The Importance of Utilizing Statistical Tools in a Business Environment - Case Study Example

The paper discusses the importance of utilizing statistical tools and thinking in a business environment. These tools have to be applied in all levels of the organization in order for it to be fully adaptable to the turbulent environment and decision making in uncertain conditions. The business process involves making predictions about the given population parameters through numerical observation of sample elements. The degree of accuracy by which the results of sample can be extended toward a population is increased by taking random samples and a large sample size. Population variation and mean are the true measurements while the sample statistics are estimates of these values but which hare still helpful in making conclusions about the whole population. This is a very basic introduction to the utilization of statistics and the tools that have been developed to help decision makers. While a bit dry, the topic has to be understood and utilized by all students of management sciences at both under graduate and graduate level. Examples and practical demonstration are much more helpful to visualize the concepts and practical usage of these tools. The limitations of the paper include an inability to discus hypothetical testing for mean and variance and degrees of freedom in detail; these would have provided a better insight on the probabilistic conclusions for population parameters taken from sample statistics. Further review should be done to discuss the results and methods of hypothetical testing and how these are used in the business setting. Statistical tools in Business H.G. Wells once said ‘Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write’. In a diverse world, no two events are the same yet for rational decision making it is necessary to be able to predict with some certainty the probable events which can occur and then plan accordingly. Statistics is the science of making decisions by analyzing any given set of variable data. Descriptive statistical techniques allow the data to be represented in an easily understandable form with clear anomalies, patterns, relationships and expected trends apparent. These include Frequency Distribution; Histograms; Boxplot; Scattergrams and Error Bar plots; and diagnostic plots. Qualitative techniques help in further analyzing and forming conclusions about certain sets of data through which important decisions can be made. For managers and those working in the business fields, they have to make many decisions which will impact the quality and productivity of the business they are running; these have to be increasingly justified in face of close scrutiny and limited resources available. Statistical tools can guide those decisions and point out the scientific support for implementation of these. To fully understand the impact that statistical thinking can have for the business, it would be effective to look at it from the three different levels of management. The Strategic level is where the top tier decisions about an organizations long term strategy are made. “Decisions at the strategic level should be based on facts supported by appropriate data and this requires an understanding of variation. Business and Industry have seen the arrival and demise of many programs such as Total Quality Management. Embracing any program that comes along without firm commitment and understanding is doomed to failure.” (Abraham, pg 3). At the middle managerial level key operation elements like robust product and process design, process control and improvement, and training are designed. A lot of variables and input factors are taken into consideration before a system can be implemented and these are checked or proved through statistical thinking. While, operation level workers do not need extensive knowledge of all different statistical tools utilized in experiment design, but they need to be able to understand concepts like regression, and control charting to be able to perform well at their jobs and to identify any unusual patterns which could indicate an unexpected problem. With the current turbulent climate of the economy and uncertain conditions which most organization are facing, it has been suggested that one way to minimize risk would be to adopt a culture where statistical tools and thinking is deeply entrenched in all aspects of operations. The role of a traditional statistician should be increased from that of a consultant and problem solver to that of a ‘management aide’, facilitator and leader as they are the most suited to form the best possible solution in face of unfavorable circumstances. Even the most basic tools of the science can provide a much stronger argument for certain decisions than simple intuition or guesswork. “Statistics is a science of making decisions with respect to the characteristics of a group of persons or objects on the basis of numerical information obtained from a randomly selected sample of the group.” (Arsham) The three main components of quantitative statistics are: mean variance and standard deviation. These measures form the basis of all statistical analysis. The mean or μ is the expected outcome E(x) of an event x such that the event is repeated infinite times and the measurement would be the average of all those outcomes. It is basically, the average of a set of measurement. Calculated by Mean =  =  Xi /n, it is the most widely used measure of location as its valuable mathematical properties make it suitable for use with inferential statistical analysis. Standard deviation and variance indicate the spread of data within a population or sample. . Variance (σ2) shows the overall degree of variance within the measurements collected, while standard deviation (σ) shows the deviation of individual measurements from the calculated mean. A simple illustrious example could be of the productivity of a factory’s 20 workers. It is estimated that each worker packs up to 150 boxes of product in a given day. The estimate is the mean