OAR Box 1811 

Prepped by Keeia Richards 

Document Number: 

30) ll-A-11 

Docket Number: 

A-84-22 

Printed 10/30/2008 1:19:24 PM Sheet 30 of 82 

p.1 
flrY-** 3r_A -ii 

RTI Project No. 893-66 July, 1976 

EXAMINING THE PROPERTIES OF QUALIFIED OBSERVER 

OPACITY READINGS AVERAGED OVER INTERVALS 

OF LESS THAN SIX MINUTES 

Prepared for 

Environmental Protection Agency 

Research Triangle Park, North Carolina 27711 

Contract No. 68-02-1325 
P.3 

RTI Project No. 893-66 July, 1976 

EXAMINING THE PROPERTIES OF QUALIFIED OBSERVER 

OPACITY READINGS AVERAGED OVER INTERVALS 

OF LESS THAN SIX MINUTES 

by 

Tyler D. Hartwell 

Research Triangle Institute 

Research Triangle Park, North Carolina 27709 

EPA Project Officer: Roy Neulicht 

Prepared for 

Environmental Protection Agency 

Research Triangle Park, North Carolina 27711 

Contract No. 68-02-1325 
P.4 

TABLE OF CONTENTS 

Page 

1. INTRODUCTION. 1 

2. DESCRIPTION OF DATA 2 

3. DATA ANALYSIS 4 

4. SUMMARY 16 

REFERENCES 20 

APPENDIX A: Frequency Distributions of Mean Deviations 

APPENDIX B: Frequency Distributions of Mean Observed 

Opacity When Mean True Opacity Less Than 

20 Percent and Mean True Opacity Less Than 10 

Percent 

APPENDIX e: Estimation of the Measurement Error of an 

Observer 
P.5 

1. INTRODUCTION 

In 1973 and 1974 EPA conducted several field tests for the purpose 

of studying the performance of qualified observers in visually assigning 

opacity to stationary sources using procedures set forth in EPA Reference 

Method 9. Previous analysis of the data from these field tests is presented in [1] and [2]. In this report, a description is given of additional statistical analysis by the Research Triangle Institute (RTI) of 

data from two of the EPA field tests. The reason for the current research 

was the following: at the present time Reference Method 9 states that 

compliance of the opacity standard will be based on an average of 24 

consecutive opacity readings (6 minutes) taken at 15-second intervals; 

however, many state and local standards are inconsistent with a standard 

based on a 6-minute averaging time. Thus, EPA asked RTI to investigate 

the effect of using averaging times of less than 6 minutes. Accordingly, 

this report presents an analysis designed to examine the effect of different 

averaging times on several different statistics such as the frequency 

distribution of mean observed opacity. 

In this report, Section 2 describes the data that RTI analyzed, 

Section 3 presents RTI's analysis and Section 4 gives a summary of the 

results. 
P.6 

2. DESCRIPTION OF DATA 

The data analyzed in this report were collected by certified observers who visually determined the opacity of emissions from stationary 

sources during two EPA field tests. The procedures used to gather these 

data are set forth in EPA Reference Method 9 (see [1]). A detailed 

description of the field tests is given in [1]. In brief, the field 

tests were the following: 

(i) A test conducted November 19-20, 1973 at the National 

Environmental Research Center, Research Triangle Park, 

North Carolina using two smoke generators with 9 certified observers (denoted hereafter as the Smoke Generator 

Test), 

(ii) A test conducted 30 September - 1 October, 1974 at the 

Riverbend Steam Station near Charlotte, North Carolina 

using 8 qualified observers (denoted hereafter as the 

Steam Station Test). Note that for the Steam Station 

Test only 4 of the observers collected data as specified 

specifically in Reference Method 9; and therefore, only 

data from these 4 observers are analyzed in this report. 

The basic procedure in each of the two- field tests was to have each 

observer assign opacities to plumes at 15-second intervals for a time 

period of 6 minutes (defined as a run). Thus, a run had a total of 24 

observations by each observer. For each field test several runs were 

observed. To determine how accurate the observers were, the plumes were 

also measured by an in-stack transmissometer. Thus, for each run there 

were 24 observations from each observer and from the transmissometer. 
P.7 

Specifically, the number of runs for each of the field tests were: 

(i) Smoke Generator Test • 20 runs with white smoke and 

16 runs with black smoke. Since each run was observed by several observers, this resulted in data 

on 170 runs with white smoke and 133 runs with black 

smoke. (Note, observer 9 did not participate in 

all of the runs.) 

(ii) Steam Station Test

 a 24 runs with white smoke. This 

resulted in data on 96 runs (=» 24 x' 4). 

The total number of readings analyzed by RTI (i.e., the number of 15-

second readings) over all runs and observers and both field tests was 

equal to 9,576 (170 x 24 + 133 x 24 + 96 x 24) readings. The range of 

the true opacities (as measured by the transmissometer) studied during 

these field tests was between 0 and 50 percent with the majority of readings being less than 30 percent opacity. 

The data on the two field tests were supplied to RTI by EPA in the 

form of observer code sheets. RTI then coded and keypunched these data 

onto computer cards. Each computer card contained a 15-second opacity 

reading by the transmissometer and the corresponding 15-second readings 

by each observer. There were a total of 1*500 computer cards. 

RTI's analysis of the opacity data is given in Section 3'. The 

majority of the computations necessary for this analysis were carried 

out by using the SAS Computer Package [3]. 
P.8 

3. DATA ANALYSIS 

In order to assess the effect of various averaging times on observed 

opacity readings, RTI used the data described in Section 2 for the Smoke 

Generator and the Steam Station Tests and.computed the following statistics 

for different averaging times and various ranges of mean true opacity. 

(Note, throughout this section the term "mean true opacity" refers to the 

mean of the 15-second readings by the in-stack transmissometer which corresponds to the mean of the 15-second readings by an observer; e.g., if 

an observer mean is based on 4 contiguous 15-second readings then the corresponding mean true opacity is based on the same 4 contiguous 15-second 

readings by the meter.) 

A. Frequency distributions of mean deviations (observer 

mean - true opacity mean). 

B. Frequency distributions of mean observed opacity. 

C. Estimates of the bias of an observer's readings. 

D. Estimates of the standard deviation of an observer's 

bias. 

E. Estimates of an observer's measurement error (i.e., 

the estimated standard deviation of an observer in 

repeated measurements during the same run). 

The above statistics were computed using the data from all runs and 

observers with separate computations being carried out for (a) the Steam 

Station Test (white smoke), (b) the black smoke data from the Smoke Generator Test, and (c) the white smoke data from the Smoke Generator Test. The 

averaging times examined were 30 seconds, 1 minute, 2 minutes, ..., 6 minutes. The initial computations were for contiguous averaging times (e.g., 
a 1-minute contiguous averaging time was obtained by averaging 4 contiguous single 15-second readings). In addition, statistics A, B, and D were 

also computed for contiguous averaging times after taking the average 

of two observer's readings (this was only done for the Steam Station 

Test). Finally, statistics A, B, C and D were computed for the mean of 

the highest 2, 4, 8 and 12 non-contiguous single 15-second readings in the 

6-minute observation periods (runs). These computations were carried 

out because many states have the following standard: "an opacity of Y 

percent is not to be exceeded more than X minutes per hour" (e.g., X = 3 

'or 4 minutes per hour are common). 

The results of computing the statistics A through E are discussed in 

the following paragraphs. When examining these statistics it should be kept 

ln mind that the sample sizes (number of means) upon which the statistics are 

based are quite different for the various averaging times. This is due to 

the fact that since a run consisted of 24 readings, contiguous averaging 

times of 30 seconds up to 3 minutes had more than one mean available for 

each observer per run (e.g., for the 30-second averaging time there were 

12 means for each observer per run while for the 6-minute averaging time 

only 1 mean per observer per run was available). Thus, the sample sizes 

for 6-minute and non-contiguous averaging times are much smaller than for 

30-second averaging times (see Appendix A for the sample sizes available). 

A. Frequency Distributions of Mean Deviations 

Appendix A presents a detailed summary of the frequency distributions of mean deviations by various ranges of mean true opacities (Table 

A-2) and over all mean true opacities (Table A-l). However, since EPA 

is particularly interested in positive mean deivations, Table 1 presents the percent of the frequency distributions for mean deviations 
I I I I I ( 

Table 1. Percent of Frequency Distribution for Mean Deviations— 

2/ Sinoke Type and Mean True Opacity— 

i/ > 

i » I ' .1 J • 

5 Percent Opacity; By Averaging Time, Station, 

Mean True 

Opacity (%) 

0-10 

10-20 

20-30 

30-40 

3/ Overall-7 

30 sec. 

% 

5.9 

9.9 

6.8 

3.6 

7.2 

1 min. 

% 

.8 

6.6 

5.1 

1.2 

4.7 

Contiguous 

Smoke 1 

Readings 

Averaging Time 

2 min. 3 min. 4 min. 

% % % 

0.0 

6.1 

3.0 

0.0 

3.3 

0.0* 

2.7 1.3 

2.0 0.0* 

0.0* 

1.9 .8 

Generator 

5 min. 

% 

1.1 

0.0* 

.8 

, Black Smoke 

6 min. 

