The data from the baseline period was initially examined to determine if significant differences existed between the three offices. If the three offices differ then the main data set should be adjusted for these differences by treating the baseline data as a covariate. The baseline data did not represent a perfectly level 'playing field' as is discussed in Chapter Two (Experimental Methodology). However it will still be of use in determining if office differences are present.
The ANOV A was run on the following data sets and the residual data was examined
to check that assumptions were met:
1. BW 4 Baseline data, week four only (three week washout);
2. BSW 4 Baseline screened data, week four only;
3. BW2-4 Baseline data, weeks 2-4 (one week washout); 4. BSW2-4 Baseline screened data, weeks 2-4.
A ssumption s underlying th e Analysis of Variance
The standardised residual data was used to check that the assumptions of normality and homogeneity of variance were met. The normality assumption was v isually examined using normal probability plots and histograms. The Shiparo-Wilks test statistic (S-W), skewness and kurtosis values were also calculated.
The normal probability plots and histograms revealed moderate non-normality. Typical examples of these graphs are shown in Figure 20 and Figure 2 1 . Skew and kurtosis values for the data sets were within the acceptance range. However all data sets gave significant Shiparo-Wilks test statistic (0.000 I <p<0.002), with data sets BW4 and BSW4 (three week washout period) showing greater non normality.
Figure 20. Standardised residual histogram plot of lethargy symptom severity with normal curve superimposed (Data set BW2-4).
40
-2.4 -1.6 -o.a 0.0 0.8 I...E1lil\RiV STOOARDISED RESIDUALS Cunle: -Normai(MJ= 31E-17 Sigml= 1.0078)
The homogeneity of the treatment data set was visually examined using standardised residual plots and by Levene's test. The majority of tests gave statistically significant values for Levene's test (O.OOOI<p<O. l ). It was clear from the standardised residual plots that Office Two had much greater variability than Offices One and Three in the majority of the data sets (Figure 22).
Figure 21. Standardised residual normal probability plot of baseline lethargy symptoms(Data set BW2-4)
0 2 21 a: x � 0 -1 • 6 10 26 15 Normal Perc:elllles
-· UrMo: -M.r- 31E-17. 81gma=1.00711
90 96 19
Examination of the extreme data points revealed that only one data point was a probable outlier. This data point was from an occupant in Office Two, who only gave one response that was included in Data Sets BW4 and BSW4. The reported symptom was substantially higher than other responses. This data point was excluded from the fmal analyses.
The variance in the majority of data sets was substantial, in some cases greater than the mean value for the offices, suggesting that transformation of the raw data may be appropriate. A comparison of the standard error for the raw and transformed data sets showed that this value may be able to be reduced by a log transformation of the data. However, as results from the baseline analysis showed similar patterns to that of the main data set49, transformations were not undertaken.
Office Differen ces - Eyestrain, Headach e a n d Lethargy Sympto m s
The results (Table 20) indicate that participants in Office Two reported higher average symptom severity than either Office One or Three. In Data Sets BW2-4 and BSW2-4, eyestrain, headache and lethargy symptoms were significantly more severe in Office
Two. For Data Set BW4 and BSW4 only eyestrain symptoms were significantly more
severe.
Figure 22. Residual vs predicted lethargy symptom severity (Data set BW2-4) c � [] 15. 2 l 0 [] -+ 0 B ID 0 � 1 8 c $ c ! • 0 .J -+ 8
1
1 -1 ��
�
c a: B -2 OFFICE o o o 1WO + + � 01£ o o o T�D iscussio n : Baselin e L igh ting Treatment Data
The intention of this analysis was to determine if the symptoms experienced by participants varied between the offices, therefore no further analysis was carried out on the data. It was clear from the results thus far, that although the data sets did not meet all ANOV A assumptions, Office Two was sufficiently different in a number of the analyses to suggest that differences between offices may be influential. However, these results should be interpreted with some caution. As was discussed in the introduction, the baseline data was not produced in a homogenous environment, and this may have affected the level of symptoms reported by the participants. In addition, the baseline data does not meet all the ANOV A assumptions and not all analyses showed that office differences were present. While ANOV A is robust to small violations of normality and homogeneity, the other limitations of the data sets suggests caution. As previously discussed, data sets BW4 and BSW4 were collected when participants were probably adapted to the baseline conditions, but only a small number of data points were used in the analysis. This was reflected in the variance in the data sets.
