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] 0.296 -0.224 0.736 -1.144 1.664 1.184 -1.064 0.216 -0.496 -1.376
[11] -0.096 0.496 0.944 0.336 -0.336 -1.064 -1.336 0.016 0.584 0.224
[21] -0.176 0.536 0.496 0.296 -0.144 -1.104 -0.616 0.704 0.864 0.576
[31] 0.144 0.944 -0.104 0.256 -0.224 -0.664 1.136 -0.864 -0.296 -0.024
[41] -0.864 -0.664 1.144 0.944 -0.496 0.856 0.856 -0.824 1.384 0.056
[51] 1.104 -0.296 -0.664 -0.776 -1.344 -0.336 0.936 -0.096 0.104 -0.224
[61] -0.504 0.296 0.096 -0.544 0.384 -1.104 0.664 0.424 0.384 -0.264
[71] 0.304 -0.064 0.216 -0.576 0.224 -1.144 0.416 0.576 -0.576 0.336
[81] 0.584 0.584 -0.096 0.744 0.576 0.944 0.104 0.904 0.704 -0.296
[91] 0.064 0.264 -0.144 0.416 -0.216 0.336 1.104 -0.024 0.344 0.784
[101] -0.496 -1.096 0.064 -1.384 0.576 0.096 -0.016 -1.136 -0.736 0.536
[111] -0.224 0.384 -1.376 1.296 -1.304 -0.184 -0.136 -0.064 0.704 0.864
[121] 0.496 -1.184 -0.264 -0.784 -0.304 -0.296 -0.384 0.264 0.176 -0.704
[131] 0.304 -0.256 1.136 0.864 0.944 0.536 1.504 0.136 0.064 0.064
[141] -0.576 -0.224 -0.744 -0.496 -0.304 0.664 -0.504 0.336 0.104 0.776
[151] -0.264 -0.424 -1.344 -0.216 0.104 -1.344 0.624 0.224 -0.496 -1.144
[161] 0.336 0.256 0.864 -0.056 1.136 -0.944 0.664 -0.584 -0.256 -0.544
[171] 0.224 0.024 1.336 0.664 -0.096 0.464 -0.384 -0.664 -0.464 -0.024
[181] -0.104 -0.944 1.384 0.216 1.384 -0.256 0.224 -0.856 0.336 0.696
[191] -0.584 -1.136 -1.144 0.504 -0.544 -0.864 -1.384 0.176 0.016 -1.664
[201] -0.944 -0.224 0.104 1.336 0.056 0.544 -0.904 -0.424 0.544 -0.576
[211] 0.304 -0.336 -0.096 -0.664 -0.104 -0.096 -0.616 -0.504 -0.016 -0.064
[221] -0.104 -0.336 0.176 0.744 -1.336 0.296 -0.304 -1.304 -1.144 -1.104
[231] 0.144 -0.864 0.896 0.544 1.136 0.336 0.224 0.256 0.504 1.696
[241] -0.496 -0.216 -0.056 0.536 -1.056 -0.776 -0.496 -0.864 0.424 0.536
[251] 0.024 0.096 -0.304 -0.296 -0.536 1.376 -0.944 -0.736 -0.064 0.536
[261] -0.024 -0.064 -1.344 0.216 -0.696 0.336 0.536 -0.224 0.016 -0.504
[271] 0.904 1.224 -0.856 -0.104 -0.144 -0.336 -0.896 -0.744 -0.184 -0.696
[281] 1.696 -0.904 0.824 1.384 0.296 0.704 -0.664 -0.064 0.176 -0.296
[291] 0.416 0.064 -0.664 -0.264 0.216 0.296 0.416 0.256 1.096 0.856
[301] -0.096 -0.176 -0.776 0.016 -0.464 0.744 -0.416 -0.864 -0.856 -0.056
[311] -0.056 -0.296 0.224 -0.544 0.336 -0.104 1.136 0.344 -0.144 -0.336
[321] 0.096 -0.776 0.504 0.376 0.056 0.056 -0.096 0.416 -0.824 -0.296
[331] 0.576 -0.544 0.104 1.304 0.944 -0.616 -0.744 -0.224 1.336 0.576
[341] -0.064 -0.736 -0.104 0.696 -0.496 -0.104 0.024 1.664 0.904 0.176
[351] 0.136 0.536 -0.296 -0.536 0.464 -0.776 0.296 -0.504 -1.224 -0.704
[361] -0.224 -0.464 1.144 -0.296 -1.336 -0.064 -0.264 0.864 -0.256 0.544
[371] 0.696 0.184 0.064 0.176 -0.256 0.184 0.864 0.256 -0.264 -1.376
[381] 0.536 0.384 -0.224 0.256 0.296 -0.064 -0.296 0.144 -0.176 -0.896
[391] 0.096 0.096 0.664 -0.944 0.664 -0.136 0.776 1.056 0.536 0.776
[401] 1.224 -0.216 -0.104 0.504 0.336 0.544 -0.064 1.304 -0.936 0.696
[411] 0.864 -0.744 0.224 0.256 0.696 0.504 0.064 -0.056 0.256 -0.696
[421] 0.344 -0.696 -0.904 -0.304 -0.864 0.864 0.856 0.504 1.064 0.256
[431] 0.056 -1.144 0.616 0.096 -0.584 0.944 0.904 -0.744 -0.256 -0.304
[441] 0.584 -1.376 0.384 0.136 -0.864 -0.256 0.376 0.144 1.144 0.304
[451] -0.336 0.704 0.136 -0.264 1.144 -0.824 -0.144 0.576 1.744 0.696
[461] 0.584 0.304 -1.696 -0.864 -0.464 0.344 -0.296 -0.376 1.336 -0.344
[471] -1.136 -0.576 -0.896 0.624 -0.296 -1.056 0.296 -0.704 -0.736 0.056
[481] -0.256 -0.896 -0.384 0.064 0.224 0.664 0.224 -0.904 0.256 -1.376
[491] 0.104 -0.536 -0.496 -0.256 -1.144 -0.904 0.504 0.824 -0.104 -0.104
[501] -0.224 -1.304 0.776 -0.664 0.016 -1.136 0.464 0.376 -0.064 -0.904
[511] 0.504 0.576 0.064 0.864 -0.304 -0.256 -0.064 -0.584 0.056 -0.944
[521] -0.864 0.024 0.296 -0.184 0.584 -0.496 -0.824 0.944 -0.296 -0.064
[531] -0.856 0.416 0.744 -0.096 -0.256 -0.376 0.304 1.136 0.376 -0.576
[541] -0.904 -0.896 -0.056 -0.336 -0.384 -0.576 -0.384 0.536 1.056 0.256
[551] -0.584 -0.584 0.744 -0.864 0.304 -0.696 -0.584 -0.184 -0.416 0.704
[561] 0.776 -0.824 0.224 1.144 1.704 0.544 -0.856 0.696 -0.344 0.696
[571] -0.624 -0.936 1.336 0.704 0.304 1.664 -0.176 0.336 0.256 -1.104
[581] -0.904 0.136 -0.136 -0.296 -0.424 -0.904 1.224 -0.696 1.136 0.104
[591] -0.744 -0.536 -0.496 -0.256 -0.336 -1.104 -0.664 0.536 0.904 -0.864
[601] 0.024 0.536 -1.104 0.136 -0.744 0.384 -0.336 -0.544 0.736 -0.536
[611] -0.664 -1.056 -0.744 -0.536 -0.576 0.224 -0.576 -0.336 1.376 0.056
[621] -0.944 1.224 0.024 -0.176 0.736 0.216 -0.584 -0.016 0.024 1.136
[631] -1.664 -0.776 -0.224 -0.584 0.144 -0.256 -0.064 1.744 0.104 0.496
[641] -0.384 -0.296 -0.064 -0.024 -0.544 -0.936 1.296 -0.216 -0.864 1.376
[651] 0.424 -1.056 -0.704 -0.144 0.736 0.344 -0.776 1.144 0.896 -0.616
[661] -0.104 1.136 0.376 -0.536 0.904 0.544 0.056 0.936 0.176 0.576
[671] -1.096 -0.104 -0.696 1.704 -0.744 -0.296 -0.904 -0.344 -0.464 -1.104
[681] -1.104 -1.344 -0.904 0.384 -1.664 -0.304 1.696 1.144 -0.504 -1.696
[691] -0.896 -1.696 -0.944 -0.896 0.584 -0.304 1.384 0.384 -0.864 -0.784
[701] 0.304 -0.384 -0.304 -0.464 -0.376 -0.064 0.544 0.344 -0.224 -0.776
[711] 0.096 -0.856 1.104 -0.056 -0.224 0.544 -0.224 -1.384 -0.496 0.776
[721] 0.304 -0.504 -0.336 1.096 0.344 1.064 0.504 0.304 0.136 0.104
[731] -0.536 -0.264 -1.056 -0.944 -0.136 0.136 0.296 1.136 0.864 0.144
[741] -0.096 -0.576 0.264 0.016 -0.104 0.056 -0.224 0.696 -0.424 1.384
[751] 1.144 -0.576 -0.584 -0.064 1.224 1.696 -1.296 0.096 1.664 0.144
[761] 1.136 1.184 -0.696 0.304 -0.576 -1.104 0.544 0.944 0.264 0.136
[771] 0.256 -0.336 0.216 0.744 0.144 0.256 0.856 0.096 -0.056 -0.504
[781] 0.296 -0.864 -0.776 -0.264 -0.296 0.384 -1.224 1.184 1.104 -0.664
[791] -0.384 0.584 -0.544 0.384 -0.704 -1.144 1.744 0.496 -0.856 0.176
[801] 0.064 0.696 -0.824 -0.664 0.224 -0.504 1.384 0.504 1.344 1.144
[811] 0.584 1.336 -0.856 -0.904 -0.496 0.744 -0.464 -0.296 -0.696 1.184
[821] -0.864 -0.696 1.376 0.544 -1.304 -0.744 -1.096 -0.064 0.944 0.744
[831] -1.384 0.584 0.064 0.424 -1.664 -0.584 0.416 -0.216 0.256 -0.304
[841] 0.144 1.104 0.296 0.616 0.856 -0.576 0.664 -1.664 -0.544 -0.744
[851] -0.576 0.824 -0.096 -0.096 0.664 -0.584 -0.096 0.544 0.176 0.696
[861] 0.304 1.704 -0.544 0.264 -0.376 0.744 0.376 -0.576 0.024 1.704
[871] -0.696 -0.424 -0.376 -0.736 0.144 -0.016 0.216 0.576 -0.384 0.384
[881] -1.704 0.744 -0.224 0.384 0.664 -1.136 -0.376 -0.296 1.104 -0.376
[891] -0.136 0.096 0.104 0.056 -0.136 -0.944 -0.144 0.664 -0.376 -0.736
[901] 0.904 0.336 -0.304 -0.544 0.616 1.376 -0.584 -0.416 -0.496 0.136
[911] 0.576 -0.576 -0.536 -0.336 0.696 0.936 -0.144 -1.144 0.064 0.536
[921] 0.136 -0.296 0.864 -0.664 0.304 0.384 -0.896 1.704 0.704 -0.336
[931] 0.224 -0.096 -0.336 1.344 -0.544 0.224 0.224 0.664 -0.536 0.624
[941] 1.704 0.864 0.344 -0.104 0.016 0.024 0.744 -0.896 0.256 -0.264
[951] 0.504 1.664 -0.096 0.384 -0.536 0.176 0.696 -1.744 1.136 -0.056
[961] -0.744 0.304 -0.256 -1.336 1.504 0.296 -0.904 0.824 -0.304 1.104
[971] -0.216 0.056 -0.504 0.176 -0.136 -0.336 0.184 -1.056 -0.856 0.376
[981] 0.496 0.504 -0.144 1.376 -0.304 -0.744 1.744 -0.384 0.096 1.696
[991] -0.544 -0.096 -1.336 -0.176 -0.144 1.136 -0.216 0.696 0.224 -0.056
[1001] -0.336 -0.256 0.384 0.904 -0.264 -0.096 -0.144 -0.376 0.784 0.504
[1011] 0.264 -0.104 -0.544 -0.416 -0.704 -0.704 -1.704 1.696 0.856 1.096
[1021] -0.904 0.696 -0.096 0.096 0.504 0.224 -0.384 -0.904 -0.104 0.384
[1031] 0.864 0.304 -0.496 -0.624 -0.304 -0.696 -0.336 -0.096 -0.424 -0.464
[1041] 0.856 0.256 -0.304 -0.384 -0.576 -0.096 -0.384 -0.696 0.216 0.144
[1051] 0.064 -0.624 0.424 -0.296 0.696 0.664 0.536 -0.936 0.504 0.304
[1061] -0.296 -0.664 -0.376 0.464 -1.344 -0.864 -1.064 -1.304 0.056 -0.216
[1071] 1.224 -0.056 -0.904 0.064 -0.544 -1.384 -0.304 1.744 0.744 -0.736
[1081] -0.864 0.696 0.304 0.104 0.336 0.136 1.136 -0.224 0.176 -0.504
[1091] -0.664 -1.696 0.056 -0.104 0.136 0.336 1.104 0.144 -1.104 1.224
[1101] -0.696 -0.744 -1.104 -0.576 0.304 0.136 -1.336 -0.064 1.744 -0.104
[1111] -1.296 0.856 0.336 0.584 -0.256 1.696 -0.064 1.696 -0.784 -0.096
[1121] -0.224 -0.104 0.304 -0.064 -1.744 1.096 -0.744 0.664 0.696 1.096
[1131] -0.424 -0.336 -0.856 -1.136 0.296 0.856 0.224 -1.224 0.696 1.336
[1141] 0.224 -0.664 -0.224 1.104 -0.264 -0.856 0.144 -0.416 0.224 -0.544
[1151] -0.896 1.664 1.224 0.104 -0.024 -0.776 0.744 -0.336 1.144 1.704
[1161] 0.784 -0.336 0.544 -0.376 0.376 -0.144 1.664 -0.144 0.856 0.744
[1171] 0.256 0.584 -0.696 -1.336 1.064 -0.864 0.304 1.344 0.104 0.064
[1181] 0.784 0.304 0.304 0.744 -0.736 0.256 0.176 0.176 -0.736 0.104
[1191] 0.264 0.224 0.864 -0.224 -1.704 -0.496 -0.664 0.056 0.544 -0.424
[1201] 0.384 0.184 0.224 -1.104 -0.136 -1.664 -0.664 -0.536 -1.384 0.144