% 

1.2 

0.0* 

.8 

No 

Highest 

2 

34.5 

17.0* 

23.4 

n-Contlguous Readi 

Averaging Time 

Highest Highest 

4 8 

22.4 10.5 

9.1* 6.5* 

0.0* 

14.2 7.1 

ngs 

Highest 

12 

4.5 

2.4* 

0.0* 

3.1 

0-10 

10-20 

20-30 

30-40 

Overall 

13.1 

15.9 

5.3 

1.1 

11.7 

9.0 

13.2 

4.1 

0.0 

9.0 

8.1 

11.7 

4.9 

0.0* 

8.1 

12.0 

9.8 

1.7 

0.0* 

8.3 

Smoke Generator, 

4.0 

15.8 

2.9* 

8.9 

3.9 

14.5 

0.0* 

7.6 

White Smoke 

0.0* 

13.1 

7.1 

28.4 

23.7* 

0.0* 

26.7 

36.3* 

30.4 

12.5* 

'. 

23.1 

•___— 

25.0 

11.9* 

18.8 

4.0* 

24.1 

6.2* 

15.1 Ok 

' 

0-10 

10-20 

20-30 

30-40 

Overall 

11.7 

5.2 

10.8 

9.8 

9.5 

7.9 

5.8 

10.7 

7.8 

7.6 

10.8 

0.0 

11.6 

5.0* 

7.3 

Riverbend Steam Station, White Smoke 

11.2 

0.0* 

7.1* 

3.1* 

6.2 

12.5* 

0.0* 

6.2 

10.0* 

0.0* 

5.2 

10.0* 

0.0* 

5.0* 

5.2 

36.0* 

29.6* 

25.0 

26.5* 

26.7* 

22.0 

15.8* 

46.1* 

10.0* 

11.5 

15.0* 

0.0* 

10.0* 

8.4 

Riverbend Steam Station, White Smoke, Average of Two Observers 

0-10 

10-20 

20-30 

30-40 

rail 

7.4 

2.2 

11.0 

7.1 

6.3 

5.0 

2.6 

11.9 

6.2 

5.6 

5.0 

0.0 

14.1 

1.7 

4,9 

6.7 

0.0 

11.9* 

4.2* 

5.2 

6.7 

0.0* 

8.3* 

0.0* 

4.2 

6.7 

0.0* 

8.3* 

0.0* 

4.2 

6.7 

0.0* 

10.0* 

4.9 

— Mean Deviations =• Observer mean - true opacity mean where true opacity measured by a transmissometer. 

2/ 

— Non-Contiguous Highest 2 =» mean of highest 2 non-contiguous single 15-second readings in a 6-minute observation 

period (i.e., in a run). 

Contiguous 30 sec. =• mean of 2 contiguous single 15-second readings. 

3/ 

— Overall = over all levels of mean true opacity (see Table A-l). 

* = Sample size between 20 and 50 observations. (Note, sample size a number of sample means) 

— = Sample size less than 20 observations. 

(Note, the sample sizes vary a great deal for the various averaging times, see Table A-2.) 

o 
P.11 

which are greater than 5% opacity by averaging time, station, smoke type 

and range of mean true opacity— . The results are given for averaging 

times based upon contiguous and non-contiguous readings. Table 1 (as 

does Table A-3) indicates the following (note in Table 1 that a * indicates that the frequency distribution is only based on between 20 and 

50 means): 

(i) In general, as averaging time increases the percent 

of the frequency distribution greater than 5% 

opacity decreases, 

(ii) The non-contiguous readings have relatively much higher percentages of their frequency distributions greater than 5% opacity than do contiguous readings. This 

is particularly true for the highest 2 and 4 noncontiguous readings, 

(iii) In most cases as the range of mean true opacity 

increases, the percentages given in Table 1 decrease (this trend is more noticeable in Table A-3). 

(iv) In general, the percentages greater than 5% are 

smaller for black smoke than for white smoke, 

(v) For black smoke, the percentages for the 3- or 4-

minute contiguous averaging times are (a) about 

the same as for the 6-minute averaging time and 

(b) relatively much smaller than for the 30-second 

averaging time. For white smoke, the results are 

not as clear-cut but it does appear that the 3- or 

— Appendix Table A-3 gives the same results for mean deviations greater 

than 0% opacity. 
P.12 

4-mihute averaging time does (a) about as well as 

the 6-minute averaging time and (b) somewhat better 

than the 30-second averaging time. 

(vi) For the steam station, the average of two observers 

usually has slightly smaller percentages greater than 

5% opacity than the corresponding percentages based 

on one observer. 

B. Frequency Distributions.of Mean Observed Opacity 

RTI computed frequency distributions of mean observed opacity for 

various ranges of mean true opacity and Appendix B presents a detailed 

summary of these frequency distributions for mean true opacity less than 

20% (Table B-1) and mean true opacity less than 10% (Table B-2). In 

addition, Table 2 presents)the percent of the frequency distribution of 

mean observed opacity greater than 10% and 20% when mean.true opacity is 

less than 10% and 20%, respectively. Thus, Table 2 indicates, for the 

various averaging times, the percent of the time that an observer would 

indicate opacity to be greater than 10% (or 20%) when, in fact, mean 

true opacity was less than 10% (or 20%). Table 2 indicates the following 

results: 

(i) In general, the percentages in-the table decrease 

with increasing averaging time, 

(ii) The percentages for the non-contiguous readings are 

much higher than for the contiguous readings, 

(iii) The percentages for mean true opacity <10% are much 

larger than for mean true opacity <20%. 

(iv) The steam station has lower percentages than the 

smoke generator. 
Table 2. Percent of Frequency Distribution of Mean Observed Opacity £10% and 20% When Mean True Opacity <10% and 20%, 

2/ 

Respectively; By Averaging Time, Station and Smoke TypeSmoke Generator, Black Smoke 

Mean TrueOpacity (%) 

<10 

<20 

<10 

<20 

<10 

<20 

<10 

<20 

Mean Observed 

Opacity (%) 

U O 

£20 

£10 

£20 

£10 

£20 

£10 

£20 

30 sec. 

% 

52.2 

12.4 

• 

41.4 

9.3 

19.8 

2.0 

14.3 

.6 

1 min. 

% 

51.6 

7.0 

39.7 

7.5 

13.2 

1.3 

9.4 

.2 

Contiguous Readings 

Averaging Time 

2 min. 3 min. 4 min. 5 min. 6 min. 

% % % % % 

39.2 

7.1 

37.0 

4.2 

16.7 

0.0 

Riverbend 

14.4 

0.0 

34.4* 

9.9 

43.0 

8.7 

2.2 3.3 2.2 

Non-Contiguous Readings 

Highest 

2 

44.8 

Smoke Generator, White Smoke 

46.0 43.1 14.0* 

9.5 5.5 3.0 30.3 

Riverbend Steam Station, White Smoke 

15.0 

0.0 

Steam 

11.7 

0.0 

22.5* 17.5* 15.0* 

0.0 0.0 0.0 

63.6* 

18.3 

Averaging Time 

Highest Highest 

4 8 

28.3 

81.8* 

26.8 

35.3* 

10.9 

13.8 

20.6 

36.8* 

7.8 

Station, White Smoke, Average of Two Observers 

15.0 11.7 8.3 

0.0 0.0 0.0 • 

Highest 

12 

16.6 

48.0* 

20.7 

27.5* 

0.0 

— True opacity measured by a transmissometer. 

2/ 

— Non-Contiguous Highest 2 and Contiguous readings defined in Table 1. 

* =» Sample size between 20 and 50 observations. 

— = Sample size less than 20 observations. 
10 

?.14 

(v) It is difficult to draw general conclusions regarding the relative sizes of the percentages for the 

various contiguous averaging times. However, except for the white smoke at the smoke generator, 3-

or 4-minute averaging times do about as well as 6-

minute averaging times. 

(vi) As was the case for the mean deviations in A, the 

average of two observers at the steam station has 

somewhat smaller percentages than the corresponding 

percentages based on one observer. 

C. Estimates of the Bias of An Observer's Readings 

Table 3 presents estimates of the bias of an observer by averaging 

time, station, smoke type and range of mean true opacity. These estimated biases were computed by averaging mean deviations over all runs 

and observers. The table indicates: 

(i) As shown in [1], the estimated bias of an observer's 

readings become increasingly negative as mean true 

opacity increases, 

(ii) As would be expected, the length of the contiguous 

averaging time has little effect on the estimated 

.bias of an observer. This is partially due to the 

fact that in the present case bias for averaging time 

T is defined as: Observer Mean (for averaging time 

T) - Mean True Opacity (for averaging time T). Thus, 

the value of mean true opacity changes with averaging 

time. If on the other hand mean true opacity were 

defined for each run for some fixed time period (say 
Table 3. 

1/ 2/ 

Estimates of the Bias of an Observer— ; By Averaging Time, Station, Smoke Type and Mean True Opacity— 

Mean True 

Opacity (Z) 

0-10 

10-20 

20-30 

30-40 

£40 

Overall-' 

30 sec. 

X 

1.0 

-1.0 

-4.0 

-7.7 

-16.4 

1 min. 

X 

1.0 

-1.1 

-3.4 

-8.6 

Contiguous Readi 

Smoke 

ngs 

Averaging Time 

2 min. 3 min. 4 min. 

X X X 

.2 

- .4 

-4.4 

-7.6 

1.1 

-1.5 

-2.9 

-8.7 

1.9 

-1.6 

-2.2 

Generator 

5 min. 

X 

-1.2 

-2.3 

, Black Smoke 

6 min. 

X 

-1.6 

-2.0 

No 

Highest 

2 

2.3 

-1.1 

- .7 

.05 

n-Contiguous Read! 

