Statistical analysis in microbiology:statnotes

This book is aimed primarily at microbiologists who are undertaking research and who require a basic knowledge of statistics to analyse their experimental data. Computer software employing a wide range of data analysis methods is widely available to experimental scientists. The availability of this software, however, makes it essential that investigators understand the basic principles of statistics. Statistical analysis of data can be complex with many different methods of approach, each of which applies in a particular experimental circumstance. Hence, it is possible to apply an incorrect statistical method to data and to draw the wrong conclusions from an experiment. The purpose of this book, which has its origin in a series of articles published in the Society for Applied Microbiology journal ‘The Microbiologist’, is an attempt to present the basic logic of statistics as clearly as possible and therefore, to dispel some of the myths that often surround the subject. The 28 ‘Statnotes’ deal with various topics that are likely to be encountered, including the nature of variables, the comparison of means of two or more groups, non-parametric statistics, analysis of variance, correlating variables, and more complex methods such as multiple linear regression and principal components analysis. In each case, the relevant statistical method is illustrated with examples drawn from experiments in microbiological research. The text incorporates a glossary of the most commonly used statistical terms and there are two appendices designed to aid the investigator in the selection of the most appropriate test.

Quantitative neuropathology:data collection and statistical analysis

The use of quantitative methods has become increasingly important in the study of neuropathology and especially in neurodegenerative disease. Disorders such as Alzheimer's disease (AD) and the frontotemporal dementias (FTD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This chapter reviews the advantages and limitations of the different methods of quantifying pathological lesions in histological sections including estimates of density, frequency, coverage, and the use of semi-quantitative scores. The sampling strategies by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are described. In addition, data analysis methods commonly used to analysis quantitative data in neuropathology, including analysis of variance (ANOVA), polynomial curve fitting, multiple regression, classification trees, and principal components analysis (PCA), are discussed. These methods are illustrated with reference to quantitative studies of a variety of neurodegenerative disorders.

A Delay Vector Variance based marker for an output-only assessment of structural changes in tension leg platforms

Although aspects of power generation of many offshore renewable devices are well understood, their dynamic responses under high wind and wave conditions are still to be investigated to a great detail. Output only statistical markers are important for these offshore devices, since access to the device is limited and information about the exposure conditions and the true behaviour of the devices are generally partial, limited, and vague or even absent. The markers can summarise and characterise the behaviour of these devices from their dynamic response available as time series data. The behaviour may be linear or nonlinear and consequently a marker that can track the changes in structural situations can be quite important. These markers can then be helpful in assessing the current condition of the structure and can indicate possible intervention, monitoring or assessment. This paper considers a Delay Vector Variance based marker for changes in a tension leg platform tested in an ocean wave basin for structural changes brought about by single column dampers. The approach is based on dynamic outputs of the device alone and is based on the estimation of the nonlinearity of the output signal. The advantages of the selected marker and its response with changing structural properties are discussed. The marker is observed to be important for monitoring the as- deployed structural condition and is sensitive to changes in such conditions. Influence of exposure conditions of wave loading is also discussed in this study based only on experimental data.

Statistical Analysis of Sea Surface Temperature and Chlorophyll-a Concentration Patterns in the Gulf of Tadjourah (Djibouti)

The sea surface temperature (SST) and chlorophyll-a concentration (CHL-a) were analysed in the Gulf of Tadjourah from two set of 8-day composite satellite data, respectively from 2008 to 2012 and from 2005 to 2011. A singular spectrum analysis (SSA) shows that the annual cycle of SST is strong (74.3% of variance) and consists of warming (April-October) and cooling (November-March) of about 2.5C than the long-term average. The semi-annual cycle captures only 14.6% of temperature variance and emphasises the drop of SST during July-August. Similarly, the annual cycle of CHL-a (29.7% of variance) depicts high CHL-a from June to October and low concentration from November to May. In addition, the first spatial empirical orthogonal function (EOF) of SST (93% of variance) shows that the seasonal warming/cooling is in phase across the whole study area but the southeastern part always remaining warmer or cooler. In contrast to the SST, the first EOF of CHL-a (54.1% of variance) indicates the continental shelf in phase opposition with the offshore area in winter during which the CHL-a remains sequestrated in the coastal area particularly in the south-east and in the Ghoubet Al-Kharab Bay. Inversely during summer, higher CHL-a quantities appear in the offshore waters. In order to investigate processes generating these patterns, a multichannel spectrum analysis was applied to a set of oceanic (SST, CHL-a) and atmospheric parameters (wind speed, air temperature and air specific humidity). This analysis shows that the SST is well correlated to the atmospheric parameters at an annual scale. The windowed cross correlation indicates that this correlation is significant only from October to May. During this period, the warming was related to the solar heating of the surface water when the wind is low (April-May and October) while the cooling (November-March) was linked to the strong and cold North-East winds and to convective mixing. The summer drop in SST followed by a peak of CHL-a, seems strongly correlated to the upwelling. The second EOF modes of SST and CHL-a explain respectively 1.3% and 5% of the variance and show an east-west gradient during winter that is reversed during summer. This work showed that the seasonal signals have a wide spatial influence and dominate the variability of the SST and CHL-a while the east-west gradient are specific for the Gulf of Tadjourah and seem induced by the local wind modulated by the topography.