[1211] -1.664 -0.696 0.776 -0.584 -0.736 0.576 -0.896 -0.104 0.944 -1.136
[1221] 0.184 1.376 0.304 0.024 -0.416 -0.056 0.904 0.296 0.544 -0.304
[1231] 0.696 -0.304 -0.664 -0.104 -0.544 0.856 -0.376 0.224 -0.544 -1.056
[1241] 1.504 -0.736 -0.064 -0.736 0.104 1.296 0.224 -0.664 -0.096 1.056
[1251] -0.544 1.704 0.496 0.584 0.496 -0.056 -1.344 -0.704 0.616 -1.664
[1261] -1.304 -0.216 -0.336 0.944 -0.056 -0.544 0.536 -0.304 0.424 -0.224
[1271] -0.864 -0.144 1.704 1.296 0.904 1.104 1.336 0.504 0.544 0.536
[1281] -0.736 0.904 0.096 -0.016 1.344 -0.336 -0.184 -0.936 0.296 0.136
[1291] -0.784 -0.064 -0.904 -0.344 -0.104 -0.224 -0.224 0.184 -0.304 0.544
[1301] -0.416 -0.584 0.784 0.904 -0.824 0.504 0.704 -0.136 -0.904 0.856
[1311] 0.296 -0.024 0.336 1.224 -0.224 0.224 0.496 1.096 -0.784 -0.776
[1321] 0.224 -0.536 -0.416 0.064 0.104 -0.544 0.536 1.224 -0.904 0.904
[1331] -0.336 1.144 -0.584 -0.504 -0.664 -0.584 -1.224 0.224 0.176 -0.696
[1341] 1.664 0.144 -0.696 0.696 0.896 0.336 -0.576 -0.936 0.416 0.744
[1351] -0.496 -0.104 0.136 0.904 0.144 0.064 -0.176 -0.944 -0.856 -0.096
[1361] -1.344 0.944 -1.056 -0.664 0.864 0.496 1.504 -0.176 -0.224 0.576
[1371] -0.304 -1.224 0.384 -0.056 0.824 -0.736 -0.256 -0.216 -0.064 1.504
[1381] 0.584 -0.944 0.144 0.864 0.576 1.504 -0.384 0.504 -1.296 0.264
[1391] -0.304 1.344 -0.664 -0.344 1.696 -0.144 0.336 -0.064 -0.784 1.104
[1401] 0.096 -0.056 -1.136 -0.744 -0.256 0.296 -0.376 -0.584 0.104 0.536
[1411] -0.104 1.144 0.856 0.096 -0.104 -0.136 -0.216 -0.376 1.504 -0.536
[1421] -0.304 0.344 -0.536 1.064 -1.336 1.336 -0.664 -0.224 0.584 1.664
[1431] 0.064 0.624 -1.744 -0.384 -0.584 0.744 -0.264 -0.104 -1.744 -0.056
[1441] 0.664 0.104 -1.144 0.064 0.664 -0.776 0.416 0.184 0.024 -0.864
[1451] -0.136 0.424 1.696 0.336 -0.096 0.896 -0.664 0.576 -0.416 -1.336
[1461] 0.784 -0.744 -0.064 0.336 -0.776 0.144 -0.264 -0.424 -0.576 -0.064
[1471] 0.904 0.416 1.336 1.696 -0.224 0.664 -0.624 -0.864 0.384 0.536
[1481] -0.944 0.536 0.536 0.544 -1.336 -1.136 0.304 1.336 0.176 -1.304
[1491] -0.624 -0.104 1.064 0.744 -0.064 -0.864 -0.224 -1.144 0.304 -1.376
[1501] -0.496 -0.536 -0.304 -0.576 0.096 -0.864 -1.144 -1.664 0.904 -0.176
[1511] -0.184 -0.256 -0.864 0.576 -0.944 1.376 -1.376 -0.424 -0.664 0.056
[1521] 0.904 0.896 -1.224 -0.904 0.424 0.576 -0.144 0.184 0.064 -0.664
[1531] 0.104 -0.864 1.184 0.096 -0.464 0.256 0.104 1.224 -0.304 -0.744
[1541] 1.096 -0.136 0.464 -0.904 0.064 -0.536 0.616 -0.624 1.384 0.544
[1551] -1.144 -0.056 0.256 1.336 -0.944 -1.104 -0.576 -0.376 0.304 -0.104
[1561] -0.664 0.104 -0.064 1.696 0.544 -0.384 0.264 -1.296 -0.904 -0.224
[1571] 0.744 -1.136 -0.744 1.304 -0.104 0.256 -1.664 -0.096 -1.136 -0.224
[1581] 0.496 -0.576 -0.144 -0.336 -0.304 -0.184 0.144 0.016 0.144 0.424
[1591] 0.664 -1.304 0.896 -0.736 0.544 -0.736 0.144 -1.224 -0.176 0.536
[1601] -0.696 0.216 -0.336 -0.504 1.376 -0.584 0.576 -0.224 0.776 -1.144
[1611] 0.536 0.624 0.176 0.536 -0.184 0.144 -1.096 -1.376 -0.936 -0.864
[1621] 0.616 1.344 -0.304 -0.744 -0.096 0.224 0.584 0.024 -0.464 0.264
[1631] 0.344 -0.544 -0.544 -0.056 -0.584 -0.864 -0.864 -0.264 0.056 0.704
[1641] 1.184 1.064 0.376 0.336 -0.096 -0.696 -0.944 -0.696 0.016 -0.544
[1651] -0.944 1.136 -0.136 0.896 1.704 -0.696 -0.936 -1.696 -0.864 -0.224
[1661] 0.384 -0.304 0.224 0.664 -0.304 -0.144 -0.824 -1.744 -0.904 0.104
[1671] 0.016 -0.776 0.904 0.064 0.056 -0.096 -0.504 -0.744 0.904 -0.424
[1681] 1.384 -0.864 0.776 0.856 0.136 0.216 0.424 0.336 0.496 0.624
[1691] -0.256 -1.384 0.384 0.376 -1.136 -0.384 -0.704 -1.104 -0.056 -0.104
[1701] 0.384 -1.224 0.704 0.256 0.736 -1.144 0.144 0.304 -1.136 0.336
[1711] -0.376 -0.504 1.136 -0.696 0.224 1.744 0.344 -0.584 -1.296 0.496
[1721] 0.624 0.064 -1.304 -0.104 -0.024 1.144 -0.224 0.264 0.104 0.056
[1731] -0.744 0.864 -0.584 0.376 0.104 1.144 -0.304 0.624 1.104 -0.096
[1741] 1.136 0.304 0.696 -0.736 -0.936 0.336 0.096 0.424 -0.936 0.544
[1751] 0.896 1.136 0.344 -1.344 -0.424 1.296 0.144 -0.776 -0.056 0.744
[1761] -1.144 0.224 1.096 0.424 0.136 -0.624 -0.864 -1.304 0.256 -0.936
[1771] -0.336 -0.144 0.096 -0.304 -0.064 -0.256 0.696 -0.496 1.344 0.096
[1781] 0.136 0.104 0.736 1.136 -0.536 -0.304 0.136 0.544 -0.304 -0.096
[1791] 0.744 1.104 -1.504 -0.224 0.056 1.336 -0.176 -0.144 0.864 0.224
[1801] 0.896 -0.864 -0.864 -0.264 0.944 0.504 -0.744 -0.696 0.544 0.856
[1811] -0.296 -0.304 0.584 -0.544 -0.024 -0.504 -0.096 0.024 0.336 -0.584
[1821] 1.104 -0.064 0.216 -0.296 -0.904 -0.104 0.576 -0.224 -0.744 -0.104
[1831] 0.896 0.944 0.896 -1.136 0.176 -0.504 -1.384 -1.136 0.704 0.544
[1841] 0.304 -0.544 1.344 1.096 -0.144 -0.136 -0.944 0.016 0.416 0.696
[1851] 0.376 -0.224 0.296 -0.584 1.744 -0.664 0.096 0.096 -1.696 -0.576
[1861] 0.776 -0.136 0.416 -0.856 -0.944 -0.304 -0.584 -0.904 -0.544 0.936
[1871] -1.696 0.544 0.696 -0.296 0.496 -0.864 1.184 -0.216 1.296 -0.336
[1881] 0.096 -0.424 -0.296 0.784 -0.376 -0.736 -0.056 0.744 -0.424 0.744
[1891] -1.064 -1.224 1.136 -0.704 -0.504 0.224 -0.336 0.096 0.056 0.336
[1901] -0.256 -0.216 -0.184 0.896 0.944 -0.304 -0.296 0.616 0.856 -0.344
[1911] 0.384 -0.616 -0.664 0.896 1.376 -1.064 -0.696 -0.864 0.136 -1.064
[1921] -0.864 -0.144 1.056 1.336 0.224 0.904 -0.856 0.256 0.136 1.056
[1931] -0.664 0.144 -0.104 0.136 0.864 -0.864 0.504 0.616 0.664 -0.664
[1941] 0.856 0.176 -0.264 0.696 -0.696 -0.064 -0.944 -0.296 0.536 0.544
[1951] 0.336 0.144 -0.504 0.096 -0.896 1.504 -0.384 -0.664 0.664 0.944
[1961] -0.664 -0.584 0.576 0.864 0.304 -0.624 -0.064 0.304 -0.264 0.144
[1971] 1.104 -0.584 -0.096 0.136 -1.296 1.064 -0.424 1.744 0.336 -1.744
[1981] 0.864 -0.576 -0.904 0.824 0.136 -0.696 0.736 0.576 -0.896 -0.536
[1991] 0.176 -1.224 0.544 0.696 -1.384 0.144 -1.376 -0.104 -0.296 0.416
[2001] 1.096 0.224 -0.064 0.336 0.464 0.136 -0.936 1.144 1.696 0.264
[2011] -1.304 -0.256 -0.216 0.304 -1.704 0.576 -0.024 -0.264 -1.304 -0.096
[2021] 0.416 0.216 -0.576 -0.736 1.344 -0.096 0.384 0.064 0.544 -0.064
[2031] 0.664 -1.704 -0.536 0.216 0.544 0.136 0.064 0.216 -0.296 0.064
[2041] 0.936 -1.104 -0.736 0.944 0.824 -0.744 0.256 0.424 1.224 0.304
[2051] -0.064 -1.104 -0.544 -0.376 -0.384 1.296 0.864 -0.224 -0.136 -0.584
[2061] -0.296 0.296 -1.184 1.504 -0.064 0.696 -0.544 0.664 0.064 0.224
[2071] 0.376 0.216 0.696 -0.904 -0.584 -0.064 0.536 0.784 1.344 -0.936
[2081] 0.864 0.736 -1.744 -0.144 -0.144 0.096 1.064 -1.064 0.736 -0.384
[2091] -0.664 1.104 1.224 -0.616 0.536 -1.184 -0.736 0.296 0.056 0.624
[2101] 0.384 0.216 0.216 0.176 0.256 0.664 -1.744 -0.856 -1.704 0.376
[2111] 0.896 -0.736 -0.936 0.096 0.104 1.144 0.576 0.144 -0.104 -0.056
[2121] 0.224 0.736 -0.376 -0.336 0.864 0.344 -1.096 1.744 -0.584 0.384
[2131] -0.776 0.304 1.224 1.136 0.616 0.136 -0.704 0.184 1.056 1.504
[2141] 0.104 -1.336 -1.376 0.864 -0.176 -0.264 0.544 -0.224 -0.504 -0.224
[2151] 1.136 -0.256 -0.224 -0.016 -0.704 0.256 0.296 0.056 0.944 0.944
[2161] -0.536 -0.384 0.256 -0.136 -1.104 0.376 -0.504 1.144 0.416 -0.336
[2171] 0.944 1.184 -1.296 -0.864 0.536 0.624 -0.744 -0.264 -1.376 -1.704
[2181] -0.384 0.856 -0.864 0.736 -1.096 -0.384 -0.216 1.096 -0.224 -0.584
[2191] 1.104 -0.304 0.544 1.144 -1.704 -0.144 -0.904 0.256 -0.176 -0.664
[2201] 0.936 -0.736 0.744 -0.384 -1.224 0.376 0.024 -0.624 -0.304 -0.904
[2211] 1.376 0.104 -0.016 -0.296 -0.864 -1.184 -0.536 0.856 0.184 0.056
[2221] -0.064 0.336 -0.064 -0.696 -1.056 0.904 -0.704 0.096 -0.096 0.384
[2231] -0.696 0.184 0.616 -0.584 0.344 -0.856 -0.224 -0.664 -1.136 0.664
[2241] -0.376 -1.096 -0.224 -0.744 0.936 -0.064 1.664 1.336 0.416 0.904
[2251] -1.384 -0.424 1.104 0.096 -0.384 0.144 0.696 -0.144 1.064 1.744
[2261] -0.544 -0.304 -1.136 -0.904 0.904 0.344 -0.504 0.904 -0.704 -0.504
[2271] 0.896 1.144 -0.296 0.504 0.496 -0.504 0.424 -0.424 0.896 0.144
[2281] -0.904 0.544 -0.896 -0.136 -0.144 -0.256 -0.544 1.504 -1.144 -0.304
[2291] 1.104 0.576 0.104 -0.464 -0.144 0.416 0.144 -0.296 -1.344 0.224
[2301] -0.224 0.336 -0.136 0.864 0.776 -1.384 0.584 -1.096 0.376 -0.584
[2311] 0.336 -0.504 0.336 1.104 0.376 -1.224 -1.376 0.064 -0.064 -0.864
[2321] -1.296 0.216 -0.336 0.304 0.136 -0.704 -0.224 0.896 -0.784 -0.496
[2331] 0.384 -0.744 1.296 -0.384 0.424 -0.336 -1.304 -0.856 -0.016 0.544
[2341] 0.544 -0.344 -0.496 0.136 -0.504 0.104 -0.376 -0.696 -0.784 -0.616
[2351] -0.384 0.304 0.016 0.824 0.584 0.384 -0.024 -0.544 0.864 -1.304
[2361] -1.304 1.096 0.224 0.216 0.664 -0.896 -0.904 -0.904 -0.056 0.264
[2371] -0.536 -1.696 -1.704 -0.144 -0.504 0.176 -0.224 1.296 0.944 0.176
[2381] 0.216 -1.664 -0.584 -0.384 -1.144 0.696 1.336 -1.104 1.184 -0.376
[2391] -0.864 -0.056 -1.104 0.056 0.256 0.064 1.096 0.344 0.024 0.376
[2401] -1.056 0.264 -0.056 -0.224 0.104 -0.544 -0.544 -0.824 0.336 -0.016
[2411] 1.384 -1.184 -0.536 1.104 -0.184 0.376 -0.024 -0.304 0.944 -1.096