Averaging Time 

Highest Highest 

4 8 

1.5 

-1.2 

-1.2 

- .49 

.7 

-1.4 

-4.0 

-1.26 

ngs 

Highest 

12 

.1 

-2.4 

-6.5 

-1.78 

0-10 

10-20 

20-30 

30-40 

£40 

.rail 

1.2 

- .3 

-5.1 

-9.6 

.9 

- .5 

-5.2 

-8.5 

.9 

- .7 

-4.7 

-8.5 

1.5 

- .8 

-5.8 

-9.1 

Smoke 

1.2 

- .5 

-4.4 

Generator, 

1.1 

- .9 

-4.2 

-8.1 

^ 

White I 

- .2 

- .5 

-4.6 

-8.2 

>moke 

5.2 

2.4 

-1.3 

-7.0 

.47 

2.8 

2.4 

-3.6 

-5.6 

.00 

2.6 

1.6 

-5.2 

-4.9 

- .69 

1.3 

.9 

-5.4 

-5.7 

- .95 

0-10 

10-20 

20-30 

30-40 

>40 

Overall 

1.7 

-2.2 

-2.6 

-6.7 

-8.2 

1.6 

-2.2 

-2.8 

-6.8 

-7.2 

1.7 

-2.7 

-2.7 

-7.2 

. 

Riverbend Steam Station, White Smoke 

1.7 

-2.7 

-3.3 

-6.1 

1.7 

-2.7 

-3.5 

-5.5 

1.7 

-2.6 

-3.8 

-5.1 

1.7 

-2.7 

-4.3 

-4.9 

3.7 

2.3 

.5 

-6.5 

-6.2 

.34 

3.1 

1.6 

-5.9 

-6.2 

.22 

3.1 

- .2 

-5.8 

- .03 

2.7 

-1.3 

.. 

-5.4 

- .35 

— Estimated Bias = [Observer Mean - Mean True Opacity] averaged over all runs and observers. 

2/ 

— Non-Contiguous Highest 2 and Contiguous readings defined in Table 1. 

3/ 

— Overall = over all levels of mean true opacity. 

— = Sample size less than 10 observations. 

' ro 
P.16 

12 

6 minutes), then the estimated bias of an observer 

would undoubtedly vary with averaging time. The point 

here is that the observer's mean for different averaging times is not being compared to the same true 

opacity mean. Instead, the true mean is also being 

allowed to vary with averaging time. 

(iii) In general, the non-contiguous readings have estimated biases which are less negative than the estimated biases for contiguous readings. In addition, 

as the averaging time of non-contiguous readings increases (e.g., from 2 to 12), the estimated biases 

become more negative. 

D. Estimates of the Standard Deviation of An Observer's Bias 

Table 4 presents estimated standard deviations (s.d.) of the estimated biases given in Table 3 by averaging time, station, smoke type, and 

range of mean true opacity. These s.d.s were computed as the s.d. of 

mean deviations over all runs and observers. Accordingly, the s.d.s given 

in Table 4 not only contain contributions from observer measurement error 

but also from differences in mean deviations between observers and between 

runs. Appendix C discusses these different contributions in detail and 

Table 5 presents estimates of observer measurement error (see E below). 

Table 4 shows the following: 

(i) In general, the standard deviations decrease with 

increasing averaging time but the decrease is • 

relatively small. This tends to indicate that the 

difference in mean deviations is relatively large 

between runs; and therefore, longer averaging times 
I I I I I f 

1/ Table 4. Estimates of the Standard Deviation of an Observer's Bias— 

2/ Mean True Opacity— 

itrii i 

By Averaging Time, Station, Smoke Type and 

Riverbend Steam Station, White Smoke, Average of Two Observers 

0-10 

10-20 

20-30 

30-40 

£40 

Overall 

2.1 

2.8 

5.7 

7.0 

5.5 

5.1 

1.8 

2.8 

6.1 

6.5 

3.8 

4.9 

1.7 

2.0 

6.0 

5.4 

4.7 

1.7 

1.9 

6.2 

5.4 

4.6 

1.7 

1.9 

5.2 

5.4 

4.3 

1.7 

1.9 

5.6 

5.2 

4.3 

-•— » .. . 

1.6 

1.9 

5.4 

6.3 

4.5 

Mean True 

Opacity (%) 

0-10 

10-20 

20-30 

30-40 

£40 

3/ Overall30 sec. 

X 

2.2 

4.4 

6.4 

6.5 

4.3 

5.8 

1 min. 

X 

1.8 

4.2 

6.1 

6.1 

5.6 

Smoke 

Contiguous Readings 

Averaging Time 

2 min.. 3 min. 4 min. 

% % % 

2.0 1.6 1.8 

3.4 4.0 4.2 

6.0 4.4 3.8 

6.2 5.3 

5.3 4.9 4.9 

Generator 

5 min. 

X 

3.6 

3.5 

4.5 

, Black Smoke 

6 min. 

X 

3.7 

3.1 

4.4 

No 

Highest 

2 

4.9 

5.6 

4.8 

6.0 

n-Contiguous Read! 

Averaging Time 

Highest Highest 

4 8 

4.3 

5.1 

5.2 

5.6 

3.4 

4.6 

6.0 

5.1 

ngs 

Highest 

12 

3.3 

4.0 

6.3 

4.7 

0-10 

10-20 

20-30 

30-40 

£40 

Overall 

3.1 

4.6 

6.2 

7.4 

5.9 

2.9 

4.5 

6.0 

7.1 

5.5 

2.9 

4.2 

6.0 

7.1 

5.4 

2.7 

3.8 

5.2 

7.0 

5.3 

Smoke 

2.3 

3.9 

4.5 

4.9 

Generator, 

2.5 

4.3 

4.4 

6.8 

5.0 

White Smoke 

1.8 

4.4 

5.1 

6.6 

5.0 

4.6 

5.0 

7.0 

6.6 

6.8 

2.4 

4.9 

7.0 

6.4 

6.3 

1.9 

4.2 

6.6 

5.5 

5.9 

1.9 

4.4 

5.8 

5.4 

5.4 

0-10 

10-20 

20-30 

30-40 

£40 

Overall 

2.7 

4.0 

6.8 

7.5 

7.0 

5.7 

2.3 

4.0 . 

7.0 

7.0 

5.6 

5.5 

2.3 

3.3 

7.0 

5.8 

5.3 

Riverbend Steam Station, White Smoke 

2.3 

3.2 

7.3 

5.8 

5.1 

2.2 

3.2 

6.3 

5.8 

4.9 

2.2 

3.1 

6.6 

5.6 

4.9 

2.1 

3.1 

6.4 

5.0 

2.9 

4.7 

7.0 

2.8 

4.6 

6.0 

6.3 

3.0 

4.0 

4.3 

5.5 

2.8 

3.4 

4.2 

5.2 

— The standard deviation given is the standard deviation of the estimated biases given in Table 3 and, therefore, 

this standard deviation contains contributions from differences between runs and observers (see Appendix C). 

2/ 

— Non-Contiguous Highest 2 and Contiguous readings defined in Table 1. 

3/ 

— Overall » Over all levels of mean true opacity. 

— = Sample size less than 15 observations. 
P.18 

14 

within a run do not appreciably reduce the overall 

s.d. (in fact, this conclusion is shown to be the 

case in Appendix C). 

(ii) The non-contiguous and contiguous readings have s.d.s 

which are about the same order of magnitude, 

(iii) It is obvious that as the range of mean true opacity 

increases so does the magnitude of the s.d.s. Thus, 

the s.d.s when mean true opacity is 20-30% are larger 

than when mean true opacity is 0-10%. 

(iv) As would be expected, the s.d.s for the average of 

two observers are somewhat less than the s.d.s based 

on only one observer. 

E. Estimates of An Observer's Measurement Error 

Table 5 presents estimates of observer measurement error for the contiguous readings by 4 averaging times, station, smoke type and for mean 

true opacity greater than 10%. The details of how these estimates were 

obtained are given in Appendix C. In brief, the estimates given in Table 5 

are the s.d. of an observer's mean deviations in repeated measurements 

during the same run. That is, the contributions to the s.d.s given in 

Table 4 from differences between observers and between runs have been removed. As would be expected, the estimate given in Table 5 show that as 

averaging time increases the measurement error of an observer decreases. 

This is to be expected, since the s.d. of an average based on n. observations will always be less than or equal to the s.d. based on an average 

of n_ observations, where n- > n„. 
P.19 

15 

Table 5. Estimates of the Measurement Error— of an Observer's Deviations 

2/ for Mean True Opacity >10%; By Averaging Time, Station, and Smoke Type— 

>10 

» 

Mean True Opacity 

>10 

Contiguous Readings 

Smoke Generator, Black Smoke 

Averaging Time 

30 sec. 1 min. 3 min. 6 min. 

4.2 4.1 2.8 1.9 

Smoke Generator, White Smoke 

3.6 2.6 2.3 1.8 

>10 

Riverbend Steam Station, White Smoke 

3.4 2.9 1.8 1.3 

1/ 

2/ 

Estimated Measurement Error *•» Estimated standard deviation of an 

observer's mean deviations in repeated measurements during the 

same run. All estimates based on sample sizes greater than 50. 

