
[4371] 0.064 1.144 1.216 1.136 0.936 0.536 1.344 1.696 0.064 0.304
[4381] 1.776 1.696 1.376 1.024 1.344 1.784 1.744 0.664 0.736 0.896
[4391] 1.304 0.704 1.136 0.864 1.064 1.184 0.936 1.464 0.736 1.296
[4401] 0.944 0.624 1.336 1.184 1.464 0.864 0.864 1.136 1.024 0.224
[4411] 1.304 0.224 1.416 0.624 0.736 0.216 0.256 0.576 1.304 0.584
[4421] 0.624 0.464 0.744 0.824 0.424 1.064 1.016 0.904 0.904 0.256
[4431] 1.464 0.304 1.136 0.704 0.824 0.016 0.536 0.784 0.984 1.064
[4441] 0.744 0.944 0.864 0.464 0.784 0.904 0.696 1.496 1.064 1.496
[4451] 1.496 0.056 1.736 1.504 1.056 1.136 0.016 2.136 1.296 0.936
[4461] 0.896 0.384 1.176 0.944 0.296 1.776 0.904 0.856 0.736 1.584
[4471] 0.784 1.504 1.344 1.736 1.704 0.544 0.504 0.744 1.256 0.864
[4481] 0.904 0.376 0.544 0.504 0.736 1.536 1.536 0.904 1.616 1.376
[4491] 0.544 1.344 0.336 0.104 1.416 0.704 0.504 0.784 0.464 0.464
[4501] 0.624 1.096 0.856 1.976 1.344 0.464 0.944 1.504 1.216 1.296
[4511] 1.424 1.056 0.584 1.264 1.784 -0.144 0.704 0.664 1.016 1.376
[4521] 1.216 0.976 0.936 1.064 0.256 1.424 0.976 0.936 0.504 1.784
[4531] 0.536 1.016 0.744 0.304 2.104 0.376 1.176 1.016 1.576 2.136
[4541] 1.176 0.576 1.536 0.976 0.064 0.624 0.904 0.496 1.096 1.224
[4551] 1.304 0.704 0.896 1.216 -0.136 0.736 1.184 1.496 0.264 1.936
[4561] 0.584 1.544 1.744 1.344 1.496 0.704 0.944 1.336 0.416 1.496
[4571] 1.536 0.056 1.224 1.136 0.696 0.984 0.016 1.616 1.264 0.304
[4581] 0.936 1.264 0.464 0.376 0.464 0.816 0.616 -0.144 0.056 1.376
[4591] 0.864 0.896 0.056 0.824 1.216 1.016 0.776 0.944 1.504 0.704
[4601] 0.336 2.096 0.896 1.224 0.896 1.016 0.464 1.096 1.344 0.584
[4611] 0.904 1.784 0.496 1.064 0.456 1.536 1.696 0.424 1.104 1.104
[4621] 1.456 1.064 1.256 1.504 1.104 -0.104 1.264 -0.144 1.136 0.944
[4631] 0.696 1.304 1.184 0.664 0.336 1.056 1.416 1.736 0.544 0.736
[4641] 0.664 0.624 0.464 1.056 1.496 0.856 0.696 0.304 0.856 0.736
[4651] 0.304 0.896 0.224 1.216 0.984 0.056 1.936 0.616 1.064 1.104
[4661] 0.496 1.464 1.104 0.896 0.664 0.904 0.704 1.376 -0.104 1.136
[4671] 2.096 0.736 0.736 0.336 1.296 0.864 1.256 1.304 0.544 0.296
[4681] 1.464 0.304 1.344 2.136 1.584 1.144 0.696 0.304 0.304 1.496
[4691] 0.464 0.504 1.944 1.456 1.024 0.016 1.224 1.384 1.136 0.464
[4701] 1.016 0.824 0.816 0.736 1.936 1.256 1.024 1.056 0.424 0.904
[4711] 0.976 1.696 0.056 1.104 2.184 1.776 1.024 0.336 1.984 0.504
[4721] 1.376 0.544 0.904 1.376 1.656 0.944 1.576 1.104 1.016 0.464
[4731] 0.904 1.544 0.096 1.176 0.264 1.584 0.256 0.864 0.576 0.744
[4741] 0.056 0.824 2.136 1.024 0.016 0.256 0.024 1.456 0.464 0.536
[4751] 1.256 0.336 1.744 1.456 0.856 0.576 0.464 1.696 1.744 1.664
[4761] 0.344 -0.184 0.464 1.304 0.336 1.136 1.704 0.456 1.984 -0.096
[4771] 0.336 0.624 1.304 1.216 1.096 0.304 -0.104 1.576 0.784 1.096
[4781] 0.696 0.984 1.504 1.104 0.816 2.104 1.416 1.384 0.224 1.976
[4791] 0.744 1.104 1.224 1.304 1.136 0.656 1.104 1.096 1.104 1.136
[4801] 1.536 0.824 0.704 1.144 1.504 0.904 0.944 0.344 0.736 0.656
[4811] 0.536 1.224 1.304 1.696 0.944 0.504 1.504 0.856 1.536 1.096
[4821] 1.416 1.304 1.944 1.224 0.736 1.504 1.944 1.576 1.016 1.104