taken by finding out the number of boxes each worker packs and then dividing it by the number of workers. The standard deviation (σ) will then indicate that how much difference is there between the calculated mean and the actual number of packages done by a worker. It is quite possible that while one can manage to complete 162 packages another can only finish 149- but the overall productivity can be correctly estimated by comparing the mean of all the workers with the expected standard deviation. Before moving on to the calculation of variance and standard deviation an examination of Population and Sample is in order. In Business Statistics the emphasis is on making predictions about certain characteristics of a population to assist in making beneficial decisions for the business. ‘Population’ refers to the collection of all the people, objects, plants or animals which are under the area of interest in any study and conclusions have to be drawn about them. These conclusions could relate to marketing campaigns e.g. this amount of the population likes to listen to radio jingles while driving, or a pharmaceutical company might be interested in knowing how an experimental drug will affect the majority population or a production company would want to know the current standard deviation of the quality of the products they manufacture. But it would be nearly impossible to measure, study or survey an entire population. It would be too time consuming and expensive and instead, statisticians prefer to make these conclusions on the basis of a random ‘Sample’ taken from the population. A sample is a subset of a population or universe which is randomly selected in order to be numerically observed. If a population is all the products manufactured by a factory, a sample could be those produced within a single day. The ‘randomness’ indicates that the sample collected was unbiased and each element of the given population had a chance to be selected- these are the ‘finite’ outcomes of an ongoing random process (Arsham). The results gathered from the numerical observation of the sample are then generalized for a homogenous population. The characteristics or ‘Parameters’ of a population are inferred from the characteristics or ‘Statistics’ of a sample. Parameters are denoted by Latin letters and Roman letters are used for statistics. These would include measures like standard deviation (σ for Parameter and s for Statistics) and variance (σ2 and s2 respectively). There would of course occur uncertainties and a degree of error in extending the results from the Sample analysis to the whole population, these are highlighted through the use of probabilistic tools as a measuring and decision criteria in statistical inference. Two ways for increasing the chances of acquiring an ‘unbiased’ Parameter (when the calculated sample distribution is exactly equal to the population) for a population from a given sample is to ensure that sample elements are randomly selected and the n (sample size) is sufficiently large. Besides random sampling, two other popular and accepted methods of sampling used in business studies are cluster sampling and stratified sampling. Cluster sampling is used for homogenous population which can be divided into smaller clusters, instead of analyzing all the clusters a sample of a small number of random clusters will be sufficient to provide a ‘good’ result. Stratified sampling is used when the population can be broken down into sub-populations on the basis of a defined characteristic; the random sample is taken from these sub populations. A probabilistic conclusive decision about a population’s parameter from a sample can be found out through Hypothesis Testing for mean and variance, which is an advanced statistical calculation. The population mean is the true value of a measurement while the sample mean is only the estimate of the population mean. The variance of the population likewise will be the true representation of the variance which exists in the whole population but the sample variance can also be applied to the whole population within a probability of accuracy. Variance of sample =  (xi -  ) 2 / (n - 1),     where n is at least 2. Variance of Population ==  (xi -  μ ) 2 / n While the formulas used for variance are the same, for sample variance division is done by ( n-1) because then the sample variance which is acquired is much closer in value to the population parameter. For large values of n (above 30) the division by n-1 doesn’t make much of a difference to the estimate and a result acquired by division with n would also be acceptable. The reason behind this that estimating the population parameter from the sample statistics, we lose one independent measurement and that will have to be subtracted. The concept is derived from ‘degrees of freedom’ which represent number of independent pieces of data being used to make a calculation. Number of degrees of freedom indicate how certain we are that the sample population will be a good representative of the whole population- the greater the n, the more chances of assurance of a good estimate. While an in-depth study would be required to discuss all the statistical tools which are utilized in further defining the relationship between parameters and statistics; Population and sample study is the core concepts utilized in business settings as far as statistical tools are concerned. These should be understood by all students and management who want to better prepare themselves for making decisions which can be backed by scientific support. Works Cited Arsham, Hossien. Statistical Thinking for Managerial Decisions. “Web site is a course in statistics appreciation” 9th Edition. Jan 18 1994. Web. 6th July, 2012. Abraham, Bovas. Implementation of Statistics in Business and Industry. Revista Colombiana de Estadística, Volume 30 No. 1. pp. 1 a. 11. June 2007. Web. 6th July, 2012. Dr. David C. Stone & Jon Ellis. Stats Tutorial - Mean, Variance and Standard Deviation. Chemistry, University of Toronto. Sep 25th, 2006. Web. 6th July, 2012 Read More