[2421] -0.376 0.856 0.744 0.096 0.256 0.904 1.744 0.856 0.336 0.864
[2431] -0.944 0.576 1.144 -0.784 0.904 -0.096 0.064 0.744 0.256 0.376
[2441] -1.104 -0.904 -0.064 -0.264 0.384 0.696 -0.696 1.296 0.104 -1.064
[2451] -0.224 -1.184 -0.016 -0.856 0.216 -0.344 0.104 0.384 0.544 0.376
[2461] -0.104 0.064 -0.536 -0.696 0.024 -0.224 1.224 -0.624 0.704 0.544
[2471] 0.784 0.304 -1.144 -0.304 0.464 -0.136 -0.224 -0.896 0.096 -0.896
[2481] -0.104 -0.416 -0.496 -1.504 0.104 -0.336 0.136 -0.264 -0.864 -0.264
[2491] 1.296 0.176 -0.944 -0.744 1.304 0.136 0.576 -0.544 0.144 0.896
[2501] -0.496 -1.184 -0.896 0.704 -0.304 0.224 0.256 -0.056 0.536 0.376
[2511] -0.224 -0.304 0.136 0.704 -1.304 0.056 0.176 0.864 -0.576 -0.544
[2521] -1.136 -0.256 0.176 -0.496 -0.056 -1.136 0.904 -0.096 -0.904 -0.256
[2531] -0.296 -0.136 -0.504 0.624 0.176 -0.744 -1.136 -0.096 -0.376 0.096
[2541] -0.664 -0.776 -0.104 -0.384 -0.664 0.336 0.296 -0.696 0.744 -0.736
[2551] -0.016 -0.944 0.936 0.176 -0.416 -0.824 -1.136 -0.624 -0.304 -0.784
[2561] -0.104 0.616 1.296 1.664 -1.696 -0.744 -0.696 0.376 -1.376 0.664
[2571] 0.136 0.336 -0.336 0.136 0.744 -0.064 -0.096 -1.104 0.944 1.224
[2581] -1.384 -0.944 0.416 0.384 -0.104 -0.696 -0.496 -1.104 1.144 0.336
[2591] 0.376 0.696 1.064 0.464 -0.264 0.216 -0.584 -0.024 0.544 -0.896
[2601] 0.024 -0.544 -0.944 -0.584 0.296 -1.136 -1.376 0.864 0.264 0.024
[2611] -0.584 0.856 0.064 0.224 -1.744 0.664 -0.064 1.296 -0.384 0.224
[2621] 0.544 0.664 -0.944 -1.304 0.344 -0.216 0.336 -0.056 -0.504 -0.384
[2631] 0.224 0.136 0.536 0.336 -0.024 0.496 0.384 0.736 -0.736 -0.144
[2641] 1.104 0.056 -0.296 -0.224 0.736 -0.544 0.144 -0.864 -0.064 0.096
[2651] 0.784 -0.256 -1.224 0.176 -0.264 -0.696 -0.576 0.744 0.096 0.376
[2661] 0.184 -0.376 -0.304 0.224 -0.104 0.936 -0.296 0.776 -0.576 -0.664
[2671] 1.664 0.104 -1.296 0.784 -0.584 0.904 -1.056 -1.056 -0.496 -1.344
[2681] 0.696 0.304 -0.864 -0.576 0.104 -0.776 1.504 0.856 -0.416 0.744
[2691] -0.216 -0.224 0.904 -0.696 -1.344 0.896 -0.864 -1.336 -0.696 0.144
[2701] -0.144 -0.184 -0.944 0.144 0.584 -0.096 0.544 0.744 -0.336 0.224
[2711] -0.536 -1.296 0.224 0.104 -1.504 1.376 0.056 0.536 0.264 -0.376
[2721] 0.304 0.056 -1.056 -0.256 -0.096 -0.696 0.016 -0.144 -1.104 -0.056
[2731] 1.504 -0.184 -0.544 0.104 0.104 0.104 0.616 0.224 0.416 0.256
[2741] -0.304 0.864 0.136 -0.144 -0.096 -1.696 0.904 -0.104 0.744 -0.136
[2751] 0.216 -0.576 -0.264 0.664 -1.704 -0.104 -0.056 -0.304 0.856 -0.624
[2761] -0.944 -0.144 1.096 0.104 -0.216 1.664 -1.696 0.376 0.744 0.096
[2771] 0.504 -0.304 -1.296 -0.336 0.304 0.176 0.576 0.016 -0.064 -0.384
[2781] 0.104 -1.104 -0.424 0.736 -0.584 0.336 -0.904 1.344 0.944 0.944
[2791] 0.016 0.544 -0.096 0.584 0.664 0.176 -0.384 1.144 -0.264 -0.064
[2801] -1.136 0.904 -0.264 -1.304 -1.136 -1.376 -0.536 -1.104 0.464 0.584
[2811] -0.136 -0.264 -1.056 -0.024 1.664 1.304 -0.056 -1.376 0.176 0.384
[2821] 0.496 -0.544 -0.584 -0.504 -0.256 0.264 -0.056 0.416 -0.176 -0.144
[2831] 0.536 -0.904 -0.216 -0.536 0.696 0.184 1.104 0.104 0.624 -0.296
[2841] -0.376 -0.896 0.776 -0.384 0.664 0.304 -0.176 -0.576 -1.304 1.696
[2851] -0.896 -1.136 -1.064 -0.904 -0.536 0.336 -0.824 0.176 -0.096 0.584
[2861] -0.304 0.376 0.696 -1.184 0.904 0.304 -1.136 0.856 -0.264 -0.136
[2871] 0.216 -0.544 -0.584 -0.256 1.296 -0.696 0.304 -0.224 -0.064 -1.096
[2881] -0.704 0.696 0.544 -0.304 0.904 0.056 -0.904 -1.376 0.264 0.096
[2891] -0.496 -0.664 -0.136 -1.096 0.856 0.856 -0.304 0.576 1.224 -1.144
[2901] -1.144 0.544 -1.064 1.144 0.496 0.304 -0.576 0.944 -0.384 -0.856
[2911] -0.176 -0.864 0.304 0.296 0.064 -0.744 -0.384 -1.144 0.944 -0.056
[2921] -0.416 0.904 1.104 -0.256 -0.944 0.504 -0.304 -0.904 -0.336 0.936
[2931] 0.504 -0.544 0.224 -0.056 1.336 0.744 -0.944 0.704 1.376 -0.696
[2941] 1.744 0.736 -0.576 0.384 0.336 0.544 -0.864 -1.336 0.704 0.264
[2951] 0.904 -0.696 -1.144 -0.216 0.264 -1.104 -0.304 0.496 -0.464 -0.336
[2961] 0.536 -0.664 -1.056 -0.536 0.904 -1.664 0.504 -0.016 0.096 0.104
[2971] -0.104 0.776 0.736 -0.056 -0.056 0.024 1.184 -1.376 0.056 -0.544
[2981] 0.584 1.144 -0.024 -0.224 0.296 1.096 0.296 -0.536 0.096 -1.704
[2991] 0.704 1.336 -0.664 -1.224 0.064 0.536 -0.464 0.904 -0.664 -1.184
[3001] -0.296 0.904 -0.496 -0.896 1.504 -0.336 -0.056 -0.264 -0.864 0.904
[3011] -0.384 -0.216 -0.024 -1.104 -0.424 0.904 0.744 0.544 0.696 0.224
[3021] 0.744 0.136 0.176 -0.856 0.504 -0.576 -0.144 -1.344 -0.944 -0.616
[3031] -0.496 0.064 -0.384 0.664 -0.704 0.136 -0.864 -0.856 -1.184 0.736
[3041] -1.696 0.024 -0.496 0.304 0.256 -0.064 0.936 0.144 -1.104 0.256
[3051] 0.104 1.664 0.736 -0.024 -0.744 0.584 -0.864 -1.136 0.216 0.216
[3061] -1.224 -0.896 -0.904 1.056 0.504 0.536 0.064 -1.664 -0.216 1.696
[3071] 1.056 -0.616 1.144 0.176 0.104 -0.744 0.384 0.864 -0.056 -0.664
[3081] 0.824 -0.856 0.096 0.944 0.064 0.864 -0.336 -0.496 -0.664 1.304
[3091] 0.336 -0.024 -0.136 -0.544 -0.864 -0.144 -0.536 -0.336 0.304 -1.744
[3101] 0.384 -0.464 -0.736 1.136 -0.144 0.576 0.136 -1.336 0.224 1.336
[3111] -1.696 -0.544 -1.136 0.376 0.824 0.024 -0.664 -1.304 -0.616 0.104
[3121] 0.016 -0.344 -0.136 -0.064 0.136 0.024 0.776 -0.696 -0.224 -0.264
[3131] 0.576 -0.696 -0.424 0.696 -0.536 0.224 0.776 -0.064 -0.584 0.296
[3141] -0.216 0.296 -0.224 0.624 -0.544 1.184 0.184 -0.144 0.096 1.224
[3151] 0.096 -0.584 -0.184 -0.424 0.056 -0.544 0.416 0.224 -0.336 -0.384
[3161] -1.184 0.496 0.384 0.936 0.696 -1.136 1.224 -0.496 -0.864 -0.856
[3171] 0.064 -0.336 -0.496 1.296 -0.064 0.536 0.384 0.696 -0.944 1.344
[3181] 0.896 0.736 -0.696 0.224 0.584 0.144 -0.544 -0.176 0.304 -0.576
[3191] 0.224 1.184 -0.544 -1.136 0.216 0.944 -0.696 0.024 0.064 -0.704
[3201] -0.736 0.376 0.064 0.864 -0.296 1.104 -0.584 -0.056 -0.376 0.536
[3211] -0.744 0.704 -0.304 0.544 -0.536 -1.144 -0.224 -0.136 -0.224 -0.144
[3221] -0.056 -0.096 -0.336 -0.224 -1.136 0.704 0.584 -0.744 -0.384 1.104
[3231] -0.144 1.104 0.616 0.064 -0.896 0.384 -1.096 -0.224 0.584 0.176
[3241] 0.824 -1.056 0.496 -0.144 -0.136 0.104 0.376 -0.864 0.376 0.864
[3251] -1.704 0.624 0.064 -0.256 0.904 0.096 0.824 -0.944 0.896 0.256
[3261] 0.496 0.064 -0.056 -0.136 -0.144 -0.264 -0.376 -1.064 0.344 -0.216
[3271] -0.584 -0.664 -0.016 1.104 -0.464 -1.336 1.104 -0.344 -0.496 -0.064
[3281] 0.696 0.216 -1.144 0.144 0.304 -0.904 -0.144 0.056 -0.304 0.304
[3291] 0.736 -0.384 0.704 -0.104 1.184 -0.384 -0.856 -0.504 -1.376 0.744
[3301] -0.256 0.696 0.056 -1.304 0.304 -0.256 -0.104 0.664 -0.664 -0.176
[3311] 0.616 0.864 -0.496 -0.144 0.664 0.904 0.944 0.384 0.464 0.776
[3321] -1.744 -0.664 0.304 0.304 1.184 -1.696 0.304 0.264 -0.144 0.944
[3331] 0.224 0.224 1.704 -0.144 0.096 -0.136 -0.304 -0.096 -0.144 0.136
[3341] 1.384 -0.176 -0.864 -0.496 -0.896 0.864 -0.264 0.776 -0.144 -0.424
[3351] -1.184 0.176 -0.376 0.736 0.056 0.136 0.184 0.944 -0.136 -0.056
[3361] -1.104 -0.664 0.256 0.864 0.304 -1.064 -0.904 0.024 -0.336 -1.224
[3371] 0.144 0.864 0.184 0.536 -1.704 0.576 -0.464 -0.016 0.224 -0.384
[3381] 0.544 -0.384 0.104 0.256 -0.704 -0.416 -0.776 -0.776 0.696 -0.664
[3391] -0.896 0.296 0.616 -0.664 -1.376 -0.264 -0.336 -0.216 -0.064 0.224
[3401] -0.384 0.944 0.904 0.864 1.296 -1.504 0.064 0.304 0.544 0.296
[3411] -0.864 0.216 1.304 -0.696 0.024 -1.144 -1.696 1.056 -1.056 -0.696
[3421] -1.344 -0.256 0.264 0.104 -0.056 0.504 -0.944 -0.336 -0.944 -0.064
[3431] 0.024 -0.944 -0.304 0.776 1.096 0.416 0.416 0.904 0.336 0.776
[3441] -0.704 0.296 0.136 -0.424 -0.024 0.424 -0.216 0.304 -0.344 0.224
[3451] 0.064 0.304 0.096 0.736 -1.064 -0.496 -0.016 0.744 -0.096 0.064
[3461] -0.424 -0.344 0.096 0.304 -0.736 -0.664 0.776 1.224 0.736 0.256
[3471] 0.704 0.256 0.616 -0.584 -1.064 1.144 -1.344 -0.416 -1.376 -0.576
[3481] 0.336 -0.864 0.216 -1.696 0.464 0.944 0.576 0.416 -0.176 0.544
[3491] -0.904 -1.336 0.256 0.336 -0.136 -0.744 0.336 -1.064 0.336 0.584
[3501] 0.264 0.936 0.576 0.144 -0.016 -0.224 -0.624 1.056 1.696 0.536
[3511] 0.024 0.704 -0.296 0.536 0.264 -0.496 -0.544 0.784 0.216 -0.936
[3521] 0.544 -1.336 0.504 0.344 0.744 0.864 0.824 0.424 -0.376 -0.304
[3531] -0.056 0.064 -0.904 0.504 0.696 1.296 -1.296 -0.344 -0.056 0.064
[3541] 0.544 1.136 0.336 0.424 0.704 -0.336 0.136 -1.664 -0.744 1.296
[3551] -0.536 -0.224 0.384 -0.384 -0.256 -1.664 -0.536 1.384 1.336 0.504
[3561] 0.904 1.704 -0.064 -0.544 -0.504 0.136 -0.064 -0.136 0.384 0.464
[3571] 0.064 -0.696 0.024 0.064 1.144 0.096 0.304 -0.616 -0.744 -0.856
[3581] 0.864 0.224 1.136 -0.296 0.264 -0.424 0.624 0.944 -0.896 -0.056
[3591] 0.584 0.896 -0.376 -0.096 0.304 0.104 0.144 0.424 -0.616 0.776
[3601] -0.904 0.784 -0.744 0.496 0.056 0.584 0.864 -0.464 -0.536 -0.584
[3611] -0.216 -1.056 -0.624 -0.416 -0.296 -0.544 1.224 -0.416 0.224 0.904
[3621] 1.664 -0.576 0.584 0.416 -0.064 0.256 0.256 -0.384 0.264 0.904