[4831] 0.656 1.256 1.184 0.896 0.904 1.096 1.704 0.864 0.976 1.224
[4841] 1.024 1.704 0.464 0.664 1.104 0.784 0.736 1.704 1.904 0.704
[4851] 0.096 0.064 0.936 0.056 1.744 1.264 1.696 0.064 0.064 1.336
[4861] 1.176 0.904 0.536 1.936 -0.184 0.784 1.264 1.576 0.656 1.976
[4871] 1.296 -0.176 1.136 0.336 0.056 0.344 0.784 1.416 0.784 0.536
[4881] 0.056 0.024 1.176 0.344 0.456 0.616 1.136 1.096 1.064 0.424
[4891] 1.896 1.736 0.464 1.024 1.776 0.936 0.064 1.456 1.304 0.096
[4901] 0.496 1.224 0.424 0.664 1.104 1.016 -0.096 1.904 2.136 0.816
[4911] 1.896 0.944 0.704 0.064 0.104 1.264 1.224 0.896 0.896 0.896
[4921] 1.496 1.944 1.696 1.696 0.744 0.096 0.336 0.064 0.416 0.416
[4931] 1.536 0.416 0.864 1.336 1.376 1.336 1.136 0.736 0.056 0.296
[4941] 0.424 1.264 0.584 0.656 0.264 1.944 1.744 0.256 1.664 0.464
[4951] 1.096 0.504 0.424 0.464 0.056 1.136 0.296 0.496 0.824 1.744
[4961] 1.056 0.904 1.584 0.304 1.096 0.224 1.624 0.384 1.136 1.456
[4971] 2.096 1.264 1.296 1.896 0.896 -0.096 0.504 0.896 -0.184 1.544
[4981] 1.344 -0.176 1.224 1.696 0.344 1.544 0.816 1.144 1.576 1.504
[4991] 1.584 0.704 0.464 -0.184 0.824 0.496 0.736 0.424 0.256 0.944Estimate Dist under HA
Power
Power
[1] 0.2274n_0 <- 5
n_1 <- 5
data.frame(stat = c(H_0, H_A),
type = factor(c(rep("Null", length(H_0)),
rep("Alt", length(H_A))))) |>
mutate(in_reject_region = ifelse(stat > right_threshold | stat < left_threshold, "Reject Null", NA)) |>
ggplot(aes(x = stat, fill = type, color = in_reject_region)) +
geom_histogram(position = "identity", alpha = .3) +
geom_vline(xintercept = c(left_threshold, right_threshold), col = "tomato") +
scale_color_manual(
values = c("Reject Null" = "black"),
na.value = NA,
guide = "none") +
labs(title = paste0("Statistical Power: ", round(power, 2)),
subtitle = paste0("n0 = ", n_0, ", n1 = ", n_1, ", tau = ", tau)) +
theme_bw()
Functions
rejection_region <- function(df, alpha = .05, reps = 1000, seed = 4892) {
# create observed schedule (with missing data)
obs_sched <- df |>
mutate(Y_0 = ifelse(d_i == 0, y_i, NA),
Y_1 = ifelse(d_i == 1, y_i, NA))
# impute the missing potential outcomes with fisher sharp null
null_sched <- obs_sched |>
mutate(Y_0 = ifelse(is.na(Y_0), Y_1, Y_0),
Y_1 = ifelse(is.na(Y_1), Y_0, Y_1))
# simulate from sampling distribution under null
set.seed(seed)
H_0 <- rand_stats(schedule = null_sched,
d_i = df$d_i,
stat = "diff in means",
reps = reps)
# find rejection region
left_threshold <- quantile(H_0, alpha/2)
right_threshold <- quantile(H_0, 1 - alpha/2)
return(list(LT = left_threshold, RT = right_threshold))
}HA_tau <- function(df, tau, reps = 1000, seed = 4892) {
# create observed schedule (with missing data)
obs_sched <- df |>
mutate(Y_0 = ifelse(d_i == 0, y_i, NA),
Y_1 = ifelse(d_i == 1, y_i, NA))
# impute the missing potential outcomes under particular HA
alt_sched <- obs_sched |>
mutate(Y_0 = ifelse(is.na(Y_0), Y_1 - tau, Y_0),
Y_1 = ifelse(is.na(Y_1), Y_0 + tau, Y_1))
H_A <- rand_stats(schedule = alt_sched,
d_i = df$d_i,
stat = "diff in means",
reps = reps)
return(H_A)
}