# Example 862 — The readings below the limit were recorded as zero `the_readings_below_the_limit_were_recorded_as_zero.eml` - A water-quality report gives the average contaminant level, and it averages the real recorded readings of every sample correctly. What a recorded zero means is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A water-quality # report gives the average contaminant level, and it averages the real recorded # readings of every sample correctly. What a recorded zero means is computed # below. # # The measurement is careful. It reads the real assay values, not estimates; it # covers every sample; the mean is the honest average of the recorded levels; and # the intent is exactly 'the average contaminant concentration'. # # The assay cannot quantify below 5 units, so every below-limit reading is stored # as 0 - and a stored 0 means 'below the limit', not 'none present'. 40000 => samples 10000 => readings_above_the_limit 30000 => readings_below_the_limit_stored_zero 8 => mean_with_below_limit_as_zero 10 => mean_with_below_limit_at_half_the_limit mean_with_below_limit_at_half_the_limit - mean_with_below_limit_as_zero => level_the_floor_hid int(level_the_floor_hid * 10000 / mean_with_below_limit_at_half_the_limit) => understated_share_per_myriad "samples : " + str(samples) ^0 " above the detection limit : " + str(readings_above_the_limit) ^0 " below the limit, stored as 0 : " + str(readings_below_the_limit_stored_zero) ^0 "" ^0 "mean, below-limit read as zero : " + str(mean_with_below_limit_as_zero) ^0 "mean, below-limit at half-limit : " + str(mean_with_below_limit_at_half_the_limit) ^0 "level the floor hid : " + str(level_the_floor_hid) ^0 "understated share of the truth : " + str(understated_share_per_myriad) + " per ten thousand" ^0 "" ^0 # ---- what the measurement verified ---- "the contaminant average" ^0 " reads : the real assay values, not estimates" ^0 " covers : every sample" ^0 " mean : the honest average of the recorded levels" ^0 " intent : the average contaminant concentration" ^0 " samples omitted : 0" ^0 " verdict : RECORDED MEAN IS 8, COMPUTED CORRECTLY" ^0 "" ^0 " averaging the real recorded values over every sample is" ^0 " the part done right here, and it is why 8 is the correct" ^0 " mean of what was stored" ^0 "" ^0 # ---- what a recorded zero means ---- "the stored zero" ^0 " the assay's limit : it cannot quantify below 5 units" ^0 " what a below-limit reading becomes : 0" ^0 " what that 0 means : below the limit, somewhere in 0 to 5" ^0 " what it is read as : none present, exactly zero" ^0 " so the mean : treats a floor as a true absence, on 30000" ^0 " of the 40000 samples" ^0 "" ^0 # ---- what the caller got ---- "the result of the report" ^0 " reported average : " + str(mean_with_below_limit_as_zero) ^0 " average if below-limit is half the limit : " + str(mean_with_below_limit_at_half_the_limit) ^0 " concentration hidden by the floor : " + str(level_the_floor_hid) ^0 " is the recorded mean wrong : no; 8 is exact for the" ^0 " stored values" ^0 " is a stored 0 an absence : no; it is a value censored at" ^0 " the detection limit and read as zero" ^0 "" ^0 # ---- null control ---- # The same samples, with below-limit readings set to half the detection limit (or # a censored-data estimator), instead of a hard zero. 8 => nc_mean_with_hard_zero 10 => nc_mean_with_half_limit_substitution 30000 => nc_readings_no_longer_read_as_absent "null control - substitute half the limit for below-limit readings" ^0 " mean with a hard zero : " + str(nc_mean_with_hard_zero) ^0 " mean with half-limit substitution : " + str(nc_mean_with_half_limit_substitution) ^0 " readings no longer read as absent : " + str(nc_readings_no_longer_read_as_absent) ^0 " no sample and no assay reading changed; the below-limit" ^0 " values stopped being read as zero and started being read" ^0 " as somewhere under the limit" ^0 "" ^0 # ---- the rule ---- "what an average of the recorded readings guarantees" ^0 " it is the correct mean of what was stored : exactly, real" ^0 " values, every sample, honest average" ^0 " it is the average concentration present : not addressed;" ^0 " the assay floors sub-limit readings to 0 and a 0 is read" ^0 " as absence, so the " + str(readings_below_the_limit_stored_zero) + " censored samples pull the mean to 8" ^0 "" ^0 "a detection limit is a floor on what can be seen, not on what is there; storing" ^0 "the unseen as zero turns 'too small to measure' into 'measured as nothing', and" ^0 "an average built on that reads a limit of the instrument as a value of the world" ^0 "" ^0 "It averages the real recorded values over every sample - 8 is the exact recorded" ^0 "mean. But the assay stores every below-limit reading as 0 and a 0 is read as" ^0 "absent; the " + str(readings_below_the_limit_stored_zero) + " censored samples give a true mean nearer " + str(mean_with_below_limit_at_half_the_limit) + ", " + str(understated_share_per_myriad) ^0 "per ten thousand understated, until the floor is estimated instead of zeroed." ^0 ``` ## Python (deterministic transpilation) ```python samples = 40000 readings_above_the_limit = 10000 readings_below_the_limit_stored_zero = 30000 mean_with_below_limit_as_zero = 8 mean_with_below_limit_at_half_the_limit = 10 level_the_floor_hid = mean_with_below_limit_at_half_the_limit - mean_with_below_limit_as_zero understated_share_per_myriad = int(level_the_floor_hid * 10000 / mean_with_below_limit_at_half_the_limit) print("samples : " + str(samples)) print(" above the detection limit : " + str(readings_above_the_limit)) print(" below the limit, stored as 0 : " + str(readings_below_the_limit_stored_zero)) print("") print("mean, below-limit read as zero : " + str(mean_with_below_limit_as_zero)) print("mean, below-limit at half-limit : " + str(mean_with_below_limit_at_half_the_limit)) print("level