[3631] 0.096 -0.784 -0.544 -0.664 0.064 -0.776 -0.304 0.624 -0.584 -0.504
[3641] -1.744 0.544 -0.176 0.224 -0.576 -0.416 0.144 -0.584 -0.224 -1.344
[3651] 0.016 1.096 -0.136 0.264 -1.096 -0.104 -0.496 -0.096 -1.184 0.664
[3661] -0.336 1.144 -0.256 -1.144 -0.176 0.424 0.056 0.376 -0.616 -0.296
[3671] -1.184 0.024 -0.424 0.864 -0.416 0.624 0.304 -0.896 -0.856 -0.584
[3681] 0.496 -1.104 0.904 0.104 1.744 -0.384 -0.024 1.384 -0.864 -0.864
[3691] -0.624 1.096 0.064 -0.664 1.104 0.536 1.104 0.864 -0.696 -0.264
[3701] 0.944 1.744 1.376 -0.744 -0.224 -0.304 0.256 0.176 0.736 0.536
[3711] -1.304 0.224 0.856 -0.696 -0.144 0.104 0.904 -0.696 0.616 1.344
[3721] 0.064 0.224 -0.224 -0.024 -0.376 0.696 0.136 -0.704 0.216 0.584
[3731] -1.504 0.744 -0.176 0.304 -0.184 -0.336 -0.376 -0.504 0.584 0.376
[3741] -1.144 0.296 0.824 -0.184 0.064 0.616 1.136 0.056 0.904 1.704
[3751] 0.576 1.224 -0.304 1.664 0.424 0.496 0.576 -0.064 0.496 -0.904
[3761] -0.696 1.704 -0.856 0.224 0.384 0.584 -0.136 -0.904 1.184 -0.304
[3771] -0.096 0.904 -0.696 -0.336 1.064 -0.216 -0.504 0.624 1.376 -0.256
[3781] -1.336 0.904 -0.336 -0.216 0.696 0.096 0.904 0.536 0.736 -0.176
[3791] 0.424 -1.096 -0.624 -0.544 -0.016 -0.864 0.296 -0.136 1.056 0.536
[3801] 0.144 -0.696 0.944 -0.536 -0.096 -1.696 0.504 -0.104 0.704 -0.056
[3811] 0.264 -0.704 0.864 -0.336 -0.384 -0.024 1.504 0.664 -0.424 0.416
[3821] -0.384 1.144 -0.384 0.856 1.136 -0.576 0.336 0.304 0.696 -0.736
[3831] -0.424 -1.104 0.896 0.904 0.304 0.336 1.304 -0.296 -0.904 0.056
[3841] -1.744 1.136 -0.024 0.056 0.104 0.536 0.056 -1.224 0.736 -0.536
[3851] -0.704 1.184 -0.384 0.224 0.336 -0.376 -0.704 -0.224 1.304 1.104
[3861] 1.296 -0.536 -0.744 0.304 0.824 -1.104 0.736 1.136 -0.424 -1.344
[3871] -0.584 -0.544 0.904 -0.536 0.176 0.304 -0.224 0.176 0.104 0.144
[3881] 0.256 0.296 0.864 -0.944 0.584 1.336 -0.304 -0.584 0.336 0.304
[3891] -0.296 -0.704 0.296 1.296 -1.296 -0.336 0.496 -0.584 0.936 0.144
[3901] 0.696 0.224 0.264 1.376 0.136 0.504 -0.544 -0.416 -0.544 -0.056
[3911] 0.776 1.336 -0.584 0.296 0.496 -0.944 -0.496 -1.664 -0.504 0.376
[3921] -1.056 0.584 -1.376 0.296 0.056 -0.264 -0.744 0.544 0.744 0.624
[3931] 0.704 0.064 0.576 0.056 -0.504 0.896 0.096 1.696 0.536 0.776
[3941] -0.184 -1.696 0.104 -0.384 0.624 -0.944 0.664 0.216 0.304 1.136
[3951] 0.336 1.696 -0.664 -1.704 0.024 0.136 -0.216 -0.096 -1.144 0.224
[3961] 1.104 1.296 0.504 -0.704 -0.904 -0.376 0.096 -0.536 -0.256 -0.336
[3971] 0.904 -1.056 0.744 -0.136 1.344 -0.744 0.584 -0.384 -0.144 0.264
[3981] -0.696 0.136 0.264 -0.896 -1.144 -1.504 -0.744 0.136 1.336 -0.096
[3991] 0.584 -0.376 -0.744 1.104 0.896 0.944 -0.216 1.744 -0.584 -0.784
[4001] 1.504 -0.176 -0.296 0.216 -0.896 0.736 0.416 1.096 0.736 -0.136
[4011] 0.224 -0.024 0.304 -0.776 -0.056 -0.856 0.304 -0.064 0.704 -0.664
[4021] -0.776 -0.544 0.544 -1.304 -0.296 0.536 -0.704 -0.064 0.304 -1.224
[4031] 0.704 -0.304 1.704 -0.216 -0.616 -0.224 0.304 -0.304 1.104 -0.904
[4041] -0.304 -0.256 -0.696 -0.096 -1.144 -0.536 -0.264 -0.416 0.064 -1.296
[4051] -0.416 0.056 0.864 -0.176 -0.136 -1.224 -0.736 -1.136 0.296 -0.416
[4061] -0.216 -0.584 0.624 -0.944 -0.384 -0.544 1.336 -0.416 1.336 -0.104
[4071] 1.144 -1.184 0.104 0.176 0.096 0.904 -1.136 -1.184 0.504 -0.024
[4081] -0.624 0.856 0.624 -0.904 0.536 -1.704 0.704 0.384 -0.936 0.136
[4091] 0.496 0.856 -1.704 -0.304 -0.504 -0.584 -0.584 -1.344 -0.496 -0.776
[4101] -0.384 0.696 -0.576 -0.824 0.224 0.536 1.224 0.824 -0.584 0.144
[4111] -1.376 -0.064 -0.416 -0.176 0.096 -0.336 0.504 -0.704 0.544 0.584
[4121] -0.216 0.584 1.696 0.176 1.704 -1.664 1.096 0.064 0.384 1.376
[4131] 1.336 1.384 -0.496 -1.664 0.736 -1.064 -0.944 0.664 -0.696 -0.504
[4141] 0.664 1.056 0.216 0.384 -0.176 -0.336 0.664 -0.584 -0.056 -1.056
[4151] 0.024 0.896 0.256 -0.064 -0.176 0.864 0.304 -0.344 -0.464 0.296
[4161] 0.664 -0.136 -1.704 -0.296 -0.944 -0.256 0.184 0.176 -0.824 -0.776
[4171] 0.104 0.304 -0.064 0.696 0.504 -0.496 0.744 0.024 -0.504 -0.336
[4181] 0.944 -0.856 -0.944 0.064 -0.224 0.256 0.496 -0.104 0.376 -0.696
[4191] -0.224 0.576 -0.224 -0.864 0.744 0.296 0.176 -0.256 0.256 0.736
[4201] -1.696 -1.184 1.136 -0.224 0.136 -0.696 0.096 0.024 0.056 -1.504
[4211] 0.696 -0.384 -0.624 0.944 0.784 -0.704 1.384 -1.296 0.536 -0.856
[4221] -0.256 1.224 0.304 -0.416 -0.784 -0.504 -0.584 0.744 0.136 1.104
[4231] -0.584 -0.384 0.336 -0.536 -0.496 -0.176 -0.536 -0.944 0.584 0.224
[4241] 1.104 0.304 0.336 -1.504 -0.336 0.776 -1.224 -0.224 0.376 0.104
[4251] 0.136 -0.056 -0.664 -0.104 0.256 0.184 -0.424 -0.264 -0.096 -0.544
[4261] 0.576 -0.416 -1.384 1.744 0.264 0.024 -0.584 0.896 -0.744 -0.504
[4271] -0.536 -0.056 0.336 -0.336 -1.504 -0.304 -0.384 0.896 -1.144 0.024
[4281] 0.664 -1.504 -0.664 1.184 0.104 0.896 -0.904 -1.104 0.904 -1.184
[4291] -0.024 0.104 -0.176 -0.336 0.424 0.104 0.064 0.536 0.856 -1.336
[4301] -0.864 0.264 0.264 0.704 -0.136 0.104 -0.856 0.264 -0.544 -0.384
[4311] -0.776 -0.384 0.384 0.504 0.544 -0.344 -0.384 0.104 -1.104 0.064
[4321] 1.376 0.776 0.224 0.304 0.544 -0.664 -0.464 0.664 -0.296 0.504
[4331] 0.744 -1.504 0.096 -1.184 -0.424 0.144 0.856 0.496 0.496 0.304
[4341] 0.104 0.776 0.464 -0.264 -0.664 0.424 1.336 0.664 -1.376 0.336
[4351] -0.944 -0.944 0.296 -0.776 0.384 -0.064 0.696 1.704 0.904 1.136
[4361] 0.536 0.336 0.504 -0.224 -1.224 -0.144 0.344 -0.576 0.696 -0.256
[4371] 0.224 0.736 0.704 0.896 -0.064 0.304 0.176 -0.056 0.056 0.736
[4381] -1.664 -1.136 -0.016 0.904 0.696 0.896 -1.704 0.136 0.744 0.664
[4391] -1.304 0.544 0.744 -0.264 1.096 0.416 -0.696 0.056 0.904 -0.296
[4401] 0.024 1.064 0.664 1.744 -0.704 0.584 -1.344 -0.064 -0.544 0.584
[4411] 0.384 -0.696 -0.064 0.264 0.944 1.144 0.496 0.384 0.416 1.144
[4421] 0.296 -1.344 -0.496 0.256 0.584 -0.224 0.384 -0.624 0.184 -0.224
[4431] 0.256 -0.704 0.304 -1.304 -0.944 0.704 -0.424 -0.704 -0.744 0.384
[4441] 1.056 0.296 -1.344 -0.224 -0.664 -0.736 1.304 -0.544 0.936 0.384
[4451] 0.056 1.104 0.296 -0.304 -0.216 0.544 -1.296 0.104 -1.184 -1.504
[4461] 0.176 -0.824 0.896 -1.504 -1.304 0.864 -0.056 0.896 -0.016 0.064
[4471] -0.144 0.904 -0.024 -0.216 -0.944 -0.136 0.904 -1.296 1.056 0.144
[4481] -1.096 1.384 0.296 0.056 0.576 -0.776 -0.016 1.384 -0.776 0.856
[4491] -0.704 0.304 -0.136 0.864 -0.864 -0.136 -0.136 -0.136 -0.744 0.664
[4501] -0.664 0.096 0.744 -0.056 -0.264 0.056 -1.384 -0.216 0.784 -1.336
[4511] 0.856 1.136 0.736 0.904 -0.664 -0.864 -0.144 0.224 0.336 0.744
[4521] -0.896 -0.424 0.376 0.864 -0.056 1.376 0.496 0.704 1.744 1.104
[4531] -0.416 -0.304 1.144 0.696 0.384 -0.544 0.664 0.536 -0.944 -1.144
[4541] 0.216 0.696 -0.304 0.904 0.464 -0.056 0.216 -0.936 -0.744 0.776
[4551] 1.056 -0.744 -0.024 0.544 0.744 0.304 -0.264 -0.624 1.336 1.744
[4561] 0.016 -1.384 -0.056 -0.384 -1.136 0.576 -0.104 -0.384 -0.024 -0.104
[4571] -0.464 -1.144 -0.144 -1.504 -0.424 -0.064 0.224 -1.744 -0.296 1.504
[4581] -0.104 -0.856 0.256 -0.224 0.216 0.904 0.336 -0.024 0.936 0.256
[4591] 0.576 -0.744 0.504 -0.136 -1.304 -0.384 -0.504 -0.504 -0.744 -0.024
[4601] 0.624 0.776 -0.736 0.056 -0.536 0.696 1.096 0.496 0.024 0.824
[4611] 0.464 -0.576 -0.056 -0.584 -1.504 0.304 -0.064 1.744 0.096 0.776
[4621] 0.504 -0.096 0.544 0.376 -0.144 0.256 0.064 -0.144 0.224 1.144
[4631] 0.536 1.696 0.216 -0.544 -1.704 0.144 -0.696 -0.064 -0.336 -0.336
[4641] 1.296 0.016 -1.296 0.944 -0.504 -0.024 1.184 0.304 -0.944 0.536
[4651] 1.744 0.736 0.864 -0.304 -0.536 -0.904 0.584 0.336 -0.776 -0.336
[4661] -0.896 0.016 -1.304 0.376 0.664 -1.336 -0.064 0.944 1.344 0.696
[4671] 0.256 -0.536 -0.704 1.344 0.336 0.344 -0.264 -0.864 -0.896 -0.744
[4681] 0.296 0.944 0.216 0.744 1.104 0.536 -0.784 0.696 0.904 -0.464
[4691] -0.584 -0.696 0.704 -0.216 0.384 -0.224 0.856 -0.176 1.296 -0.184
[4701] 1.096 -0.496 0.344 -0.696 1.056 0.776 0.304 -1.696 0.296 -0.336
[4711] -0.384 -0.616 -0.576 -0.224 -0.104 0.224 1.344 0.704 0.416 -1.144
[4721] -1.104 0.296 1.104 -0.496 1.344 -0.616 0.464 0.704 0.384 -1.144
[4731] -1.184 -0.736 0.536 1.136 1.144 0.056 -0.056 -0.224 0.776 0.296
[4741] -0.344 -0.056 -0.544 -0.104 1.136 -0.536 0.304 -0.296 0.896 0.224
[4751] -0.144 0.856 0.256 0.336 0.464 0.696 0.736 0.144 0.744 -0.304
[4761] 0.384 0.424 1.376 0.664 -1.184 0.504 -0.864 -0.624 -0.576 0.064
[4771] -0.224 -0.416 -0.224 -1.696 -0.824 0.544 0.016 -0.584 1.696 0.136
[4781] 0.224 0.384 -0.536 0.336 0.584 -0.464 -0.864 0.736 0.296 0.304
[4791] 0.704 -1.104 -0.064 0.504 -0.336 -0.296 0.184 0.024 -0.176 -0.224
[4801] 0.064 0.304 -0.696 1.744 0.136 -0.104 -0.176 -0.744 0.096 0.144
[4811] -0.184 -0.744 0.136 -0.184 1.096 0.776 -0.576 -0.904 0.224 0.704
[4821] 0.216 1.296 -0.104 0.256 -1.104 0.144 0.064 0.544 0.416 0.384
[4831] 0.176 0.296 0.896 0.336 0.296 -0.056 0.544 -0.024 -0.416 0.384