Appendix C gives the procedure used to estimate the measurement 

error. 
P.20 

16 

4. SUMMARY 

The present study, using qualified observer visual opacity readings 

collected by procedures set forth in EPA Reference Method 9, examined 

the effect of utilizing averaging times of less than 6 minutes to determine the opacity of smoke plumes (where a 6-minute averaging time • mean 

of 24 contiguous single 15-second opacity readings). In addition, the 

study also examined the effect of determining opacity as the average of 

non-contiguous 15-second opacity readings. The effect of the various contiguous and non-contiguous averaging times was assessed by comparing observer readings with true opactiy readings as determined by an in-stack 

transmissometer. The data analyzed were from two field tests conducted in 

1973 at the National Environmental Research Center, Research Triangle Park, 

North Carolina using two smoke generators with 9 qualified observers and 

in 1974 at the Riverbend Steam Station near Charlotte, North Carolina with 

4 qualified observers. The analysis of the data was done separately for 

black and white smoke plumes. The averaging times examined were 30 seconds, 

1 minute, 2 minutes, ..., 6 minutes. 

To determine the effect of the various averaging times, RTI computed 

several statistics by averaging time and level of mean true opacity. 

Although general conclusions are difficult to draw, an examination of 

these statistics indicated that in most cases a 3- or 4-mlnute averaging 

time determines average opacity (a) about as well as a 6-minute averaging time and (b) better than a 30-second averaging time. In addition, 

non-contiguous averaging times appear to be a relatively poor method of 

obtaining average opacity. 

More specifically, the statistics computed by RTI included the 
— 

— 

» 

_ 

* • 

« 

following: 

(D 

(11) 

17 

the percent of the frequency distribution for mean 

deviations (observer mean - true opacity mean) greater than 5% opacity (denote this statistic by A); 

the percent of the frequency distribution of mean 

P.21 

-

observed opacity greater than 10% (20%) opacity when 

mean true opacity is less than 10% (20%) (denote this 

statistic by B); 

(iii) the estimated bias of an observer's readings (where 

bias - observer mean - true opacity mean); 

(iv) the estimated standard deviation of an observer's bias; 

and 

(v) the estimated measurement error of an observer. 

Examination of these statistics indicated the following: 

(i) For contiguous readings, as averaging time Increases: 

Statistics A and B generally decrease 

(however, in many cases statistics A 

and B have about the same relative magnitude for a 3- or 4-minute averaging time 

as they do for a 6-minute averaging time); 

there is little effect on the estimated 

bias of an observer; 

the estimated standard deviation of an 

observer's bias decreases slightly; and 

the estimated measurement error of an 

observer always decreases, 

(ii) For non-contiguous readings (particularly, the aver-
P.22 

18 

age of the highest 2 and 4 non-contiguous readings) 

statistics A and B have relatively much larger magnitudes than for contiguous readings. These relatively large magnitudes for the non-contiguous readings 

indicate that this method of averaging observer 

opacity readings would give mean observed opacity greater than mean true opacity in a relatively -large number of 

cases. Thus, average percent opacity should probably 

not be obtained in this manner. The estimated observer biases for the non-contiguous readings are less 

negative than for the contiguous readings while estimated standard deviations of these biases are approximately the same as for the contiguous readings, 

(iii) In general, for the contiguous readings, the following statistics based on the average of two observers 

have somewhat smaller magnitudes than those based on 

one observer: 

A, B and the estimated s.d. of an observer's bias (Note, measurement error was 

not estimated based on the average of two 

observers), 

(iv) In general, as the level of mean true opacity increases: 

Statistics A and B decrease; 

the estimated bias of an observer becomes more negative; 

the estimated standard deviation of 
19 

an observer's bias increases; and 

the measurement error of an observer 

increases. 

The fact that the above statistics vary with level 

of mean true opacity, is the reason the tables presented by RTI in this report are given for different 

mean true opacity levels. 

Finally it should be noted that in carrying out the present study, 

RTI found that the sample sizes (number of means) available for (a) the 

contiguous averaging times of 4, 5 and 6 minutes and (b) the non-contiguous averaging - times, were severely limited (see, for example, Table 

1). Thus, many of the statistics computed for these averaging times 

were based on insufficient data. Accordingly, if accurate estimates of 

all the statistics presented in this report are desired, for these averaging times then additional data should be examined. In addition, the 

current data did not allow a direct investigation of state opacity regulations such as "opacity cannot exceed 20% for more than 3 minutes an 

hour." To accurately assess this regulation would require data on 

single minute opacity averages over one hour periods. If this type of 

data were available then frequency distributions of the highest 3 noncontiguous single minute averages in an hour could be examined directly. 
P.24 

20 

REFERENCES 

[1] Hammill, H. F., R. E. Thomas, and N. F. Swynnerton, "Evaluation and 

Collaborative Study of Method for Visual Determination of Opacity 

of Emissions from Stationary Sources," Environmental Monitoring 

Series, EPA-650/4-75-009, January 1975. 

[2] "EPA Response to Remand Ordered by U.S. Court of Appeals for the 

District of Columbia in Portland Cement Association V. Ruckelshaus 

(486 F. 2d 375)," EPA-450/2-74-023, November 1974. 

[3] Barr, Anthony J., and Goodnight, James H., A Users Guide to the 

Statistical Analysis System, Department of Statistics, North Carolina 

State University, August 1972. 

[4] Anderson, R. L. and Bancroft, T. A., Statistical Theory in Research, 

New York: McGraw-Hill Book Co., Inc., 1952. 
P.25 

Appendix A • 

Frequency Distributions of Mean Deviations 
P.26 

A-l 

Table A-l Frequency Distributions of Mean Deviations— 

(Over All Mean True Opaciites) for Contiguous 

2/ 

and Non-Contiguous Readings— ; By Averaging 

3/ Time, Station and Smoke Type— 

Smoke Generator, Black Smoke, Contiguous Readings 

Mean 

Deviation 

% 

<-20 

-20 to -15 

-15 to -10 

-10 to -5 

-5 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

1.0 

2.3 

7.1 

14.0 

32.6 

35.8 

6.8 

.4 

100 

1596 

1 min. 

% 

.8 

2.5 

8.5 

13.8 

32.3 

37.5 

4.4 

.3 

100 

798 

Averaging Time 

2 min. 

% 

0.0 

2.8 

8.5 

13.8 

34.1 

37.6 

3.0 

.3 

100 

399 

3 min. 

% 

0.0 

.8 

9.8 

15.0 

36.1 

36.5 

1.9 

0.0 

100 

266 

4 min. 

% 

0.0 

.8 

12.0 

9.0 

38.3 

39.1 

.8 

0.0 

100 

133 

5 min. 

% 

0.0 

.8 

10.5 

9.0 

40.6 

38.3 

.8 

0.0 

100 

133 

6 min. 

% 

0.0 

.8 

10.5 

10.5 

42.1 

35.3 

.8 

0.0 

100 

133 

Smoke Generator, White Smoke, Contiguous Readings 

<-20 

-20 to -15 

-15 to -10 

-10 to -5 

-5 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

.7 

1.2 

5.8 

13.5 

29.8 

37.3 

10.1 

1.6 

100 

2029 

.6 

1.0 

5.7 

13.1 

32.7 

37.9 

8.5 

.5 

100 

1015 

.6 

.8 

5.5 

13.8 

34.8 

36.4 

7.9 

.2 

100 

508 

.6 

0.0 

7.4 

13.6 

34.2 

36.0 

8.0 

.3 

100 

339 

.6 

0.0 

4.7 

14.2 

36.1 

35.5 

8.9 

0.0 

100 

169 

.6 

0.0 

3.5 

15.9 

39.4 

32.9 

7.6 

0.0 

100 

170 

.6 

0.0 

4.1 

15.3 

41.2 

31.8 

7.1 

0.0 

100 

170 
P.27 

A-2 

Table A-l Continued 

Riverbend Steam 

Mean 

Deviation 

% 

<-20 

-20 to -15 

-15 to -10 

-10 to -5 

-5 to 0 

0 to 5 

5 to 10 . 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

.3 

1.9 

5.2 

14.7 

28.3 

40.1 

7.3 

2.2 

100 

1152 

Station, 

1 min. 

% 

0.0 

1.9 

5.6 

14.2 

28.8 

41.8 

6.4 

1.2 

100 

576 

White Smoke, Contiguous 

Averaging Time 

2 min. 

% 

0.0 

1.7 

4.9 

14.9 

30.6 

40.6 

6.3 

1.0 

100 

288 

3 min. 

% 

0.0 

1.0 

7.8 

14.1 

29.2 

41.7 

5.2 

1.0 

100 

192 

4 min. 

% 

0.0 

1.0 

5.2 

13.6 

31.3 

42.7 

5.2 

1.0 

100 

96 

Reading 

5 min. 

% 

0.0 

2.1 

4.2 

11.4 

30.2 

46.9 

4.2 

1.0 

100 

96 

LS. 

6 min. 

