• Can statistical methods help to solve these problems?
In today's global marketplace success - often survival - hinges on an organization's ability to improve everything it does. Many businesses today find themselves "drowning" in data, yet many managers lack the ability to employ the data for competitive advantage. Every moment decisions are being made in businesses that reveal if companies are profitable and growing or if they are stagnating and dying. Most of these decisions are made with the help of information gathered on the marketplace, the economic and financial environment, the work force, the competition, and other relevant factors. Statistics is the tool through which such information that usually comes in the form of data is analyzed and interpreted. Thus, statistics plays a vital role in the unending saga of decision-making within the vibrant world of business. Businesses also employ statistical analysis of data to help in improving their processes. Precisely, statistical methods help to demonstrate the need for improvements, identify ways to make improvements, assess whether or not improvement activities have been successful, and estimate the benefits of improvement strategies.Thus, the ultimate goal of statistical analysis in business is to improve the performance of business processes. For instance, we might use descriptive and inferential statistics to compare the risk and return characteristics of different investment choices in order to improve the way we manage an investment portfolio, or we might use statistical process control to improve a manufacturing or service process. Similarly, we might use regression analysis to predict demand for a product in order to improve the way we manage inventories, or we might use design of experiments to study the effects of several different advertising campaigns in order to improve how a product is marketed. In each case, we are improving the performance of a business process by taking informed action on the basis of statistical analysis. This theme provides the philosophical reason for conducting statistical studies in business.What should a manager know about statistics? Today successful managers in both the public and private sectors must have a working knowledge of statistics not as a general tool of data analysis but as a specific method for addressing issues and questions in their daily business environment. His knowledge should include a broad overview of the basic concepts of statistics, with some details. He should be aware that the world is random and uncertain in many aspects. He should be able to effectively perform two important activities:
Several statistical methods help to decompose the errors
Libraries of 16S rRNA genes provide insight into the membership of microbial communities. Statistical methods help to determine whether differences in library composition are artifacts of sampling or are due to underlying differences in the communities from which they are derived. To contribute to a growing statistical framework for comparing 16S rRNA libraries, we present a computer program, ∫-LIBSHUFF, which calculates the integral form of the Cramér-von Mises statistic. This implementation builds upon the LIBSHUFF program, which uses an approximation of the statistic and makes a number of modifications that improve precision and accuracy. Once ∫-LIBSHUFF calculates the P values, when pairwise comparisons are tested at the 0.05 level, the probability of falsely identifying a significant P value is 0.098 for a study with two libraries, 0.265 for three libraries, and 0.460 for four libraries. The potential negative effects of making the multiple pairwise comparisons necessitate correcting for the increased likelihood that differences between treatments are due to chance and do not reflect biological differences. Using ∫-LIBSHUFF, we found that previously published 16S rRNA gene libraries constructed from Scottish and Wisconsin soils contained different bacterial lineages. We also analyzed the published libraries constructed for the zebrafish gut microflora and found statistically significant changes in the community during development of the host. These analyses illustrate the power of ∫-LIBSHUFF to detect differences between communities, providing the basis for ecological inference about the association of soil productivity or host gene expression and microbial community composition.
The Six Sigma method aims at optimising processes through a target-oriented application of statistics. Process-relevant data is evaluated and visualised using statistics. Statistical methods help to recognise deviations in process stability. Actions are defined and implemented for processes with identified problems. New measured data is compared to existing data.