[4841] 0.216 0.416 -0.064 -0.136 1.344 -0.256 0.264 -1.136 1.144 0.104
[4851] 0.056 0.904 0.864 1.096 -0.376 0.864 0.744 0.744 0.576 0.616
[4861] 0.096 -0.224 0.624 -0.784 -0.336 0.216 -0.904 1.136 -0.864 -0.256
[4871] 0.296 -0.416 0.576 -0.104 0.904 0.896 -0.896 0.904 1.144 -1.224
[4881] -0.464 -0.224 -0.064 -0.056 0.416 0.176 0.144 -0.544 1.376 0.856
[4891] -0.336 -0.056 -0.224 0.104 -0.296 0.256 -0.664 -1.224 -0.264 0.896
[4901] -0.696 -0.496 -0.856 -0.464 -0.376 0.944 0.424 0.944 -0.664 1.064
[4911] 1.224 -0.104 -0.424 -0.376 0.576 0.904 -0.544 0.896 -0.416 0.664
[4921] 0.584 -1.504 -0.784 0.176 0.024 0.056 0.624 0.704 -0.616 -1.296
[4931] 0.376 1.504 0.904 0.064 -0.576 0.096 -0.096 0.056 0.536 -0.584
[4941] 0.136 0.776 1.136 -0.904 0.224 0.176 1.104 0.136 -1.136 -0.064
[4951] 0.344 0.056 -0.776 0.576 -1.144 -0.176 -0.896 -0.296 0.944 -0.416
[4961] 0.016 0.224 1.384 -0.184 -0.504 0.544 0.696 -0.224 0.696 -0.696
[4971] -0.664 -0.104 0.104 -0.424 1.096 1.344 -0.936 -0.584 -0.536 -1.096
[4981] 1.704 0.776 -0.144 0.144 0.696 0.664 0.096 0.856 0.216 -0.824
[4991] 1.504 0.144 -0.384 0.344 -1.376 0.184 -0.064 -0.136 0.384 0.224Estimate 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] 0.056 1.416 1.664 0.584 -0.136 0.856 1.616 0.624 1.624 1.016
[11] 1.296 0.616 1.104 0.304 0.256 0.744 1.096 0.096 0.424 -0.096
[21] 0.264 1.504 1.896 1.704 1.224 0.936 1.056 1.096 1.184 1.184
[31] -0.176 0.576 0.256 1.016 0.704 0.936 0.456 0.864 1.464 0.816
[41] 0.656 0.624 0.904 2.104 1.704 0.696 1.456 1.456 0.344 1.704
[51] 1.696 1.744 -0.104 1.376 0.696 2.136 0.216 0.896 0.264 1.304
[61] 0.984 0.296 0.416 1.176 1.976 0.824 1.576 0.896 1.736 1.504
[71] 1.264 1.944 1.504 0.024 1.104 0.896 1.544 1.656 0.304 1.144
[81] 0.536 0.056 1.376 -0.096 0.944 1.016 1.624 0.864 1.344 1.496
[91] 0.496 1.296 1.216 0.864 0.896 1.064 0.296 1.016 2.184 0.944
[101] 1.056 1.264 1.464 0.696 0.656 1.304 1.176 0.944 1.304 0.824
[111] -0.136 1.504 1.096 0.336 0.736 0.016 1.976 0.664 0.504 1.784
[121] -0.096 0.296 1.664 0.896 0.304 0.464 1.344 0.984 0.536 0.056
[131] 1.136 1.344 0.456 0.944 0.704 1.136 1.424 0.936 0.536 0.464
[141] 0.656 1.024 0.656 1.344 0.744 0.536 1.776 1.136 0.384 1.096
[151] 1.584 1.776 0.256 1.264 1.016 0.904 1.144 1.704 1.136 0.656
[161] 1.256 0.296 0.864 1.376 1.224 0.624 1.096 0.856 1.504 0.864
[171] 0.216 1.656 1.576 1.344 0.584 1.536 0.536 0.816 1.176 0.984
[181] 0.344 1.944 0.664 1.136 2.176 0.936 0.584 1.664 0.904 1.176
[191] 0.376 0.256 1.456 0.544 0.384 1.264 1.184 1.504 1.944 1.144
[201] 0.456 0.296 0.264 0.496 0.704 0.904 1.144 2.104 1.104 1.264
[211] 0.504 0.904 1.016 0.504 0.936 0.264 1.216 1.704 0.904 0.864
[221] 0.744 1.104 0.056 0.056 0.584 0.664 1.696 1.504 1.936 0.696
[231] 0.776 1.176 0.264 1.336 0.296 1.544 0.976 0.304 1.416 0.064
[241] 2.096 1.304 0.656 0.944 1.536 0.696 1.296 1.096 1.264 0.896
[251] 0.856 0.464 1.616 1.176 -0.096 1.536 0.256 0.744 0.936 1.544
[261] 1.064 1.384 1.104 1.136 0.496 0.776 1.256 1.296 0.976 2.104
[271] 0.816 0.904 1.736 0.096 0.664 1.344 1.104 0.056 0.944 0.464
[281] 1.936 1.616 1.344 0.856 0.504 0.704 0.296 1.136 1.696 1.016
[291] 1.696 1.504 0.944 0.696 0.344 0.816 1.944 0.344 1.216 1.296
[301] 1.016 0.344 0.704 1.744 0.424 0.744 1.424 0.776 0.656 1.776
[311] 1.304 -0.096 1.664 0.824 0.424 0.776 1.624 1.136 1.744 1.424
[321] 1.536 0.536 1.256 0.536 1.696 0.496 0.056 0.456 1.144 1.696
[331] 1.264 0.416 0.304 0.624 1.096 0.304 0.584 0.856 1.136 1.296
[341] 1.536 1.064 0.424 1.696 1.144 0.936 0.704 0.736 1.064 1.224
[351] 1.264 0.736 1.096 0.824 1.936 1.056 1.696 1.464 0.056 1.584
[361] 0.736 0.944 0.536 1.104 1.224 1.096 1.384 0.296 2.136 0.544
[371] 1.776 1.104 0.656 0.424 1.704 1.144 1.616 0.304 1.296 1.984
[381] 1.496 0.496 0.616 0.224 0.696 1.944 0.304 1.344 0.704 1.176
[391] 1.736 2.176 1.536 0.656 1.376 0.976 1.504 0.936 2.096 0.576
[401] 1.736 0.464 0.496 1.896 0.456 1.216 0.824 0.536 0.504 1.064
[411] 0.776 1.584 0.856 1.096 0.304 0.256 1.104 0.536 1.416 1.976
[421] 0.776 1.384 0.024 1.304 0.616 0.376 0.896 1.264 1.264 0.336
[431] 1.456 1.336 1.424 1.096 0.864 0.864 0.456 0.904 0.216 0.056
[441] 1.304 1.744 1.944 1.704 1.496 0.344 -0.144 1.496 1.016 1.104
[451] 0.936 0.744 0.624 0.656 1.776 0.864 1.224 1.416 1.096 2.184
[461] 0.696 1.896 1.416 0.856 1.504 0.976 0.984 1.024 1.344 0.896
[471] 0.656 0.416 1.424 1.136 0.096 1.736 0.936 0.104 1.104 0.736
[481] 0.464 0.544 0.384 1.064 0.704 0.864 1.096 0.696 1.064 0.936
[491] 0.416 1.424 0.864 0.864 1.536 1.064 1.136 1.064 0.664 1.264
[501] 0.664 1.696 0.936 1.416 0.704 1.224 0.616 0.976 1.064 1.456
[511] 0.056 1.336 1.584 0.704 1.344 0.944 1.456 0.736 1.504 1.104
[521] 1.496 0.896 0.784 -0.144 0.896 0.736 0.896 1.664 0.904 1.936
[531] 0.264 2.136 0.656 1.544 -0.176 1.064 0.064 0.904 1.576 0.664
[541] 1.544 1.136 0.776 1.264 0.424 0.944 1.336 2.176 1.464 1.344
[551] 1.704 0.624 -0.176 1.704 0.856 0.896 1.624 0.824 1.976 0.336
[561] 0.336 0.504 2.184 1.136 1.224 1.304 1.056 1.376 1.376 2.144
[571] 0.496 0.576 1.096 1.464 1.136 0.544 1.464 1.944 2.104 1.456
[581] 0.016 1.256 0.864 2.176 1.584 1.344 0.824 1.056 0.656 0.904
[591] 1.216 1.784 1.704 1.024 1.016 1.736 0.696 0.984 0.944 1.944
[601] 1.016 1.896 2.176 1.184 1.536 1.336 0.496 0.456 0.856 0.496
[611] 1.616 1.344 0.904 1.304 0.824 0.864 0.416 1.056 1.464 0.744
[621] 0.664 1.064 1.216 1.136 0.464 0.864 1.536 1.096 2.104 1.144
[631] 1.104 0.864 1.064 1.784 1.024 0.296 0.224 1.104 0.264 0.304
[641] 0.304 1.464 1.096 1.016 0.584 1.704 0.816 1.416 0.624 0.496
[651] 0.904 0.256 1.936 0.504 1.104 0.064 -0.104 0.704 0.704 0.856
[661] 1.096 1.536 0.704 1.104 1.736 1.704 0.856 0.064 1.536 1.224
[671] 0.664 0.896 1.656 0.736 0.376 1.376 1.664 0.056 1.656 1.184
[681] 1.096 0.496 1.576 0.904 0.304 1.464 1.296 1.504 1.184 0.576
[691] 1.544 0.776 0.056 1.296 1.104 0.456 1.064 0.496 1.256 2.096
[701] 0.744 0.704 1.016 1.616 1.296 2.136 0.536 1.216 1.144 1.096
[711] 1.216 0.736 0.936 0.496 0.496 0.664 1.304 1.736 0.624 0.664
[721] 1.784 0.776 0.504 0.504 1.416 0.896 0.736 1.096 1.584 1.104
[731] 1.304 1.416 1.936 1.224 0.776 0.944 0.584 0.224 1.264 1.936
[741] 1.576 1.496 1.536 1.336 1.456 0.744 1.016 0.464 0.936 0.824
[751] 0.984 1.896 1.136 1.136 0.824 -0.136 1.456 0.216 0.944 1.016
[761] 1.096 0.936 0.416 0.744 1.536 0.336 1.296 0.464 0.736 1.256
[771] 1.984 1.944 1.496 0.704 1.016 0.656 0.464 0.456 0.696 0.064
[781] 1.536 -0.096 0.784 0.664 1.216 1.136 0.784 1.696 1.696 0.496
[791] 0.416 1.296 0.936 1.744 0.504 0.064 0.304 0.576 0.504 1.384
[801] 1.216 1.216 0.984 0.424 0.896 0.864 1.664 0.584 0.736 1.096
[811] 0.776 0.584 0.536 0.864 1.056 1.216 0.664 1.016 0.224 1.096
[821] 1.544 0.776 0.216 0.496 0.936 0.904 0.016 1.416 0.776 0.936
[831] 0.304 1.544 0.336 1.464 0.824 1.576 0.744 1.584 0.656 0.464
[841] 1.936 0.544 0.824 2.176 1.744 0.736 0.584 0.576 0.736 0.504
[851] 1.184 1.664 1.424 1.016 1.104 0.336 1.136 1.184 0.504 1.504
[861] 1.304 0.824 1.536 1.336 0.944 0.784 1.296 0.376 0.736 1.744
[871] 0.624 1.536 0.344 1.016 0.304 1.456 0.904 1.696 1.216 1.776
[881] 1.064 0.896 1.904 1.704 -0.144 0.936 0.896 1.176 1.104 1.056
[891] 1.264 0.744 1.296 1.264 1.536 1.176 0.416 1.536 1.104 0.896
[901] 2.104 -0.176 0.664 1.096 1.096 1.064 1.096 1.264 0.904 0.536
[911] -0.104 0.504 0.456 0.064 0.816 0.744 1.776 0.464 0.904 1.016
[921] 1.664 1.184 0.816 1.544 0.624 0.496 1.416 0.576 0.776 0.864
[931] 0.464 1.144 0.696 2.136 1.096 1.504 1.576 1.376 1.584 1.104
[941] 0.784 0.696 1.376 1.416 1.416 1.336 0.056 0.584 0.896 1.336
[951] 1.456 1.504 -0.096 0.904 -0.104 0.656 1.144 0.776 0.904 1.264
[961] 1.136 0.264 1.736 0.224 1.136 1.504 1.224 0.936 1.096 0.744
[971] 0.424 0.464 1.696 1.584 0.936 0.304 0.584 1.536 0.936 1.176
[981] 0.704 0.704 1.216 1.424 0.696 1.264 0.696 0.584 0.016 1.104
[991] 1.256 0.256 1.464 0.744 0.864 1.104 2.144 0.784 1.304 1.224
[1001] 2.096 1.064 1.256 0.896 0.656 1.104 2.136 0.664 1.736 0.024
[1011] 1.384 1.944 0.896 0.896 0.696 1.136 1.576 1.104 1.664 1.344
[1021] 0.944 2.136 0.816 1.096 -0.144 0.944 1.624 1.104 1.664 0.096
[1031] 1.704 1.064 0.696 1.064 0.296 1.896 2.144 1.024 2.144 1.376
[1041] 0.584 0.896 0.936 1.576 2.096 0.904 0.264 1.376 0.936 1.416
[1051] 1.704 1.096 2.184 0.536 1.336 0.736 1.416 1.184 1.464 0.256
[1061] 0.584 0.216 0.736 1.464 0.896 1.424 1.704 0.824 0.416 0.704
[1071] 1.544 0.256 1.264 1.256 1.456 1.344 0.584 1.544 0.224 0.256
[1081] 1.376 1.576 0.936 1.384 0.696 0.664 0.824 0.536 0.864 0.424
[1091] 0.544 0.936 0.016 1.136 0.864 0.656 1.096 0.104 -0.176 1.184
[1101] 1.024 0.424 1.784 1.184 1.016 2.184 0.736 0.896 0.944 1.536
[1111] 0.224 0.904 0.296 1.544 0.704 0.696 1.704 0.656 1.504 0.576
[1121] 0.416 0.776 1.056 0.624 0.744 0.936 1.336 1.696 0.896 1.336