Quality evaluation of cortex berberidis from different geographical origins by simultaneous high performance liquid chromatography combined with statistical methods

Purpose: To develop an effective method for evaluating the quality of Cortex berberidis from different geographical origins. Methods: A simple, precise and accurate high performance liquid chromatography (HPLC) method was first developed for simultaneous quantification of four active alkaloids (magnoflorine, jatrorrhizine, palmatine, and berberine) in Cortex berberidis obtained from Qinghai, Tibet and Sichuan Provinces of China. Method validation was performed in terms of precision, repeatability, stability, accuracy, and linearity. Besides, partial least squares discriminant analysis (PLS-DA) and one-way analysis of variance (ANOVA) were applied to study the quality variations of Cortex berberidis from various geographical origins. Results: The proposed HPLC method showed good linearity, precision, repeatability, and accuracy. The four alkaloids were detected in all samples of Cortex berberidis. Among them, magnoflorine (36.46 - 87.30 mg/g) consistently showed the highest amounts in all the samples, followed by berberine (16.00 - 37.50 mg/g). The content varied in the range of 0.66 - 4.57 mg/g for palmatine and 1.53 - 16.26 mg/g for jatrorrhizine, respectively. The total content of the four alkaloids ranged from 67.62 to 114.79 mg/g. Moreover, the results obtained by the PLS-DA and ANOVA showed that magnoflorine level and the total content of these four alkaloids in Qinghai and Tibet samples were significantly higher (p < 0.01) than those in Sichuan samples. Conclusion: Quantification of multi-ingredients by HPLC combined with statistical methods provide an effective approach for achieving origin discrimination and quality evaluation of Cortex berberidis. The quality of Cortex berberidis closely correlates to the geographical origin of the samples, with Cortex berberidis samples from Qinghai and Tibet exhibiting superior qualities to those from Sichuan.

Long-term trends in fine particle number concentrations in the urban atmosphere of Brisbane : the relevance of traffic emissions and new particle formation

The measurement of submicrometre (< 1.0 m) and ultrafine particles (diameter < 0.1 m) number concentration have attracted attention since the last decade because the potential health impacts associated with exposure to these particles can be more significant than those due to exposure to larger particles. At present, ultrafine particles are not regularly monitored and they are yet to be incorporated into air quality monitoring programs. As a result, very few studies have analysed their long-term and spatial variations in ultrafine particle concentration, and none have been in Australia. To address this gap in scientific knowledge, the aim of this research was to investigate the long-term trends and seasonal variations in particle number concentrations in Brisbane, Australia. Data collected over a five-year period were analysed using weighted regression models. Monthly mean concentrations in the morning (6:00-10:00) and the afternoon (16:00-19:00) were plotted against time in months, using the monthly variance as the weights. During the five-year period, submicrometre and ultrafine particle concentrations increased in the morning by 105.7% and 81.5% respectively whereas in the afternoon there was no significant trend. The morning concentrations were associated with fresh traffic emissions and the afternoon concentrations with the background. The statistical tests applied to the seasonal models, on the other hand, indicated that there was no seasonal component. The spatial variation in size distribution in a large urban area was investigated using particle number size distribution data collected at nine different locations during different campaigns. The size distributions were represented by the modal structures and cumulative size distributions. Particle number peaked at around 30 nm, except at an isolated site dominated by diesel trucks, where the particle number peaked at around 60 nm. It was found that ultrafine particles contributed to 82%-90% of the total particle number. At the sites dominated by petrol vehicles, nanoparticles (< 50 nm) contributed 60%-70% of the total particle number, and at the site dominated by diesel trucks they contributed 50%. Although the sampling campaigns took place during different seasons and were of varying duration these variations did not have an effect on the particle size distributions. The results suggested that the distributions were rather affected by differences in traffic composition and distance to the road. To investigate the occurrence of nucleation events, that is, secondary particle formation from gaseous precursors, particle size distribution data collected over a 13 month period during 5 different campaigns were analysed. The study area was a complex urban environment influenced by anthropogenic and natural sources. The study introduced a new application of time series differencing for the identification of nucleation events. To evaluate the conditions favourable to nucleation, the meteorological conditions and gaseous concentrations prior to and during nucleation events were recorded. Gaseous concentrations did not exhibit a clear pattern of change in concentration. It was also found that nucleation was associated with sea breeze and long-range transport. The implications of this finding are that whilst vehicles are the most important source of ultrafine particles, sea breeze and aged gaseous emissions play a more important role in secondary particle formation in the study area.

Bayesian versus frequentist statistical inference for investi gating a one-off cancer cluster reported to a health department

Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.