% 

0.0 

1.0 

7.3 

10.4 

32.3 

43.8 

4.2 

1.0 

100 

96 

Riverbend Steam Station, White Smoke, Average of Two Observers, 

Contiguous Readings 

<-20 

-20 to -15 

-15 to -10 

-10 to -5 

-5 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.1 

1.7 

4.8 

11.9 

34.3 

40.9 

5.3 

1.0 

100 

1728 

0.0 

2.0 

4.9 

12.2 

33.8 

41.5 

5.3 

0.3 

100 

864 

0.0 

0.9 

6.5 

10.2 

36.1 

41.4 

4.4 

0.5 

100 

432 

0.0 

0.0 

6.9 

11.5 

34.0 

42.4 

4.9 

0.3 

100 

288 

0.0 

0.0 

5.5 

13.2 

35.4 

41.7 

4.2 

0.0 

100 

144 

0.0 

0.0 

6.2 

10.4 

36.8 

42.4 

4.2 

0.0 

100 

144 

0.0 

0.0 

5.5 

11.8 

36.1 

41.7 

4.9 

0.0 

100 

144 
P.28 

A-3 

Table A-l Continued 

Non-Contiguous Readings 

Smoke Generator, Black Smoke 

Mean • 

Deviation 

<-20 

-20 to -15 

-15 co -10 

-10 to -5 

-5 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

lighest 

2 

I 

0 

.9 

4.7 

11.7 

22.7 

36.7 

19.5 

3.9 

100 

128 

Averaging Time 

Highest 

4 

1 

0 

3.1 

3.1 

14.1 

21.9 

43.7 

13.3 

.9 

100 

128 

Highest 

8 

Z 

0 

.8 

7.0 

13.3 

28.1 

43.8 

6.3 

.8 

100 

128 

Highest 

12 

1 

0 

.8 

5.5 

18.0 

32.0 

40.6 

3.1 

0 

100 

128 

Smoke Generator, White Smoke 

Mean 

Deviation 

<-20 

-20 to -15 

-15 to -10 

-10 to -5 

-5 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

lighest 

2 

I 

.6 

.6 

5.6 

7.5 

21.3 

37.5 

18.8 

8.1 

100 

160 

Averaging 

Highest 

4 

I 

0.0 

2.5 

4.4 

9.4 

23.8 

36.9 

18.1 

.5.0 

100 

160 

Time 

Highest 

8 

I 

0.0 

2.5 

5.0 

11.9 

26.9 

35.0 

17.5 

1.3 

100 

160 

Highest 

12 

I 

0.0 

0.0 

6.3 

15.6 

26.9 

36.3 

13.8 

1.3 

100 

160 

Riverbend Steam Station, White Smoke 

<-20 

-20 to -15 

-15 to -10 

-10 to -5 

-5 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

1.0 

1.0 

6.3 

8.3 

26.0 

32.3 

19.8 

5.2 

100 

96 

0.0 

1.0 

7.3 

8.3 

25.0 

36.5 

18.8 

3.2 

100 

96 

0.0 

0.0 

6.3 

11.5 

28.1 

42.7 

9.4 

2.1 

100 

96 

0.0 

0.0 

3.1 

14.6 

29.2 

44.8 

6.3 

2.1 

100 

96 

1 / 

2/ 

— Mean Deviations « observer mean - true opacity mean 

3/ 

Contiguous 30 sec. • mean of 2 contiguous single 15-second readings. Non-Contiguous 

Highest 2 = mean of highest 2 non-contiguous single 15-second readings in a 6-minute 

observation period (i.e., in a run). 

— Table A-2 gives the frequency distributions by level of mean true opacity. 
P.29 

A-4 

1/ Table A-2 Frequency Distributions of Mean Deviations— for Contiguous 

2/ Readings— ; By Averaging Time, Station, Smoke Type and Mean 

True Opacity 

Smoke Generator, Black Smoke, Contiguous Readings 

Mean True Opacity ° 0 to 10% 

Mean 

Deviation 

% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

0.0 

0.0 

21.1 

73.0 

5.9 

0.0 

100 

270 

1 min. 

% 

0.0 

0.0 

20.5 

78.7 

0.8 

0.0 

100 

122 

Averaging Time 

2 min. 

% 

0.0 

0.0 

31.1 

68.9 

0.0 

0.0 

100 

74 

3 min. 4 min. 

%. % 

0.0 

0.0 

40.6 

59.4 

0.0 

0.0 

100 . 

32 

5 min. 

% 

-

6 min. 

% 

-

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.0 

2.6 

52.9 

35.3 

8.6 

0.6 

100 

730 

Mean True Opacity 

0.0 

2.7 

54.9 

35.8 

6.6 

0.0 

100 

366 

0.0 

0.0 

53.3 

40.6 

6.1 

0.0 

100 

165 

= 10 to 

0.0 

6.0 

47.7 

43.6 

2.7 

0.0 

100 

149 

20% 

0.0 

10.7 

49.3 

38.7 

1.3 

0.0 

100 

75 

0.0 

6.6 

46.1 

46.2 

1.1 

0.0 

100 

91 

0.0 

7.3 

50.0 

41.5 

1.2 

0.0 

100 

82 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

3.2 

10.5 

56.4 

23.1 

6.0 

0.8 

100 

381 

Mean True 

2.3 

11.2 

53.5 

•27.9 

4.2 

0.9 

100 

215 

Opacity 

0.0 

17.0 

56.0 

24.0 

2.0 

1.0 

100 

100 

» 20 to 

0.0 

4.0 

70.0 

24.0 

2.0 

0.0 

100 

50 

30% 

0.0 

3.0 

63.7 

33.3 

0.0 

0.0 

100 

33 

0.0 

3.0 

69.7 

27.3 

0.0 

0.0 

100 

33 

0.0 

2.9 

70.6 

26.5 

0.0 

0.0 

100 

34 
A-5 

Table A-2 Continued 

P.30 

Smoke Generator, Black Smoke, Contiguous Readings 

Mean 

Deviation 

% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

.5 

39.1 

42.6 

14.2 

3.6 

0.0 

100 

197 

Mean True 

1 min. 

% 

0.0 

53.5 

31.4 

13.9 

1.2 

0.0 

100 

86 

Opacity = 30 to 40% 

Averaging Time 

2 min. 

% 

0.0 

46.7 

40.0 

13.3 

0.0 

0.0 

100 

60 

3 min. 

% 

0.0 

48.6 

48.6 

2.8 

0.0 

0.0 

100 

35 

4 min. 

% 

-

5 min. 

% 

-

6 min. 

% 

-

Smoke Generator, White Smoke, Contiguous Readings 

0 to 10% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.0 

0.0 

22.9 

64.0 

11.3 

1.8 

100 

611 

0.0 

0.0 

28.9-

62.1 

8.7 

.3 

100 

343 

0.0 

0.0 

33.7 

50.2 

8.1 

0.0 

100 

184 

0.0 

0.0 

24.0 

64.0 

12.0 

0.0 

100 

100 

0.0 

0.0 

22.0 

74.0 

4.0 

0.0 

100 

50 

0.0 

0.0 

29.4 

66.7 

3.9 

0.0 

100 

51 

0.0 

0.0 

53.5 

46.5 

0.0 

0.0 

100 

43 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.0 

0.5 

52.7 

30.9 

13.3 

2.6 

100 

854 

Mean True 

0.0 

0.0 

56.0 

30.8 

12.2 

1.0 

100 

390 

Opacity 

0.0 

0.0 

60.9 

27.4 

11.2 

.5 

100 

179 

= 10 to 

0.0 

0.0 

59.5 

30.7 

9.2 

• 6. 

100 

153 

20% 

0.0 

0.0 

61.8 

22.4 

15.8 

0.0 

100 

76 

0.0 

0.0 

65.8 

19.7 

14.5 

0.0 

100 

. 76 

0.0 

0.0 

56.5 

30.4 

13.1 

0.0 

100 

92 
P.31 

A-6 

Table A-2 Continued 

Smoke Generator, White Smoke, Contiguous Readings 

Mean True Opacity - 20 to 30% 

Mean 

Deviation 

% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

0.5 

21.2 

51.8 

21.2 

5.3 

0.0 

100 

378 

1 min. 

% 

0.5 

20.8 

53.8 

20.8 

4.1 

0.0 

100 

197 

Averaging Time 

2 min. 

% 

0.0 

19.6 

52.9 

22.6 

4.9 

0.0 

100 

102 

3 min. 

% 

0.0 

28.3 

55.0 

15.0 

1.7 

0.0 

100 

60 

4 min. 

% 

0.0 

14.7 

64.7 

17.7 

2.9 

0.0 

100 

34 

5 min. 

% 

0.0 

7.7 

69.2 

23.1 

0.0 

0.0 

100 

26 

6 min 

% 

-

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

7.0 

31.2 

49.4 

11.3 

1.1 

0.0 

100 

186 

Mean True 

5.9 

31.8 

49.4 

12.9 

0.0 

0.0 

100 

85 

Opacity 

7.0 

27.9 

51.2 

13.9 

0.0 

0.0 

100 

43 

- 30 to 40% 

7.7 

30.7 

53.9 

7.7 

0.0 

0.0 

100 

26 -

Riverbend Steam Station, White Smoke, Contiguous Readings 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.0 

0.0 

17.0 

71.3 

9.8 

1.9 

100 

460 

Mean True 

0.0 

0.0 

14.9 

77.2 

7.9 

0.0 

100 

228 

Opacity 

0.0 

0.0 

16.7 

72.5 

10.8 

0.0 

100 

120 

» 0 to 

0.0 

0.0 

16.3 

72.5 

11.2' 

0.0 

100 

80 

10% 

0.0 

0.0 

12.5 

75.0 

12.5 

0.0 

100 

40 

0.0 

0.0 

10.0 

80,0 

10.0 

0.0 

100 

40 

0.0 

0.0 

15.0 

75.0 

10.0 

0.0 

100 

40 
P.32 

A-7 

Table A-2 Continued 

Riverbend Steam Station, White Smoke, Contiguous Readings 

Mean True Opacity = 10 to 20% 

Mean 

Deviation 

% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

0.0 

0.3 

69.2 

25.3 

4.6 

.6 

100 

308 

1 min. 

% 

0.0 

0.0 

69.2 

25.0 

5.1 

.7 

100 

156 

Averaging Time 

2 min. 