Given the possible flaws in the baseline data it would be inappropriate to only consider analyses that treat the baseline period as a covariate. However, these
analyses should certainly be included in order to enable useful inferences to be made.
Data sets BW2-4 and BSW2-4 were treated as covariates in analyses CW-CVB and
SW-CVB respectively.
Table 20. Results of AN OVA - Baseline data.
Data set BW4 - Complete data set: three-week washout
Symptom MSE F Test p-value Treatment Mean Dun
value 5° Eyestrain 0.97 5 . 1 7 0.01 Off. 1 1 0 1 . 1 8 B symptoms Off. 2 1 5 2.30 A Off. 3 12 1 .3 1 B 0.90 2.2 1 0. 1 3 Off. 1 1 0 1 .49 A symptoms Off. 2 14 2.05 A Off. 3 1 2 1 .30 A Lethargy 1 .22 1 .5 0.23 Off. I 1 0 1 .44 A symptoms Off. 2 I S 2.20 A Off. 3 12 2.03 A
Data set BSW4 - Screened data set: three week washout
Eyestrain 0.96 5.57 0.01 Off. 1 1 0 1 . 1 8 B symptoms Off. 2 1 5 2.30 A Off. 3 1 1 1 .21 B Headache 1 .32 2. 1 2 0. 1 4 Off. 1 1 0 1 .44 A symptoms Off. 2 1 5 1 .90 A Off. 3 1 1 1 .33 A Lethargy 0.98 1 .01 0.38 Off. 1 10 1 .43 A symptoms Off. 2 1 3 2.01 A Off. 3 1 1 1 .70 A
Data set BW2-4 -Complete data set: one week washout
Eyestrain 0.85 14.35 0.0001 Off. 1 14 1 .22 B
symptoms Off. 2 1 9 2.74 A
Off. 3 1 8 1 .40 B
50 The MSE value is the Mean Squared Error value and is an estimate of the within-group variance ( cr2). Table 21 provides the standard deviations for each lighting treatment condition for the complete data set.
51 The average monthly symptom severity provided by N participants exposed to this lighting treatment
condition.
52 Groups with the same letter are not significantly different. 53 One outlier was removed.
Headache 0.84 5. 1 2 0.01 Off. 1 14 symptoms Off. 2 1 9 Off. 3 1 8 Lethargy 1 .38 4.43 0.02 Off. 1 14 symptoms Off. 2 1 9 Off. 3 1 8
Data set BSW2-4 • Screened data set: one week washout
Eyestrain 0.80 1 5.63 0.0001 Off. 1 14 symptoms Off. 2 19 Off. 3 17 Headache 0.86 4.61 0.02 Off. 1 14 symptoms Off. 2 19 Off. 3 1 7 Lethargy 1 .28 3.55 0.04 Off. 1 14 symptoms Off. 2 17 Off. 3 1 7
3.4 Monthly Average Symptoms Analysis
1 .67 B 2.35 A 1 .42 B 1 .45 B 2.64 A 1 .90 AIB 1 .20 B 2.72 A 1 .32 B 1 .54 B 2.30 A 1 .45 B 1 .41 B 2.47 A 1 .80 AIB
The following data sets (monthly average) were tested to determine if there were differences in the symptoms experienced by participants in the different l ighting treatments, offices, trials or if any interaction was present.
The following data sets were considered. 1. c
2. cw 3. SW
Complete data set;
Complete data set with one week washout; Screened54 data set with one week washout;
4. CW-CVB Complete data set with washout - covariate baseline;
5. SW -CVB Screened data set with washout - covariate baseline; 6. CW-CVA Complete data set with washout - covariate age; 7. CW-CVG Complete data set with washout - covariate gender; 8. C-S Complete data set - symptoms only;
54 Responses from participants in which symptoms did not reduce or disappear at the end of the work shift were excluded.
9. CW-S 10. SW-S
Complete data set with washout - symptoms only; Screened data set with washout - symptoms only.