Odour Threshold Investigation 2012 - Bay of Plenty Regional Council

14
Histogram of MnH2S_Whakatāne
12
10
Frequency
8
6
4
2
0
0
MED
GMEAN
MEAN
1
2
MnH2S_Whakatāne
3
4
Figure 7
Distribution of Whakatāne thresholds.
We now (finally) give the results of useful analyses comparing locations which show the clear
difference in average thresholds between the locations. Although our full analysis used data
with all results per session per panellist, it is sufficient to simply compare the log thresholds
at the two locations using a two-sample t-test. The test is justified by the approximate
normality of the logged form of the data. And given that there are only two locations it is also
simple to allow the variability at the locations to be different.
Two-sample T for log10MnH 2 S
Location N Mean StDev SE Mean
Rotorua 29 0.159 0.291 0.054
Whakatāne 30 -0.208 0.362 0.066
Difference = mu (Rotorua) - mu (Whakatāne).
Estimate for difference: 0.3671.
95% CI for difference: (0.1960, 0.5381).
T-Test of difference = 0 (vs not =): T-Value = 4.30 P-Value < 0.0005 DF = 55.
We have shown there is very strong evidence that the geometric mean thresholds at Rotorua
are higher than at Whakatane. Our point estimate of the difference in the log scale is 0.3671
which corresponds to a ratio in geometric means of 10 0.367 = 2.3. We are 95% sure that the
ratio is somewhere between 10 .196 and 10 .538 i.e. between 1.6 and 3.5. Note that the
estimated geometric means are 10 -.208 =0.62 and 10 .159 = 1.44 as listed previously.
Estimating other useful characteristics of the threshold
distributions
As an alternative to using transformations, some statistical software offers alternative
approaches to leaving the data in the untransformed state and estimating various percentiles
(such as the median), the mean, and also the proportion of the data in various data ranges.
The results below used such a procedure and included fitting the threshold data with a threeparameter
lognormal distribution (equivalent to the data transformation Y = log e (threshold –
0.16)).
Environmental Publication 2012/06–A review of odour properties of H 2 S Odour Threshold Investigation 2012 67