% 

0.0 

0.0 

76.4 

23.6 

0.0 

0.0 

100 

72 

3 min. 4 min. 

% % 

0.0 0.0 

0.0 0.0 

77.1 75.0 

22.9 25.0 

0.0 0.0 

0.0 0.0 

100 100 

48 24 

5 min. 

% 

0.0 

0.0 

70.8 

29.2 

0.0 

0.0 

100 

24 

6 min. 

% 

0.0 

0.0 

75.0 

25.0 

0.0 

0.0 

100 

24 

<-20 

r-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.0 

10.9 

59.4 

18.9 

6.1 

4.7 

100 

212 

Mean True 

0.0 

12.5 

58.0 

18.8 

5.4 

5.3 

100 

112 

Opacity 

0.0 

11.5 

57.7 

19.2 

5.8 

5.8 

100 

52 

=» 20 to 30% 

0.0 

17.9 

57.1 

17.9 

0.0 

7.1 

100 

28 - -

Mean True Opacity = 30 to 40% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

1.5 

33.3 

44.0 

11.4 

6.8 

3.0 

100 

132 

0.0 

35.9 

50.0 

6.3 

7.8 

0.0 

100 

64 

0.0 

32.5 

60.0 

2.5 

5.0 

0.0 

100 

40 

0.0 

37.5 ' 

50.0 

9.4 

3.1 

0.0. 

100 

32 -
P.33 

A-8 

Table A-2 Continued 

Riverbend Steam Station, White Smoke, Average of Two Observers, 

Contiguous Readings 

Mean True Opacity = 0 to 10% 

Mean 

Deviation 

% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

0.0 

0.0 

13.2 

79.4 

6.4 

1.0 

100 

690 

1 min. 

% 

0.0 

0.0 

12.3 

82.7 

5.0 

0.0 

100 

342 

Averaging Time 

2 min. 

% 

0.0 

0.0 

10.6 

84.4 

5.0 

0.0 

100 

180 

3 min. 

% 

0.0 

0.0 

6.7 

86.6 

6.7 

0.0 

100 

120 

4 min. 

% 

0.0 

0.0 

8.3 

85.0 

6.7 

0.0 

100 

60 

5 min. 

% 

0.0 

0.0 

6.7 

86.6 

6.7 

0.0 

100 

60 

6 min. 

% 

0.0 

0.0 

6.7 

86.6 

6.7 

0.0 

100 

60 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.0 

0.0 

80.7 

17.1 

2.2 

0.0 

100 

462 

Mean True 

0.0 

0.0 

81.6 

15.8 

2.2 

.4 

100 

234 

Opacity 

0.0 

0.0 

89.8 

10.2 

0.0 

0.0 

109 

108 

» 10 to 

0.0 

0.0 

91.7 

8.3 

0.0 

0.0 

100 

72 

20% 

0.0 

0.0 

94.4 

5.6 

0.0 

0.0 

100 

36 

0.0 

0.0 

94.4 

5.6 

0.0 

0.0 

100 

36 

0.0 

0.0 

94.4 

5.6 

0.0 

0.0 

100 

36 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

0.0 

7.2 

63.5 

18.3 

7.9 

3.1 

100 

318 

Mean True 

0.0 

10.7 

60.7 

16.7 

10.7 

1.2 

100 

168 

Opacity 

0.0 

10.3 

62.8 

12.8 

11.5 

2.6 

100 

78 

- 20% 

0.0 

11.9 

64.3 

11.9 

9.5-

2.4 

100 

42 

to 30% 

0.0 

8.3 

75.0 

8.4 

8.3 

0.0 

100 

24 

0.0 

12.5 

70.9 

8.3 

8.3 

0.0 

100 

24 

0.0 

6.7 

80.0 

3.3 

10.0 

0.0 

100 

30 
P.34 

A-9 

Table A-2 Continued 

Riverbend Steam Station, White Smoke, Average of Two Observers, 

Contiguous Readings 

Mean True Opacity = 30 to 40% 

Mean Averaging Time 

Deviation 

% 

<-20 

-20 to -10 

-10 to 0 

0 to 5 

5 to 10 

10 to 15 

Total 

Sample Size 

30 sec. 

% 

0.5 

35.8 

47.0 

9.6 

6.6 

0.5 

100 

198 

1 min. 

% 

0.0 

36.5 

45.8 

11.5 

6.2 

0.0 

100 

96 

2 min. 

% 

0.0 

40.0 

51.6 

6.7 

1.7 

0.0 

100 

60 

3 min. 

% 

0.0 

31.2 

56.3 

8.3 

4.2 

0.0 

100 

48 

4 min. 

% 

0.0 

25.0 

54.2 

20.8 

0.0 

0.0 

100 

24 

5 min. 

% 

0.0 

25.0 

54.2 

20.8 

0.0 

0.0 

100 

24 

6 min. 

% 

-

— Mean Deviations - observer mean - true opacity mean. 

2/ 

-<• Contiguous 30 sec. = mean of 2 contiguous single 15-second readings. 

- =» Sample size less than 20 observations. 
Appendix Table A-3 Percent of Frequency Distribution for Mean Deviations— £0 Percent Opacity; By 

2/ Averaging Time, Station, Smoke Type and Mean True Opacity— 

Mean True 

Opacity (%) 

0-10 

10-20 

20-30 

30-40 

3/ Overall30 sec. 

% 

78.9 

45.2 

29.9 

17.8 

43.0 

1 min. 

% 

79.5 

42.4 

33.0 

15.1 

42.2 

Smoke 

Contiguous Readings 

Averaging Time 

2 min. 3 min. 4 min. 

X X X 

68.9 59.4* 

46.7 46.3 

27.0 26.0 

13.3 2.8* 

• 40.9 38.4 

40.0 

33.3* 

39.9 

Generator 

5 min. 

% 

47.3 

27.3* 

39.1 

, Black Smoke 

Non-Contiguous Readings 

6 min. 

% 

42.7 

26.5* 

36.1 

Highest 

2 

79.3 

44.7* 

60.1 

Averaging Time 

Highest Highest 

4 8 

72.4 

45.5* 

57.9 

64.9 

43.5* 

35.0* 

50.9 

Highest 

12 

59.0 

31.7* 

19.0* 

43.7 

0-10 

10-20 

20-30 

30-40 

Overall 

77.1 

46.8 

26.5 

12.4 

49.0 

71.1 

44.0 

24.9 

12.9 

46.9 

66.3 

39.1 

27.5 

13.9* 

44.5 

76.0 

40.5 

16.7 

7.7* 

44.3 

Smoke 

78.0 

38.2 

20.6* 

44.4 

Generator, 

70.6 

34.2 

23.1* 

40.5 

White Smoke 

46.5* 

43.5 

38.9 

79.0 

44.8* 

17.4* 

64.2 

100.0* 

69.6 

35.0* 

60.0 

61.9 

23.8* 

53.8 

59.7 

21.8* 

51.4 

T 

0-10 

10-20 

20-30 

30-40 

rail 

83.0 

30.5 

29.7 

21.2 

49.6 

85.1 

30.8 

29.5 

14.1 

49.4 

83.3 

23.6 

30.8 

7.5* 

47.9 

83.7 

22.9* 

25.0 

12.5* 

47.9 

Steam Station, 

87.5* 

25.0* 

48.9 

90.0* 

29.2* 

52.1 

White Smoke 

85.0* 

25.0* 

49.0 

90.5* 

66.6* 

57.3 

88.3* 

63.4* 

58.5 

86.9* 

88.4* 

45.0* 

54.2 

87.5* 

37.. 5* 

55.0* 

53.2 

0-10 

10-20 

20-30 

30-40 

Overall 

86.8 

19.3 

29.3 

16.7 

47.2 

87.7 

18.4 

28.6 

17.7 

47.1 

89.4 

10.2 

26.9 

8.4 

46.3 

93.3 

8.3 

23.8* 

12.5* 

47.6 

91.7 

5.6* 

16.7* 

20.8* 

45.9 

93.3 

5.6* 

16.6* 

20.8* 

46.6 

«_:*.:,.-i 

93.3 

5.6* 

13.3* 

46.6 

Mean Deviations •= Observed mean - true opacity mean. 

Non Contiguous Highest 2 and contiguous readings defined ln Table A-l. 

1/ 

If 

3/ 

— Overall = over all levels of mean true opacity. 

* = Sample size between 20 and 50 observations. 

- = Sample size less than 20 observations. 

co 

Ol 
P.36 

Appendix B 

Frequency Distributions of Mean Observed Opacity 

for Mean True Opacity Less Than 20 Percent 

and Mean True Opacity Less Than 10 Percent 
P.37 

B-1 

Table B-1 Frequency Distributions of Mean Observed Opacity When 

Mean True Opacity <20% for Contiguous and Non-Contiguous 

Readings— ; By Averaging Time, Station and Smoke Type 

Smoke Generator, Black Smoke, Contiguous Readings 

Mean 

Observed 

Opacity 

0 to 5 

5 to 10 

10 to 15 

.15 to 20 

20 to 25 

25 to 30 

30 to 35 

>35 

Total 

Sample Size 

30 sec. 

% 

2.3 

20.8 

39.1 

25.4 

10.8 

1.6 

0.0 

0.0 

100 

1000 

1 min. 

% 

3.3 

23.4 

44.5 

21.9 

6.6 

.4 

0.0 

0.0 

100 

488 

Averaging Time 

2 min. 