the floor hid : " + str(level_the_floor_hid)) print("understated share of the truth : " + str(understated_share_per_myriad) + " per ten thousand") print("") print("the contaminant average") print(" reads : the real assay values, not estimates") print(" covers : every sample") print(" mean : the honest average of the recorded levels") print(" intent : the average contaminant concentration") print(" samples omitted : 0") print(" verdict : RECORDED MEAN IS 8, COMPUTED CORRECTLY") print("") print(" averaging the real recorded values over every sample is") print(" the part done right here, and it is why 8 is the correct") print(" mean of what was stored") print("") print("the stored zero") print(" the assay's limit : it cannot quantify below 5 units") print(" what a below-limit reading becomes : 0") print(" what that 0 means : below the limit, somewhere in 0 to 5") print(" what it is read as : none present, exactly zero") print(" so the mean : treats a floor as a true absence, on 30000") print(" of the 40000 samples") print("") print("the result of the report") print(" reported average : " + str(mean_with_below_limit_as_zero)) print(" average if below-limit is half the limit : " + str(mean_with_below_limit_at_half_the_limit)) print(" concentration hidden by the floor : " + str(level_the_floor_hid)) print(" is the recorded mean wrong : no; 8 is exact for the") print(" stored values") print(" is a stored 0 an absence : no; it is a value censored at") print(" the detection limit and read as zero") print("") nc_mean_with_hard_zero = 8 nc_mean_with_half_limit_substitution = 10 nc_readings_no_longer_read_as_absent = 30000 print("null control - substitute half the limit for below-limit readings") print(" mean with a hard zero : " + str(nc_mean_with_hard_zero)) print(" mean with half-limit substitution : " + str(nc_mean_with_half_limit_substitution)) print(" readings no longer read as absent : " + str(nc_readings_no_longer_read_as_absent)) print(" no sample and no assay reading changed; the below-limit") print(" values stopped being read as zero and started being read") print(" as somewhere under the limit") print("") print("what an average of the recorded readings guarantees") print(" it is the correct mean of what was stored : exactly, real") print(" values, every sample, honest average") print(" it is the average concentration present : not addressed;") print(" the assay floors sub-limit readings to 0 and a 0 is read") print(" as absence, so the " + str(readings_below_the_limit_stored_zero) + " censored samples pull the mean to 8") print("") print("a detection limit is a floor on what can be seen, not on what is there; storing") print("the unseen as zero turns 'too small to measure' into 'measured as nothing', and") print("an average built on that reads a limit of the instrument as a value of the world") print("") print("It averages the real recorded values over every sample - 8 is the exact recorded") print("mean. But the assay stores every below-limit reading as 0 and a 0 is read as") print("absent; the " + str(readings_below_the_limit_stored_zero) + " censored samples give a true mean nearer " + str(mean_with_below_limit_at_half_the_limit) + ", " + str(understated_share_per_myriad)) print("per ten thousand understated, until the floor is estimated instead of zeroed.") ``` ## stdout (executed) ```text samples : 40000 above the detection limit : 10000 below the limit, stored as 0 : 30000 mean, below-limit read as zero : 8 mean, below-limit at half-limit : 10 level the floor hid : 2 understated share of the truth : 2000 per ten thousand the contaminant average reads : the real assay values, not estimates covers : every sample mean : the honest average of the recorded levels intent : the average contaminant concentration samples omitted : 0 verdict : RECORDED MEAN IS 8, COMPUTED CORRECTLY averaging the real recorded values over every sample is the part done right here, and it is why 8 is the correct mean of what was stored the stored zero the assay's limit : it cannot quantify below 5 units what a below-limit reading becomes : 0 what that 0 means : below the limit, somewhere in 0 to 5 what it is read as : none present, exactly zero so the mean : treats a floor as a true absence, on 30000 of the 40000 samples the result of the report reported average : 8 average if below-limit is half the limit : 10 concentration hidden by the floor : 2 is the recorded mean wrong : no; 8 is exact for the stored values is a stored 0 an absence : no; it is a value censored at the detection limit and read as zero null control - substitute half the limit for below-limit readings mean with a hard zero : 8 mean with half-limit substitution : 10 readings no longer read as absent : 30000 no sample and no assay reading changed; the below-limit values stopped being read as zero and started being read as somewhere under the limit what an average of the recorded readings guarantees it is the correct mean of what was stored : exactly, real values, every sample, honest average it is the average concentration present : not addressed; the assay floors sub-limit readings to 0 and a 0 is read as absence, so the 30000 censored samples pull the mean to 8 a detection limit is a floor on what can be seen, not on what is there; storing the unseen as zero turns 'too small to measure' into 'measured as nothing', and an average built on that reads a limit of the instrument as a value of the world It averages the real recorded values over every sample - 8 is the exact recorded mean. But the assay stores every below-limit reading as 0 and a 0 is read as absent; the 30000 censored samples give a true mean nearer 10, 2000 per ten thousand understated, until the floor is estimated instead of zeroed. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done