[1131] 0.304 0.656 0.824 0.024 1.256 -0.184 0.104 1.264 1.664 0.256
[1141] 1.744 0.464 0.864 0.464 1.136 0.784 1.536 1.464 1.064 1.624
[1151] 1.384 1.504 1.256 1.496 1.104 1.536 0.536 1.104 1.776 -0.096
[1161] 1.736 1.016 1.104 1.264 0.304 1.296 1.664 1.984 1.224 0.664
[1171] 1.576 0.264 1.104 1.136 1.144 0.656 0.936 1.336 -0.144 -0.136
[1181] 1.224 1.344 0.744 0.864 0.864 1.016 0.344 0.376 1.904 1.424
[1191] 0.896 0.424 0.504 0.984 0.736 0.336 0.736 1.704 0.296 0.536
[1201] 0.544 0.984 1.096 2.176 1.296 0.944 1.416 0.736 1.184 0.064
[1211] 1.336 1.216 1.944 0.864 -0.144 1.536 0.704 1.736 0.264 1.696
[1221] 1.304 0.296 0.744 1.096 0.704 1.104 0.656 0.944 1.576 0.504
[1231] 0.256 0.664 1.696 1.016 1.184 1.304 0.816 0.464 1.304 1.536
[1241] 1.696 0.696 1.696 1.344 0.696 1.344 -0.104 0.816 0.736 0.696
[1251] 0.864 1.536 1.376 0.336 0.464 0.536 0.496 -0.136 1.064 1.176
[1261] 0.824 1.624 0.584 0.536 1.104 1.296 1.944 0.856 1.944 0.776
[1271] 0.936 1.576 1.104 0.784 1.416 0.264 0.224 0.616 0.296 0.496
[1281] 0.376 1.336 0.696 1.024 1.504 0.696 1.296 1.776 1.464 1.736
[1291] 0.936 0.456 1.064 0.976 0.744 1.664 0.696 1.064 -0.184 1.376
[1301] 0.104 0.904 1.584 1.096 1.344 1.136 0.496 0.976 0.656 0.496
[1311] 1.896 1.464 0.504 0.224 1.064 0.504 1.104 0.344 0.736 0.416
[1321] 0.816 0.456 0.896 0.504 1.296 1.376 0.216 0.536 1.536 0.096
[1331] 0.496 1.296 1.384 0.856 0.664 1.384 1.144 1.336 0.864 1.664
[1341] 2.176 0.976 0.504 0.976 0.264 1.224 0.496 0.544 1.704 0.656
[1351] 0.704 1.696 1.704 1.744 0.896 1.056 1.304 0.704 0.944 1.336
[1361] 2.184 0.424 1.664 0.296 0.544 0.256 1.176 -0.136 1.704 0.544
[1371] 0.704 0.624 1.536 1.184 0.624 1.936 0.936 1.136 1.144 0.424
[1381] 0.336 0.824 0.496 1.936 0.424 0.416 2.104 1.576 1.664 0.704
[1391] 0.064 1.784 1.064 0.944 0.696 0.736 0.776 0.896 1.304 1.144
[1401] 1.376 0.744 1.424 1.136 0.504 1.536 1.784 0.744 0.696 1.224
[1411] 1.976 1.504 1.264 1.296 0.296 1.384 1.464 0.256 1.344 0.544
[1421] 0.496 1.536 1.104 1.256 1.376 0.296 0.544 1.736 1.024 0.736
[1431] 1.664 1.504 0.904 0.624 0.864 0.024 1.704 0.504 1.144 1.776
[1441] 1.304 1.704 1.336 0.904 0.496 0.784 1.576 1.064 1.664 1.696
[1451] 0.584 0.664 0.944 1.544 1.784 1.144 0.944 0.376 1.136 1.896
[1461] 1.616 1.984 0.936 0.904 1.264 0.624 0.096 1.144 1.944 0.224
[1471] 1.344 0.816 0.256 1.296 1.536 -0.136 0.304 1.504 0.704 1.904
[1481] 1.336 0.096 0.816 1.464 1.264 1.784 1.376 1.144 0.536 1.264
[1491] 1.384 1.064 1.096 1.424 0.896 1.536 0.416 0.944 2.176 0.256
[1501] 1.096 1.064 0.584 1.264 0.744 1.784 0.936 0.904 1.896 0.984
[1511] 0.904 -0.096 1.064 1.664 0.656 0.744 1.296 1.704 1.336 0.536
[1521] 1.304 0.576 1.016 0.496 1.384 0.584 0.856 1.456 0.256 0.056
[1531] 0.376 0.896 0.936 1.544 0.984 0.576 1.064 1.296 0.784 1.464
[1541] 1.736 1.024 0.296 1.704 0.984 0.336 1.096 0.896 1.176 1.696
[1551] 0.384 1.344 0.056 0.856 1.784 1.936 0.816 0.616 1.144 0.736
[1561] 0.896 1.256 0.384 0.464 1.264 1.344 0.536 0.736 0.416 1.544
[1571] 1.296 1.056 0.344 1.024 0.736 1.536 0.776 0.696 1.136 1.384
[1581] 0.936 1.704 1.264 1.024 0.664 0.736 0.456 1.296 0.504 0.504
[1591] 1.424 1.264 1.304 1.896 0.384 1.944 0.064 0.224 0.904 1.616
[1601] 0.904 0.416 1.096 1.056 0.256 0.984 0.064 1.104 0.256 0.904
[1611] 0.744 1.704 1.224 1.944 1.584 1.496 0.656 0.064 1.136 1.424
[1621] 0.696 1.456 0.784 0.104 0.224 0.504 1.536 0.784 1.416 0.544
[1631] 1.376 0.536 0.096 1.176 0.256 1.736 0.264 1.656 1.464 1.264
[1641] 1.264 1.304 0.784 1.144 0.824 1.744 1.136 0.784 1.704 0.056
[1651] 1.496 0.264 0.744 0.656 1.176 1.936 0.624 0.864 0.296 0.624
[1661] 0.616 1.696 0.824 1.224 0.864 1.504 1.296 1.136 1.144 0.704
[1671] 1.456 1.416 1.456 0.536 0.776 0.864 1.584 1.584 -0.104 1.536
[1681] 0.536 1.096 1.216 0.416 2.096 0.904 0.384 1.016 1.744 0.504
[1691] 0.496 1.296 1.056 1.336 0.776 0.944 0.464 1.056 1.704 0.904
[1701] 0.584 1.136 0.344 1.224 0.896 1.536 0.024 1.224 1.064 1.096
[1711] 0.104 0.824 0.864 1.416 0.536 1.264 0.904 0.064 0.656 1.504
[1721] 1.224 0.944 1.064 0.936 0.064 0.544 0.984 0.896 0.696 1.184
[1731] 1.984 0.984 0.904 0.944 0.504 1.904 1.656 1.064 1.464 0.104
[1741] 1.104 1.936 0.784 0.696 1.096 0.496 0.464 0.296 1.304 1.584
[1751] 0.784 0.896 0.456 -0.184 0.904 0.896 1.704 0.544 1.504 1.744
[1761] 1.176 -0.184 1.104 1.064 1.184 1.464 1.224 1.224 0.296 1.376
[1771] 0.616 0.016 1.616 1.616 1.456 0.856 1.624 1.456 1.696 1.496
[1781] 1.544 2.176 1.136 0.304 0.864 0.256 0.944 1.184 1.224 0.704
[1791] 0.944 1.264 1.216 1.944 0.544 -0.104 0.824 0.456 0.296 1.096
[1801] 1.064 0.656 0.376 1.296 1.536 1.736 0.104 0.656 1.704 1.576
[1811] -0.096 0.984 1.224 1.056 0.744 1.584 1.704 0.504 1.096 0.856
[1821] 0.784 1.464 0.704 1.104 1.456 1.064 1.504 1.736 0.904 1.304
[1831] 0.936 1.296 0.736 1.056 1.264 0.056 1.104 0.856 1.216 0.784
[1841] 0.984 0.896 1.696 1.936 0.784 1.744 2.136 1.976 1.256 1.424
[1851] 1.216 0.336 0.624 0.664 1.144 1.376 1.416 0.504 -0.176 0.664
[1861] 1.464 0.336 1.744 1.024 0.856 1.744 1.064 1.304 0.936 0.576
[1871] 0.504 1.144 0.664 1.096 0.944 0.736 1.016 0.504 0.304 0.904
[1881] 1.584 0.696 1.064 0.376 1.696 0.704 1.776 0.936 0.896 1.256
[1891] 0.416 1.216 0.264 0.896 1.664 -0.176 1.656 1.696 1.176 1.936
[1901] 1.136 1.104 1.696 0.464 1.104 0.784 -0.184 0.424 0.384 2.184
[1911] 1.464 0.936 1.304 0.776 1.104 1.584 0.496 2.104 0.776 2.176
[1921] 0.584 1.264 0.496 1.336 1.256 0.304 0.496 0.904 1.344 1.424
[1931] 0.424 0.824 1.144 2.104 1.296 0.824 1.456 1.504 1.304 1.296
[1941] 1.424 1.424 0.736 0.304 2.136 1.744 1.224 1.384 0.904 1.424
[1951] 0.496 0.256 0.736 0.336 0.464 0.664 1.936 1.456 1.304 1.936
[1961] 0.784 1.464 1.216 0.864 1.296 1.344 0.976 0.824 0.656 0.296
[1971] 0.904 1.136 0.536 0.864 0.776 0.024 0.984 1.056 1.416 0.464
[1981] 1.344 0.936 0.856 1.424 1.504 1.984 0.744 2.136 1.944 1.904
[1991] 1.696 0.736 1.064 1.464 1.064 1.576 0.664 1.304 0.936 1.464
[2001] 1.064 1.256 0.696 1.264 0.624 0.616 1.424 0.384 0.984 0.504
[2011] 0.856 1.504 1.256 1.744 1.104 0.664 1.504 1.304 1.064 1.096
[2021] 1.136 1.344 1.176 1.096 0.536 1.984 0.944 1.296 0.464 0.384
[2031] 1.304 0.856 2.144 1.744 0.664 0.256 1.096 0.864 1.256 1.304
[2041] 0.256 0.896 0.784 0.544 -0.184 0.416 1.096 -0.096 0.504 1.504
[2051] 0.896 0.944 1.784 0.904 1.576 0.264 1.504 1.424 0.344 1.776
[2061] 1.896 1.696 1.536 1.184 1.184 0.704 1.496 1.696 1.264 0.536
[2071] 1.704 1.464 1.344 1.296 0.616 0.904 0.256 1.976 1.344 1.096
[2081] 2.176 0.944 0.376 2.144 0.696 0.776 0.216 1.704 1.176 0.624
[2091] 0.784 1.136 1.336 1.776 1.744 0.504 0.584 1.536 0.336 0.504
[2101] 0.736 1.224 0.984 1.144 0.064 0.376 0.024 1.504 0.096 1.416
[2111] 0.496 1.096 -0.144 2.144 0.064 0.896 1.696 0.904 0.704 1.376
[2121] 0.816 1.296 1.664 1.424 0.424 0.944 0.296 -0.096 0.656 1.064
[2131] 1.416 1.264 1.264 1.704 1.344 1.104 2.184 1.304 1.064 1.744
[2141] 1.096 0.624 1.264 1.096 1.536 1.336 0.624 1.264 1.624 0.936
[2151] 0.736 0.496 0.736 0.976 1.136 2.176 0.304 0.464 1.016 1.056
[2161] 1.496 1.696 0.056 0.936 0.864 1.304 1.264 0.424 0.624 1.496
[2171] 1.224 2.104 1.416 0.776 1.296 0.576 1.184 1.344 1.264 1.264
[2181] 1.784 0.864 1.344 1.544 1.536 0.696 1.176 0.344 0.936 0.304
[2191] 0.416 1.296 1.096 0.256 1.496 0.464 0.976 0.736 -0.136 1.696
[2201] 1.936 0.464 1.304 1.624 0.984 1.456 0.936 0.896 1.504 0.224
[2211] 1.504 0.984 0.936 2.104 1.224 0.576 0.504 0.816 1.256 1.144
[2221] 1.136 0.936 0.984 0.744 1.184 1.184 1.536 1.576 0.904 0.896
[2231] 0.056 0.744 1.176 0.304 -0.184 0.816 1.256 1.296 0.464 1.096
[2241] 1.744 1.616 1.704 1.704 1.344 1.376 0.704 0.896 0.304 1.696
[2251] 0.784 1.464 0.264 0.624 1.336 1.376 0.024 1.344 2.136 1.544
[2261] 0.904 1.264 0.576 0.296 0.256 1.144 0.544 0.744 0.776 1.096
[2271] 0.656 0.776 0.656 0.736 1.376 1.936 0.936 2.104 1.296 0.384
[2281] -0.104 2.104 1.376 1.096 1.936 0.744 0.064 0.664 0.624 1.056
[2291] 1.016 0.336 0.576 1.536 1.584 1.216 1.344 1.936 0.504 0.656
[2301] 1.104 0.544 1.976 1.104 0.864 1.664 1.264 1.096 0.624 -0.144
[2311] 0.856 0.896 0.496 0.064 0.256 1.296 0.264 0.744 0.896 0.904
[2321] 0.824 1.016 0.224 1.544 1.144 0.256 0.536 1.544 0.456 1.264
[2331] 1.256 0.656 1.184 1.024 1.696 1.736 0.496 0.584 0.504 1.544
[2341] 1.496 0.936 1.096 1.056 0.624 1.064 1.144 0.824 0.624 1.416
[2351] 1.536 0.736 0.264 1.744 1.224 1.976 1.344 0.656 0.264 0.656
[2361] 0.736 0.696 1.456 1.136 2.104 1.664 0.896 1.376 1.304 1.224
[2371] 1.224 1.936 1.064 1.416 1.064 0.024 0.656 1.304 0.224 0.904
[2381] 0.296 1.304 1.696 0.896 1.064 1.776 0.704 0.744 0.856 0.904
[2391] 0.336 0.256 0.456 0.296 2.184 0.784 1.736 0.856 1.984 0.584
[2401] 0.304 0.896 1.144 1.376 1.144 0.104 1.184 0.976 1.016 1.096
[2411] 1.104 0.496 1.104 0.056 1.136 0.896 1.624 0.424 0.664 1.344
[2421] 1.376 1.064 1.616 -0.176 0.984 1.256 1.496 1.496 0.984 1.096