% 

.8 

28.5 

44.8 

18.8 

7.1 

0.0 

0.0 

0.0 

100 

239 

3 min. 

% 

2.2 

27.1 

44.2 

16.6 

8.8 

1.1 

0.0 

0.0 

100 

181 

4 min. 

% 

6.6 

14.3 

60.4 

16.5 

2.2 

0.0 

0.0 

0.0 

100 

91 

5 min. 

% 

5.5 

13.2 

59.3 

18.7 

3.3 

0.0 

0.0 

0.0 

100 

91 

6 min. 

% 

2.2 

17.7 

56.7 

21.1 

2.2 

0.0 

0.0 

0.0 

100 

90 

Smoke Generator, White Smoke, Contiguous Readings 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

30 to 35 

>35 

Total 

Sample Size 

2.5 

33.2 

38.5 

16.4 

7.5 

1.8 

0.0 

0.0 

100 

1465 

3.8 

36.6 

38.7 

13.4 

6.4 

1.1 

0.0 

0.0 

100 

733 

6.1 

39.7 

37.7 

12.4 

3.9 

.3 

0.0 

0.0 

100 

363 

7.5 

34.4 

39.5 

9.9 

8.3 

.4 

0.0 

0.0 

100 

253 

1.6 

42.9 

37.3 

8.7 

9.5 

0.0 

0.0 

0.0 

100 

126 

.8 

48.0 

33.1 

12.6 

5.5 

0.0 

0.0 

0.0 

100 

127 

.7 

45.2 

31.1 

20.0 

3.0 

0.0 

0.0 

0.0 

100 

135 
Table B-1 Continued 

P.38 

Riverbend Steam Station, White Smoke, Contiguous Readings 

Mean 

Observed 

Opacity 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

30 to 35 

>35 

Total 

Sample Size 

30 sec. 

% 

2.0 

58.1 

26.8 

11.1 

1.8 

.1 

.1 

0.0 

100 

768 

1 min. 

% 

2.9 

62.0 

24.2 

9.6 

1.3 

0.0 

0.0 

0.0 

100 

384 

Averaging Time 

2 min. 

% 

4.2 

60.9 

27.6 

7.3 

0.0 

0.0 

0.0 

0.0 

100 

192 

3 min. 

% 

4.7 

62.5 

26.6 

6.2 

0.0 

0.0 

0.0 

0.0 , 

100 

128 

4 min. 

% 

4.7 

56.2 

34.4 

4.7 

0.0 

0.0 

0.0 

0.0 

100 

64 

5 min. 

% 

4.7 

57.8 

29.7 

7.8 

0.0 

0.0 

0.0 

0.0 

100 

64 

6 min. 

% 

3.1 

64.1 

25.0 

7.8 

0.0 

0.0 

0.0 

0.0 

100 

64 

Riverbend Steam Station, White Smoke, Average of Two Observers, 

Contiguous Readings 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

30 to 35 

>35 

Total 

Sample Size 

3.6 

60.4 

29.3 

6.1 

0.4 

0.2 

0.0 

0.0 

100 

1152 

5.2 

62.3 

27.4 

4.9 

0.2 

0.0 

0.0 

0.0 

100 

576 

6.6 

61.8 

28.5 

3.1 

0.0 

0.0 

0.0 

0.0 

100 

288 

7.8 

61.5 

28.1 

2.6 

0.0 

0.0 

0.0 

0.0 

100 

192 

6.3 

62.5 

28.1 

3.1 

0.0 

0.0 

0.0 

0.0 

100 

96 

8.3 

59.4 

28.1 

4.2 

0.0 

0.0 

0.0 

0.0 

100 

96 

6.3 

63.5 

28.1 

2.1 

0.0 

0.0 

0.0 

0.0 

100 

96 
P.39 

B-3 

Table B-1 Continued 

Non-Contiguous Readings 

Smcke Ccncraccr. Slack Smoke 

licai. 

Observed 

Opacity 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

30 to 35 

>35 

Total 

Sample 

Size 

Highest 

2 

I 

0 

0 

15.5 

39.7 

37.9 

6.9 

0 

0 

100 

58 

.-i w ti I a g. L 

Highest 

4 

I 

0 

0 

23.3 

48.3 

2.5 

3.3 

0 

0 

100 

60 

l i g 1 i.Ult---

Highest 

8 

1 

0 

5.2 

34.5 

46.6 

12.1 

1.7 

0 

0 

100 

58 

Highest 

12 

_% 

0 

10.6 

37.9 

34.8 

13.6 

3.0 

0 

0 

100 

66 

Smcke Generate: V.liite Seek 

L'lcaii 

Observed 

Opacity 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

30 to 35 

>35 

Total 

Sample 

Size 

Highest 

2 

Z 

0.0 

3.0 

31.3 

35.4 

13.1 

16.2 

1.0 

0.0 

100 

99 

r.vferagi 

Highest 

4 

I 

0.0 

3.7 

34.7 

34.7 

14.9 

11.9 

0.0 

0.0 

100 

101 

:.£ iiZle 

Highest 

8 

% 

0.0 

9.8 

45.1 

24.5 

16.7 

3.9 

0.0 

0.0 

100 

102 

Highest 

12 

_% 

0.0 

18.8 

45.5 

15.2 

18.8 

1.9 

CO 

0.0 

100-

112 

Riverbend Steam 

Z to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

30 to 35 

>35 

Total 

Sample Size 

0 

21.7 

36.7 

23.3 

16.7 

1.7 

0 

0 

100 

60 

Station, 

0 

35.9 

28.1 

25.0 

10.9 

0 

0 

0 

100 

64 

White Smoke 

0.0 

42.2 

35.9 

14.1 

7.8 

0 

0 

0 

100 

64 

0.0 

51.6 

29.7 

18.8 

0.0 

0.0 

0.0 

0.0 

100 

64 

— Non-contiguous and contiguous readings defined in Table A-l. 
B-4 

P.40. 

Table B-2 Frequency Distributions of Mean Observed Opacity 

When Mean True Opacity < 10% for Contiguous and 

1/. Non-Contiguous ReadingsStation, and Smoke Type 

By Averaging Time, 

Smoke Generator, Black Smoke, Contiguous Readings 

Mean 

Observed 

Opacity 

0 to 5 " 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

Total 

Sample Size 

30 sec. 

% 

2.6 

45.2 

47.0 

5.2 

0.0 

0.0 

100 

270 

1 min. 

% 

4.1 

44.3 

51.6 

0.0 

0.0 

0.0 

100 

122 

Averaging Time 

2 min. 

% 

2.7 

58.1 

39.2 

0.0 

0.0 

0.0 

100 

74 

3 min. 4 

% 

0.0 

65.6 

34.4 

0.0 

0.0 

0.0 

100 

32 

min. 

% 

— 

5 min. 

% 

— 

6 min. 

. '/ 

— 

Smoke Generator, White 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

Total 

Sample Size 

5.6 

53.0 

32.7 

7.7 

1.0 

0.0 

100 

611 

7.9 

52.5 

33.2 

6.1 

0.3 

0.0 

100 

343 

Smoke, 

12.0 

51.1 

30.4 

6.5 

0.0 

0.0 

100 

184 

Contiguous 

18.0 

39.0 

33.0 

10.0 

0.0 

0.0 

100 

100 

Readings 

4.0 

50.0 

42.0 

4.0 

0.0 

0.0 

100 

50 

2.0 

54.9 

39.2 

3.9 

0.0 

0.0 

100 

51 

2.3 

83.7 

14.0 

0.0 

0.0 

0.0 

100 

43 

Riverbend Steam 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

Total 

Sample Size 

3.3 

77.0 

15.7 

3.9 

0.2 

0.0 

100 

460 

Station, 

4.8 

82.0 

10.5 

2.6 

0.0 

0.0 

100 

228 

White Smoke 

6.7 

76.7 

13.3 

3.3 

0.0 

0.0 

100 

120 

., Cont 

7.5 

77.5 

12.5 

2.5 

0.0 

0.0 

100 

80 

Lguous Readings 

7.5 

70.0 

22.5 

0.0 

0.0 

0.0 

100 

40 

7.5 

75.0 

15.0 

2.5 

0.0 

0.0 

100 

40 

5.0 

80.0 

12.5 

2.5 

0.0 

0.0 

100 

40 
P.41 

B-5 

Table B-2 Continued 

Riverbend Steam Station, White Smoke, Average of Two Observers, 

Contiguous Readings 

Mean 

Observed 

Opacity 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

Total 

Sample Size 

30 sec. 

% 

6.1 

79.6 

12.8 

1.6 

0.0 

0.0 

100 

690 

1 min. 

% 

8.8 

81.9 

8.2 

1.2 

0.0 

0.0 

100 

342 

Averaging Time 

2 min. 3 min. 

% % 

10.6 12.5 

75.0 75.8 

11.7 9.2 

2.8 2.5 

0.0 0.0 

0.0 0.0 

100 100 

180 120 

4 min. 

% 

10.0 

75.0 

15.0 

0.0 

0.0 

0.0 

100 

60 

5 min. 

% 

13.3 

75.0 

8.3 

3.3 

0.0 

0.0 

100 

60 

6 min. 