[2431] 0.496 0.464 1.536 0.696 1.776 1.536 1.376 0.624 1.976 1.576
[2441] 0.944 1.184 1.784 0.424 0.624 1.424 1.256 1.544 1.616 1.496
[2451] 1.344 1.344 1.904 0.504 0.296 0.504 1.776 0.016 0.336 1.464
[2461] 1.224 0.456 0.544 1.184 1.576 1.656 1.136 0.256 0.576 2.184
[2471] -0.184 -0.184 1.104 1.416 1.776 1.376 1.224 1.536 1.496 0.296
[2481] 0.736 1.264 1.784 1.464 0.456 0.896 0.736 1.336 0.896 1.056
[2491] 0.264 1.336 1.504 0.424 1.336 0.896 1.536 0.296 0.864 0.856
[2501] 0.896 1.456 2.096 1.064 0.904 0.624 1.504 1.264 1.904 0.856
[2511] 0.224 1.576 1.144 1.744 0.704 0.464 1.696 1.024 0.856 0.624
[2521] 0.856 0.976 1.104 0.496 1.664 0.264 1.776 0.104 1.304 1.296
[2531] 1.344 1.104 0.296 0.864 1.096 1.544 0.704 0.584 1.104 0.056
[2541] 2.096 0.464 0.784 0.424 0.904 1.136 0.664 0.624 1.576 1.136
[2551] 0.696 1.296 0.664 1.176 1.336 0.304 0.216 1.336 0.696 0.896
[2561] 1.984 0.464 1.936 1.376 1.536 0.904 1.144 1.176 0.256 2.184
[2571] 0.464 0.976 1.136 1.096 0.904 1.424 1.056 0.456 0.296 1.136
[2581] 0.504 1.456 1.296 1.296 1.016 0.224 1.064 1.136 1.304 1.456
[2591] 0.816 1.064 1.616 0.704 0.856 1.416 0.624 1.344 2.136 1.104
[2601] 0.456 1.224 1.344 1.696 0.856 0.296 0.504 1.104 0.096 0.216
[2611] 1.016 1.136 0.824 0.416 0.336 0.464 0.624 1.536 0.264 1.064
[2621] 1.496 0.824 1.744 1.096 1.536 1.696 -0.176 1.264 1.136 0.296
[2631] 0.816 1.096 0.904 1.896 1.304 0.896 0.856 0.536 1.144 0.856
[2641] -0.104 1.776 1.584 0.936 0.576 0.616 0.896 1.264 1.096 0.776
[2651] 0.704 1.136 0.304 1.296 0.624 1.904 2.184 0.304 0.856 0.504
[2661] 1.696 0.496 1.736 0.336 0.224 1.536 0.736 1.184 0.736 1.464
[2671] 0.976 1.744 0.064 0.864 1.096 0.736 1.096 0.664 1.784 1.024
[2681] 0.704 1.136 1.536 1.296 0.824 1.144 1.696 1.344 1.136 0.376
[2691] 1.616 1.504 1.376 0.536 0.256 0.904 0.904 0.864 1.304 0.696
[2701] 1.664 0.536 2.096 1.296 1.736 0.896 0.936 1.304 0.784 1.064
[2711] 1.064 0.824 1.704 1.616 1.624 1.416 1.776 1.056 1.544 0.824
[2721] 1.024 0.944 0.504 0.336 1.616 0.344 1.336 1.984 1.136 1.456
[2731] 0.856 0.984 0.424 1.264 1.296 1.264 1.376 1.264 0.744 1.424
[2741] 1.936 1.144 0.696 0.256 0.704 1.296 0.704 1.744 1.224 1.464
[2751] 0.056 1.296 0.984 1.496 1.136 1.624 1.464 0.536 1.544 0.056
[2761] 1.224 1.136 1.176 1.016 1.104 0.296 0.424 1.936 -0.104 0.984
[2771] 0.024 1.296 0.896 1.984 1.264 1.016 0.696 1.224 0.904 1.944
[2781] 1.344 1.304 1.264 1.464 1.384 0.016 0.416 0.704 1.016 1.696
[2791] 0.336 1.744 0.296 0.864 0.584 0.856 0.464 1.704 1.544 0.936
[2801] 0.224 0.304 1.064 1.344 0.304 0.816 0.904 1.424 0.504 0.336
[2811] 0.256 1.696 0.776 1.736 0.024 0.904 0.896 0.584 1.016 1.136
[2821] 0.656 1.536 1.576 0.896 0.584 0.256 1.296 1.736 0.104 0.904
[2831] 0.816 1.696 1.344 1.376 0.776 1.416 1.496 0.536 1.504 0.336
[2841] 0.936 0.864 -0.176 1.256 1.216 1.536 1.216 1.344 1.776 1.144
[2851] 1.176 0.976 0.656 0.624 1.704 0.456 1.184 1.464 0.024 0.904
[2861] 1.184 -0.144 1.176 0.576 1.944 -0.184 1.704 0.696 -0.136 1.904
[2871] 0.336 0.896 1.944 1.024 0.416 1.344 0.856 1.056 1.016 1.944
[2881] 1.976 0.816 1.424 0.864 1.376 1.256 1.264 0.696 1.344 1.336
[2891] 0.624 0.904 0.664 0.864 0.824 1.424 1.464 0.864 -0.104 0.896
[2901] 1.416 0.504 0.696 1.216 0.696 1.536 1.256 1.024 0.464 0.544
[2911] 0.824 1.936 1.584 0.784 1.464 0.256 0.224 1.584 1.624 1.104
[2921] 0.896 1.024 1.464 1.536 1.376 1.696 1.576 1.624 0.984 0.944
[2931] 0.824 1.936 1.096 0.736 0.544 0.376 0.936 1.176 0.896 0.456
[2941] 1.344 1.176 0.896 0.056 0.296 0.296 0.424 1.536 1.504 0.056
[2951] 1.656 0.864 1.216 0.536 1.144 1.304 0.624 1.744 1.504 1.224
[2961] 0.896 0.824 0.296 1.704 0.304 0.784 1.304 1.616 0.496 1.744
[2971] 1.704 1.704 1.536 1.136 1.176 0.936 1.296 1.336 0.656 0.296
[2981] 0.456 0.896 1.584 0.704 0.936 1.464 0.776 1.304 2.136 1.096
[2991] 1.336 1.544 1.224 1.136 0.776 1.384 1.296 1.496 1.104 0.664
[3001] -0.184 1.904 1.576 0.464 0.904 2.096 0.304 0.336 0.536 0.696
[3011] 1.736 1.584 1.544 0.896 0.664 0.104 1.544 0.656 1.536 0.816
[3021] 1.064 0.896 1.024 0.744 0.464 2.184 0.896 0.616 1.904 1.744
[3031] -0.136 1.616 0.616 0.496 1.416 0.504 1.336 0.976 0.496 0.416
[3041] 0.056 1.136 0.936 0.624 1.896 0.056 1.504 1.104 0.704 1.656
[3051] 0.736 1.584 1.184 1.224 0.624 0.256 1.584 1.696 1.904 0.016
[3061] 0.856 0.736 0.856 0.664 0.456 0.744 0.656 1.936 0.576 1.456
[3071] -0.136 1.136 1.744 1.136 0.584 0.496 1.136 0.264 1.696 0.776
[3081] 1.016 0.216 0.016 1.064 0.744 1.304 1.416 1.544 1.496 -0.136
[3091] 0.984 1.064 0.744 1.944 1.016 0.864 0.744 1.744 1.176 0.464
[3101] 0.936 1.104 0.896 0.496 1.576 1.424 0.216 1.176 0.656 1.104
[3111] 1.016 1.336 1.056 0.456 0.944 1.776 1.056 1.296 0.584 1.136
[3121] 0.464 0.584 0.504 1.704 0.936 0.584 0.936 1.096 1.536 1.456
[3131] 1.016 1.744 0.704 1.064 1.656 0.736 1.056 1.576 1.296 0.744
[3141] 1.296 1.944 1.384 1.544 1.144 -0.184 0.576 1.176 0.784 1.344
[3151] 1.256 1.104 0.944 0.896 0.496 1.136 1.696 1.456 0.864 1.264
[3161] 1.184 0.616 1.016 1.744 0.464 1.456 1.696 1.936 1.464 0.256
[3171] 0.816 1.224 0.696 1.256 0.624 1.064 1.664 0.736 1.584 1.176
[3181] 0.496 0.896 0.944 1.464 0.424 0.904 1.496 1.344 1.664 0.544
[3191] 0.584 1.264 1.224 2.104 1.136 1.624 1.144 0.496 1.136 0.896
[3201] 1.224 0.984 1.056 1.984 -0.176 1.024 1.216 1.696 1.296 0.384
[3211] 1.784 1.496 1.664 1.696 1.296 1.664 0.784 1.344 0.704 1.496
[3221] 0.816 1.296 1.504 1.344 1.776 0.536 0.024 0.704 1.376 1.176
[3231] 0.736 1.064 0.944 1.296 0.256 1.536 0.736 1.064 0.864 0.424
[3241] 0.504 1.296 1.136 1.184 1.096 1.056 2.184 1.656 1.104 1.016
[3251] 1.264 0.776 1.616 1.496 0.496 1.656 1.184 1.144 0.416 0.856
[3261] 0.656 1.184 0.904 1.064 0.944 1.464 0.256 1.016 1.304 0.944
[3271] 1.104 1.064 1.944 0.856 1.504 1.376 -0.176 0.304 1.464 0.624
[3281] 0.936 2.144 0.504 0.664 1.936 0.336 -0.104 0.264 1.456 0.344
[3291] 1.296 0.824 1.344 0.464 1.584 0.584 1.664 0.744 0.976 1.744
[3301] 2.136 2.184 0.744 1.376 1.536 0.704 1.544 1.304 1.624 0.584
[3311] 0.344 0.656 1.936 0.936 1.776 0.824 0.936 0.704 0.936 1.176
[3321] 0.936 0.464 2.144 1.296 -0.136 0.944 1.936 1.736 0.656 1.576
[3331] 1.264 1.256 2.104 0.496 0.064 -0.136 0.696 1.376 1.144 1.104
[3341] 1.024 0.416 0.496 0.656 1.336 0.416 1.176 0.976 0.504 1.536
[3351] 2.136 0.864 0.616 0.944 0.976 1.264 0.104 1.096 0.864 1.256
[3361] 2.176 0.704 1.424 1.016 1.136 1.784 1.456 0.784 0.824 0.544
[3371] 0.784 0.496 1.104 1.456 0.864 0.936 0.976 1.744 0.064 1.256
[3381] -0.136 0.896 0.496 1.584 0.256 -0.144 1.976 2.096 1.304 1.544
[3391] 1.936 1.304 0.536 0.824 0.656 1.264 0.496 1.616 0.536 1.656
[3401] 0.776 0.656 0.864 0.696 1.536 0.984 2.096 1.056 1.616 0.976
[3411] 2.104 1.104 1.264 0.464 0.864 1.536 0.576 1.696 0.696 1.584
[3421] 1.944 1.024 0.704 0.744 1.136 0.776 1.216 1.224 1.256 0.944
[3431] 1.104 1.944 1.056 1.296 1.104 1.144 0.256 1.104 0.856 1.176
[3441] 0.936 1.336 1.064 0.464 1.336 1.144 -0.136 0.824 1.104 0.216
[3451] 1.144 1.504 1.624 0.704 1.504 0.504 1.216 0.336 0.296 1.344
[3461] 1.296 1.144 1.256 0.864 1.696 0.704 1.096 0.464 0.064 0.304
[3471] 1.304 1.024 0.696 0.896 0.824 0.496 1.224 0.304 0.464 1.536
[3481] 0.496 0.464 0.376 1.504 0.656 0.976 0.464 1.096 0.056 0.904
[3491] 1.376 0.904 -0.136 1.384 0.624 0.696 0.856 1.064 1.664 1.696
[3501] 0.296 1.216 1.064 1.376 1.496 0.904 1.696 1.184 0.664 0.216
[3511] 0.096 0.216 0.456 1.376 0.064 0.904 2.184 0.656 0.056 0.504
[3521] 1.056 1.096 1.704 1.376 1.544 1.584 0.816 0.856 0.744 0.856
[3531] 0.944 1.064 0.624 0.696 1.064 1.536 0.984 0.696 1.544 0.576
[3541] 0.824 1.176 1.216 1.304 1.504 1.536 1.704 0.504 0.704 1.136
[3551] 0.616 1.576 1.976 1.424 1.264 0.896 0.576 1.064 0.704 -0.104
[3561] 1.536 0.776 0.696 0.936 1.696 0.064 1.184 1.504 2.096 -0.176
[3571] 1.064 1.936 1.296 1.144 -0.176 1.256 1.536 0.704 0.896 1.504
[3581] 0.984 1.504 1.096 0.416 1.536 0.096 0.824 1.304 0.744 0.896
[3591] 0.504 -0.176 0.024 0.496 1.184 0.936 0.496 0.904 1.336 1.944
[3601] 0.336 0.464 0.304 0.904 0.424 0.416 1.496 0.496 0.984 0.624
[3611] 0.784 0.376 1.264 0.064 1.304 1.464 1.144 1.216 0.736 0.504
[3621] 1.064 0.616 1.456 0.544 1.704 0.424 0.896 1.216 1.256 1.936
[3631] 0.696 0.656 1.224 1.064 0.456 0.304 1.504 0.056 0.864 0.944
[3641] 0.856 1.096 0.744 0.056 1.736 0.256 1.504 1.064 0.824 0.704
[3651] 0.824 0.296 1.504 0.664 2.176 0.296 0.736 0.536 0.464 0.216
[3661] 1.944 0.464 0.536 0.896 1.296 0.856 0.744 0.984 0.256 1.016
[3671] 1.064 -0.144 1.096 1.304 1.176 1.576 1.136 0.576 0.616 -0.184
[3681] 0.904 1.656 0.944 0.496 1.096 1.176 0.904 1.776 0.544 1.984
[3691] 0.304 1.344 0.064 0.904 1.264 0.824 0.936 1.344 0.384 0.096
[3701] 1.416 0.544 1.256 1.176 0.464 0.224 1.696 1.984 1.656 1.216
[3711] 0.784 0.944 0.336 0.896 1.376 1.296 0.936 0.784 1.296 1.704