% 

10.0 

81.7 

8.3 

0.0 

0.0 

0.0 

100 

60 

Smoke Generator, White Smoke, Non-Contiguous Readings 

Highest 

2 

Highest 

4 

Highest 

8 

Highest 

12 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

Total 

Sample Size 

0.0 

18.2 

68.2 

13.6 

0.0 

0.0 

100 

22 

52.0 

44.0 

4.0 

0.0 

0.0 

0.0 

100 

25 

Steam Station, White Smoke, Non-Contiguous Readings 

0 to 5 

5 to 10 

10 to 15 

15 to 20 

20 to 25 

25 to 30 

Total 

Sample Size 

0.0 

36.4 

48.5 

15.2 

0.0 

0.0 

100 

33 

0.0 

64.7 

26.5 

8.8 

0.0 

0.0 

100 

34 

0.0 

63.2 

28.9 

5.3 

2.6 

0.0 

100 

38 

0.0 

72.5 

20.0 

7.5 

0.0 

0.0 

100 

40 

— Non-contiguous and contiguous readings defined in Table A-l. 

- = Sample size less than 20 observations. 
P.42 

Appendix C 

Estimation of the Measurement Error of An Observer 
P.43 

C-1 

Estimation of the Measurement Error of An Observer 

In Section 3 of this report, mention was made of the various contributions to the variance of mean deviations over all runs and observers 

(e.g., between run variation, measurement error...). In this appendix, a 

description is given of how RTI estimated these contributions for different 

averaging times. In particular, RTI was interested in removing the contributions to the variance of mean deviations of differences between runs 

and observers so that an observer's measurement error (i.e., the s.d. of 

an observer's deviations in repeated measurements) could be examined for 

different averaging times. 

To begin with RTI assumed that the following model represented the 

mean deviation, Y, , , for run i, observer j and averaging time t: 

Yijk = u + Ri + °j + ROij + eijk i = 1,2,... ,r; (C-1) 

j » 1,2,...,o; and 

k =• 1,2,.. .,n(t). 

where r = number of runs, 

o = number of observers, 

n(t) = number of averaging times per run per observer for averaging 

time t (e.g., n(t) = 1 for a 6-minute averaging time), 

u = overall mean which is a constant, 

2 

R. *-» effect of run i with zero mean and variance a , i r 

2 

0. = effect of observer j with zero mean and variance a , 

3 o 

RO.. = effect of interaction between observer j and run i with zero 

1J 2 

mean and variance a , 

ro 

e.., = random error for t averaging time with zero mean and 

variance a (i.e., square of observer measurement error). 

2 

The model given in (C-1) is called a variance components model and a , 
C-2 

2 2 2 <z , 7 and a are called variance components. Using the above model, 

o ro et 

the variance of Y , is given by: 

Var(Y,(^) = o2 + a2 + a2 + a* (C-2) 

ijk r o ro et 

Equation (C-2) represents the variance of mean deviations taken over runs 

and observers. The standard deviations given in Table 4 of this report 

estimate the square root of Equation (C-2) for various averaging times. • 

However, if one is only interested in estimating the variance of a single 

observer in repeated measurements during the same run (i.e., observer 

"2 

measurement error) then an estimate of only a is desired. Thus, Table 5 

of this report presents estimates of Wo = a . 

2 2 2 

In order to estimate the variance component a (as well as a , o 

2 

and a ) RTI used the Analysis of Variance Procedure (see [4]) which 

ro 

equates calculated mean squares to their expected values and solves the 

resulting equations for the variance components. Table C-1 presents the 

2 2 2 2 resulting estimates of o , a , a and a by averaging time, station and 

2 smoke type. Note in the table that the estimate of o is equal to the 

Error MS (except for averaging time = 6 minutes) since the expected value 

2 

of the Error MS under model (C-1) is equal to o . For averaging time 

equal to 6 minutes there is only one observation per run; and therefore, 

2 2 the expected value of the Error MS is equal to CJ + a Thus, in this 

ro et 

2 "2 *2 

case RTI estimated a as u = MSE - a (at 3 minutes). The estimates 

et et ro 

2 2 2 

of a , a and a in the table are approximate estimates (slightly biased) 

in the sense that the expected mean squares were assumed to be for balanced 

data (i.e., equal numbers of observations for each run and observer). 

However, this bias should be small. It is also important to note that the 

estimates given in Table C-1 are only for averaging times where mean true 
P.45 

C-3 

opacity is greater than 10 percent. RTI computed the estimates for this 

level of true opacity to account somewhat for the fact that the variance 

of mean deviations depends on the level of mean true opacity (this is 

quite evident in Table 4). The estimates for mean true opacity less 

than 10 percent were not computed in the present study. 

"2 Table C-1 indicates, as one would expect, that a decreases significantly with averaging time while in general a , a and a do not. This 

is due to the fact that increasing the averaging time implies averaging 

over additional observations within a run and observer; and therefore, only 

2 2 2 

a is affected. The table also indicates that o is much larger than a . 

et r ° o 

2 2 2 Tests of significanc 6 e of a , a and a indicate, for almost all cases 

 r o ro 

given in Table C-1, that these variance components are significantly 

different from zero. 

~2 

In examining the estimates of a given in Table C-1, one would expect that the estimates for a 6-minute averaging time would be even smaller 

than observed, relative to a 30-second averaging time if an observer's 

readings within a run were uncorrelated. However, the presence of correlation between contiguous readings by an observer tends to somewhat reduce the effect of averaging. As an example of the effect of this correlation, consider the following: 

Suppose that the variance of an observer's reading (X.) within 

2 

a run = a . Now if one averages two of the observer's readings 

(X.. and X_) within the run and the readings are independent, 

then the variance of the average will be 

X,+X, a

2

 , 

TT / 1 2^ e . 2 Var(—=—) = —-r = .5 a . 

z i. e 

However, if the two readings are not independent but have a 
P.46 

C-4 

correlation = r, then the variance of the average will be 

Xl+ X2 ae Var(-^—£) =-f (2+2r). 

Thus, if r a .8 then 

X.+X, 3.6 a2 ' 

VarH^ ) - —,-S - = .9 a

l

& 

and the averaging of the two correlated readings has decreased 

the variance by a relatively small amount compared to the case 

of averaging two independent readings. 
C-5 

Table C-1. Analysis of Variance and Estimates of Variance Components 

for Mean True Opacity >10%; By Averaging Time, Station 

j c , -r 1/2/ 

and Smoke Type 

Source of 

Variation 

Run 

Observer 

Run x Observer 

Error 

TOTAL 

Estimates 

of,Variance 

Components 

"2 

a =

B 

r 

n

2 

a = 

'2 

a = 

ro 

'2 

et 

30 

df 

15 

^ 

45 

532 

595 

Smoke Generator, 

sec. 

MS 

641.00 

605.00 

54.24 

17.34 

15.77 

3.70 

3.97 

17.34 

Black 

Averaging Time 

1 min. 

df MS 

15 325.20 

3 290.67 

45 27.71 

240 16.63 

303 

15.66 

3.46 

2.34 

16.63 

3 

df 

15 

3 

45 

48 

111 

Smoke 

min. 

MS 

115.27 

88.67 

9.36 

7.86 

15.13 

2.83 

.85 

7.86 

6 

df 

14 

3 

— 

42 

59 

min. 

MS 

64.29 

37.00 

4.48 

14.95 

2.17 

3.63^ 

Run 

Observer 

Run x Observer 

Error 

TOTAL 

Estimates 

of Variance 

Components 

. 2 

a =• 

r -2 

a = 

o 

~2 

a = 

ro 

~2 

a ,. = 

et 

df 

18 

32/ 

54 

512 

587 

MS 

693.44 

72.00 

43.07 

12.66 

20.99 

.20 

3.92 

12.66 

moke 

df 

17 

3 

51 

232 

303 

Generator, 

MS 

393.41 

48.67 

21.63 

6.54 

22.02 

. .36 

3.58 

6.54 

White 

df 

17 

3 

51 

32 

103 

Smoke 

MS 

114.53 

15.23 

7.06 

5.20 

18.66 

.32 

1.29 

5.20 

df 

13 

3 

— 

39 

55 

MS 

92.38 

3.33 

4.38 

22.00 

.00 

3.09^ 
C-6 

Table C-1. Continued 

Source of 

Variation 

Run 

Observer 

Run x Observer 

Error 

TOTAL 

Estimates 

of Variance 

Components 

«2 

a = 

r ~2 

a =• 

0 

"2 

a =• 

r o 

~2 

<* -

 a 

et 

30 

df 

15 

3 

45 

604 

667 

Riverbend Steam Station, White Smoke 

sec. 

MS 

776.47 

565.00 

103.73 

11.61 

16.17 

2.77 

8.86 

11.61 

Averaging Time 

1 min. 

df MS 

15 408.13 

3 372.33 

45 52.20 

276 8.64 

339 

16.79 

3.78 

8.20 

8.64 

3 

df 

13 

3 

39 

56 

111 

min. 

MS 

146.54 

146.67 

19.03 

3.40 

15.94 

4.56 

7.82 

3.40 

6 

df 

13 

3 

— 

39 

55 

min. 

MS 

73.23 

73.33 

9.51 

15.87 

4.54 

1.69*/ 

— Analysis for contiguous readings only. 

2/ 

— df

 3 degrees of freedom, MS = mean square 

3/ 

— For the smoke generator, only data from 4 of the 9 observers was used 

to estimate the variance components. This was done to eliminate a 

computational problem due to the relatively large number of degrees 

of freedom for the interaction between runs and observers. 

4/ "2 2 2 

— a estimated for 6 minutes by assuming a for 6 minutes • a for 

e ro- ro 

3 minutes; e.g., for black smoke at 6 minutes; a = 4.48 - .85 =» 3.63. 

et