[3721] 0.864 0.984 0.704 0.696 0.456 0.624 1.216 -0.144 0.696 0.544
[3731] 1.024 0.936 1.136 0.536 -0.104 0.704 0.656 1.544 1.064 0.264
[3741] 0.464 0.696 0.776 1.496 1.376 1.264 0.304 1.056 1.344 1.304
[3751] 1.584 1.056 1.064 1.056 0.856 1.296 0.464 0.656 0.664 1.296
[3761] 1.264 0.984 2.184 1.256 1.624 1.224 1.056 1.656 1.536 0.624
[3771] 1.264 1.056 0.264 0.904 1.136 1.016 1.456 1.456 0.776 1.344
[3781] 1.104 0.656 2.176 1.776 1.056 1.096 0.264 0.576 0.264 0.096
[3791] 1.304 1.496 1.376 0.496 0.536 2.136 0.744 1.344 0.736 1.304
[3801] 0.864 1.504 0.744 1.024 0.864 1.784 0.304 1.464 1.224 0.024
[3811] 0.304 0.816 0.904 1.056 0.296 1.104 0.496 1.216 1.136 -0.184
[3821] 0.624 0.504 -0.176 1.056 0.696 1.504 1.096 0.984 0.864 1.256
[3831] 0.504 0.664 1.096 0.696 0.736 1.424 0.704 1.144 1.376 0.344
[3841] 1.296 1.696 0.344 0.256 1.624 0.576 0.424 -0.104 0.256 1.384
[3851] 1.056 0.904 1.696 0.504 0.624 1.064 -0.176 1.496 0.064 0.504
[3861] 1.336 0.504 1.216 1.224 1.696 0.256 -0.104 0.456 0.736 0.784
[3871] 1.376 1.536 0.656 1.344 2.096 2.144 0.504 0.776 1.016 0.904
[3881] 0.696 1.264 1.744 1.496 0.256 0.496 1.136 0.824 1.344 1.736
[3891] 0.304 0.264 1.376 1.104 0.904 0.856 0.024 1.536 0.736 0.576
[3901] 0.224 1.936 0.776 0.064 1.096 0.496 1.736 1.264 0.736 1.136
[3911] 1.504 0.544 1.096 -0.136 0.096 2.104 1.296 1.216 0.264 0.736
[3921] 1.504 1.224 0.944 1.136 0.944 0.816 1.216 1.536 1.504 1.064
[3931] 1.136 1.504 1.696 1.216 0.576 2.096 0.736 0.256 -0.184 0.256
[3941] 0.576 -0.144 0.296 0.664 0.424 1.384 0.976 0.056 1.104 0.984
[3951] 1.376 -0.144 0.016 1.176 0.056 1.536 0.664 0.856 1.264 0.544
[3961] -0.184 1.456 0.896 1.576 1.096 1.736 1.416 1.136 1.024 1.144
[3971] 0.256 1.944 0.456 0.936 1.056 0.936 0.344 1.656 -0.096 1.216
[3981] 1.136 1.104 0.256 0.736 2.184 1.696 1.216 0.984 1.536 0.744
[3991] 1.744 1.936 1.376 -0.184 0.536 1.136 0.304 1.096 0.736 0.936
[4001] 1.104 0.496 0.336 0.536 0.464 0.736 0.904 1.536 1.216 1.264
[4011] 0.736 0.464 -0.144 1.984 1.744 1.544 0.896 0.584 1.256 1.336
[4021] 1.344 1.216 1.136 1.096 1.576 1.744 1.496 1.464 1.696 1.464
[4031] 0.584 1.216 0.544 1.104 0.544 1.304 -0.096 1.224 1.416 1.384
[4041] 1.144 0.816 1.136 0.496 1.056 0.224 1.224 -0.096 1.016 1.216
[4051] 1.464 0.896 0.424 1.536 1.496 1.584 1.936 0.344 0.504 0.864
[4061] 2.096 0.496 1.104 1.144 0.736 1.456 1.224 0.704 1.104 0.664
[4071] 0.984 0.824 1.744 1.304 0.896 1.656 1.416 1.696 1.736 1.704
[4081] 0.824 0.736 1.776 1.176 -0.104 0.016 1.344 0.944 0.496 0.456
[4091] 1.056 1.344 1.416 1.536 0.896 0.016 0.416 0.824 0.696 1.064
[4101] 0.696 1.504 0.304 0.624 0.944 1.504 1.336 0.864 0.496 0.816
[4111] 0.784 1.296 1.424 0.944 0.936 1.696 1.384 1.016 1.776 1.136
[4121] 1.256 1.496 0.536 0.776 0.896 1.144 1.336 0.896 1.424 1.064
[4131] 0.424 2.104 0.736 0.704 0.504 1.064 1.496 1.696 1.104 1.504
[4141] 1.224 1.536 2.136 2.104 0.736 1.104 0.464 1.016 1.704 1.696
[4151] 1.304 0.736 1.024 1.096 0.616 0.304 1.184 1.456 0.504 0.704
[4161] 0.584 0.344 1.344 1.496 1.664 0.576 0.464 1.264 0.784 1.336
[4171] 0.336 -0.104 1.424 0.624 1.776 1.104 0.944 0.904 -0.176 0.496
[4181] 0.456 1.936 0.864 0.864 1.136 0.224 1.744 0.816 0.256 1.424
[4191] 1.056 1.416 1.016 1.504 1.576 0.896 1.536 1.576 0.056 1.256
[4201] 1.496 1.464 0.944 1.296 1.304 1.184 0.496 0.984 0.776 1.736
[4211] 0.656 0.624 1.256 0.776 1.304 0.736 0.656 1.704 1.576 0.536
[4221] 1.896 0.584 0.784 0.856 1.736 0.224 0.624 0.736 0.984 1.624
[4231] 0.296 1.264 0.344 1.024 1.256 1.216 1.456 1.344 0.744 1.256
[4241] 0.736 1.744 0.464 0.744 0.936 0.936 0.704 1.456 1.064 0.656
[4251] 1.784 0.976 0.536 0.944 -0.176 0.784 0.016 1.064 0.304 0.824
[4261] 1.264 0.464 0.584 0.704 1.256 0.824 0.736 1.056 1.104 1.096
[4271] 0.496 0.304 0.624 0.664 1.264 0.024 1.936 1.664 1.776 1.184
[4281] 1.304 0.504 0.536 0.256 0.584 0.464 0.704 1.264 0.656 1.216
[4291] 1.264 0.296 0.096 0.624 1.256 0.976 1.744 1.496 1.624 0.984
[4301] 0.816 0.824 1.424 2.104 1.904 1.736 0.936 0.544 0.936 1.944
[4311] 0.536 0.576 0.984 0.864 1.136 1.184 0.656 1.016 0.696 1.064
[4321] 1.096 1.296 1.176 0.904 1.704 1.336 1.304 1.496 0.464 1.656
[4331] 1.104 1.184 1.376 0.224 1.936 1.136 1.296 0.304 1.104 0.936
[4341] 1.224 0.736 0.456 1.464 1.304 -0.176 0.736 0.304 0.224 0.544
[4351] 0.904 0.016 0.904 0.984 0.536 0.936 0.944 0.904 0.024 1.104
[4361] 0.544 1.616 0.704 1.176 -0.144 0.664 0.816 1.256 0.024 -0.136
[4371] 1.176 1.704 -0.136 1.224 1.176 1.224 0.896 1.984 0.344 1.064
[4381] 1.536 1.136 1.104 0.864 1.184 0.944 0.336 0.944 1.056 1.424
[4391] 1.664 1.896 0.064 1.704 0.824 0.736 0.296 1.576 1.736 1.056
[4401] 1.016 0.824 0.464 1.464 0.496 -0.096 0.056 -0.136 0.704 1.056
[4411] 0.664 1.216 0.224 0.376 0.736 0.896 0.744 1.064 1.296 0.704
[4421] 0.336 1.256 1.016 0.016 1.224 0.736 0.944 1.176 0.896 -0.104
[4431] 0.464 1.216 1.264 1.936 1.344 0.696 1.696 0.696 0.456 1.136
[4441] 1.696 1.216 1.104 0.416 0.944 1.064 0.304 0.496 0.424 1.544
[4451] 1.744 1.256 1.136 1.904 0.984 0.976 0.776 0.936 1.584 0.736
[4461] 2.104 0.776 0.016 1.024 -0.176 0.264 1.304 1.464 0.536 0.984
[4471] 1.064 1.056 0.656 1.936 0.504 0.896 1.576 1.776 1.064 1.944
[4481] 1.736 0.464 0.736 0.464 1.104 1.176 0.744 0.544 0.816 1.024
[4491] 0.576 0.624 -0.184 1.784 1.136 0.936 1.336 2.184 1.376 0.704
[4501] 1.744 1.496 1.264 1.344 1.136 1.496 0.296 0.736 0.296 1.056
[4511] 1.144 1.056 0.736 0.704 0.736 0.896 0.696 1.936 0.256 1.536
[4521] 1.376 1.096 0.336 0.656 0.376 1.624 0.984 0.984 1.224 0.464
[4531] 1.256 1.696 0.296 1.376 1.104 1.664 1.136 1.104 1.056 1.744
[4541] 0.456 0.856 0.064 1.184 1.464 0.416 1.264 0.896 1.416 1.984
[4551] 0.976 1.696 1.904 0.224 1.256 0.856 1.256 0.736 1.216 1.424
[4561] 1.216 0.744 1.944 1.376 0.624 1.016 1.096 1.704 1.704 1.096
[4571] 1.184 1.056 0.064 0.736 0.256 1.704 1.256 1.376 1.384 0.256
[4581] 1.096 1.096 0.864 1.496 0.496 0.736 0.984 1.064 0.736 0.864
[4591] 0.496 1.416 0.736 1.096 1.536 0.504 1.096 1.176 0.664 0.376
[4601] 0.504 0.056 0.464 0.704 1.344 1.336 0.656 0.896 0.776 1.416
[4611] 0.864 1.704 2.104 0.376 0.624 1.576 0.936 0.624 0.304 1.296
[4621] 0.824 1.176 1.336 0.536 0.456 1.744 1.024 0.296 1.264 1.296
[4631] 1.336 1.104 -0.104 1.136 1.336 1.656 0.896 0.024 0.536 0.776
[4641] 0.424 1.744 0.296 1.944 1.064 1.104 0.704 0.216 -0.144 0.536
[4651] 1.776 2.176 1.344 1.104 0.296 1.264 1.104 0.984 1.944 1.376
[4661] 2.096 0.824 1.296 1.376 1.416 1.056 0.856 2.144 1.264 0.304
[4671] 1.104 0.536 0.904 1.336 0.416 1.144 0.856 0.896 0.336 -0.104
[4681] 0.464 0.664 1.504 1.696 2.136 0.536 0.544 1.064 1.104 1.064
[4691] 1.496 0.544 1.264 1.216 0.616 1.536 0.944 0.216 1.696 1.976
[4701] 1.264 1.264 1.016 0.736 0.944 0.904 1.376 0.936 0.096 0.904
[4711] 0.264 1.704 0.064 1.504 0.376 1.296 1.704 0.904 1.144 1.384
[4721] 0.824 0.696 0.744 0.336 1.696 0.696 0.896 0.936 0.656 0.304
[4731] 0.696 0.896 0.496 1.776 0.744 0.976 1.384 1.704 0.424 0.896
[4741] 1.744 1.224 1.376 0.264 0.824 1.176 0.616 1.304 0.664 1.336
[4751] 1.176 0.264 0.544 1.536 1.664 1.536 2.136 1.744 1.304 1.424
[4761] 1.744 1.496 1.136 1.296 0.744 1.936 1.136 1.304 0.736 0.904
[4771] 1.016 1.944 1.024 1.264 0.784 1.936 1.416 0.296 0.896 0.256
[4781] 1.936 1.144 1.416 0.984 0.776 2.096 1.616 1.024 2.104 0.504
[4791] 0.704 1.216 0.064 1.336 0.744 0.544 0.944 2.176 0.856 0.896
[4801] 1.104 0.864 1.296 0.416 1.336 1.416 1.504 0.864 0.944 0.816
[4811] 1.144 0.536 1.464 0.624 0.456 1.216 0.584 0.904 0.824 1.664
[4821] 0.416 0.904 0.936 0.456 1.056 1.296 1.744 1.176 1.976 0.864
[4831] 1.304 1.264 0.904 0.056 0.864 1.584 0.624 1.224 0.264 1.544
[4841] 1.656 0.744 1.216 0.496 1.376 0.544 1.216 2.104 1.664 0.936
[4851] -0.144 0.336 0.944 1.016 1.344 1.096 1.504 0.664 0.496 0.064
[4861] 1.424 0.976 0.216 0.544 1.264 0.656 1.744 0.464 0.424 0.896
[4871] 0.744 0.536 0.656 1.584 1.344 1.184 1.664 0.656 0.744 1.504
[4881] 0.056 0.016 1.936 0.496 0.944 0.784 1.256 1.176 0.864 0.224
[4891] 0.496 0.896 0.696 0.016 0.016 0.656 1.064 0.624 1.576 0.944
[4901] 1.976 1.016 0.464 0.576 0.984 1.944 1.536 0.336 0.936 1.064
[4911] 0.856 0.424 1.064 0.624 1.696 1.256 0.856 1.376 1.224 0.824
[4921] 0.624 1.264 0.856 1.064 0.296 0.304 1.736 1.184 1.616 0.536
[4931] 1.016 1.264 1.064 1.704 0.736 2.176 1.504 0.056 1.144 1.544
[4941] 1.344 1.504 1.584 1.376 1.944 0.464 1.744 0.464 1.176 1.104
[4951] 1.096 0.016 0.824 0.744 0.896 1.096 1.024 1.736 0.224 0.864
[4961] 0.536 0.704 1.224 1.016 0.064 1.984 1.776 1.984 1.096 1.544
[4971] 0.264 0.576 0.664 1.544 0.016 -0.096 1.256 0.744 0.824 1.384
[4981] 1.416 1.696 0.656 1.024 1.536 0.296 0.784 1.376 1.184 0.456
[4991] 1.504 2.176 1.064 0.864 0.744 1.464 0.576 0.624 1.104 0.816Estimate Dist under HA
Power
Power
[1] 0.2406n_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)
}