The Role of Statistics in Decisionmaking - Research Paper Example

 Statistics Introduction Statistics is a process in which scientific methods are used in collecting, organizing, summarizing presenting and analyzing data for the benefit of drawing and making reasonable conclusions and decisions. Therefore, it is useful in every aspect in organizing and running of day today activities both in the state and private entities. It plays an important role in agriculture, biology, business, economics, engineering, medicine, education, politics, and sociology among other fields. Statistics refers to the data collected or data derived from previous data e.g. averages. It is from this data we get to know more information about the population or universe. The data is obtained from small portion of population (sample), carefully selected to represent the all population. Analyzing such a small data is easier and cheap as compared to analyzing the whole population. It is worth noting that population is either infinite or finite and sometimes, in the process of analyzing, sample may be destroyed e.g. testing compression strength in concrete bricks. Therefore, it is advisable that the sample must be representative of the population so that whatever conclusion made based on the sample infer also to the population. This is never absolutely certain hence inductive or statistical inference. The phase of statistics that only describe and analyze a given data without drawing conclusions or inferences about a population is descriptive or deductive statistic (Murray & Larry, 1999). Variable is a symbol representing the aspect being investigated. This can be height of trees or students, rebound strength value on the brick. It is constant when a variable takes one value otherwise it is either continuous or discrete. Discrete variables are variables whose values are integers i.e. 1, 2, 3, 4, 5… Examples are number of children in a family, number of cows in a flock etc. on the other end, continuous variable takes all values including those between the integers of the domain. Example is the height of students in college (Murray & Larry, 1999). Descriptive statistics It is the art of only describing and summarizing a given group of data. The results presented does not represent anything of the larger group. For instance, the hospitals regularly collect information on the most used drug, the prevalent disease, number of births etc. This enables the concern hospital management; to organize for the next shipment of the drug concern, to hire the correct number of the doctors with the requirements meeting the prevalent disease, to know the required number of nurses to assist in child birth. Note that the information from the data does not infer to the population but rather only helps the administration to run their affair. Where the data is not available, statistical theory can be designed to generate the required data. For instance, a farmer wanted to know the better fertilizer he/she can use in the farm for maximum yield. To study this, the farmer might divide his/her farm in to two equal portions and use different fertilizer in each portion. Then, later compare the yields from two portions. For valid conclusion to be made, the farmer should be not be biased in any way. Be it fertilizer application rate or season of planting. The set up should be controlled so that the only variable should be the type of fertilizer used. At the end, the yields are described and presented. This statistical approach is descriptive (Sheldon, 2004). Inferential statistics Any conclusion made after describing and summarizing the previous experiment based on the type of the fertilizer, is inferential. To do this, we consider the possibility of chance. On assuming that the yield from portion A is higher than that of portion B. Could this be attributed to the fact different fertilizer was used or it chance happened by chance. Performing the same experiment ten times and eight out of ten represent one fertilizer superior than the other does not an absolute test that indeed the fertilizer in favor is actually the superior. However, on doing it many times, say hundred times, and ninety out of it turns out in favor of the superior fertilizer, then we can conclude that indeed the in favor fertilizer is superior. The inferential statistics is guided by assumptions about the chances of obtaining the different data values (Sheldon, 2004). Hypothesis development and testing Hypothesis is a statement about some aspect of the system in which it is scrutinized. For example, a teacher wound wish to know if the students passed an exam, say attained an average grade of 60. Then, the teacher would be testing the hypothesis that the average grade attained by the students exceeds 60. Therefore development a hypothesis is driven by the need of experiment or the known norm in a society. Children are known to report to school early, 7am, so, one can test if this true by testing the hypothesis that children report to school early 7am. It worth noting that hypothesis is statement that have to be proved. Therefore, it should be verifiable or vice versa, neither too specific nor too general, valuable and is a prediction of consequences. Hypothesis can be either null or alternative. Null hypothesis represent a theory that has been put forward as an obvious choice but has not been proved while alternative hypothesis is the actual desired conclusion of the researcher i.e. opposite of null hypothesis and is reached when null hypothesis is rejected. Testing the hypothesis begins with stating the hypothesis (null or alternative), setting the criteria for a decision, collecting data and finally evaluate the null hypothesis. While evaluating the null hypothesis, the result are interpreted and decision made. In the process of making decision, one can make wrong decision resulting to errors. Type I error occur when null hypothesis is wrongly rejected. Type II error occurs when null hypothesis is indeed false but it is not rejected (Montogometry & Runger, 2011). Decision Reject H0 Don’t reject H0 Truth H0 Type I Error Right Decision H1 Right Decision Type II Error Selection of appropriate statistical tests Selection of appropriate statistical test is very important for analysis of research data and depends on the kind of data being dealt with, the nature of the data i.e. normal or not and the objective of the research. Data can be nominal, ordinal, interval or ratio. For nominal, observation is given a particular name e.g. male or female for persons. Such data are normally presented by contingency table. The data in ordinal type is ranked in order of magnitude. Most of the scores and scales used in research fall in this category e.g. rating score/scale for color etc. Interval data has a meaningful order and also has the quality that equal intervals between measurements represent equal changes in the quantity of what is being measured but have no natural zero. Example is IQ test. In the other hand, ratio data resembles the interval data but has natural zero e.g. height, length. After ascertaining the type of data, distribution of the data then follows the suit in determining the appropriate statistical tests. These is no need in checking the distribution in the case of ordinal and nominal data. If the data is for ratio and interval is normal then parametric statistical test is applied or otherwise nonparametric tests is used. Various ways of checking data distribution are plotting histogram, plotting box and whisker plot, plotting Q-Q plot, measuring skewness and kurtosis. All these tests are based on based on null hypothesis that the data is taken from the population which follows the normal distribution. If p values is less than 0.05, data is not normal. The purpose of the research dictates also the appropriate statistical tests used. For comparison purpose or facts finding mission. Analysis of variance (ANOVA), and regression and correlation are performed to compare averages of two or more groups, and to compare two variables measured as numeric respectively. The three forms major factors considered for selection of statistical test (Jarkaran, 2010). Evaluating statistical results When we get the statistical evidence, which are logical and very persuasive, the decisions we make are well informed. Researchers report the ‘significant’ results of survey or experiment. This means that it is not expected to get extreme results if the null hypothesis (H0) is true. This is done by establishing a value for alpha (α) such as 0.05, 0.01 depending on how sure they want to be of their conclusion. The smaller α, the more confident they want to be to be making the right decision. Then, p-value (probability of obtaining a particular result if the null hypothesis is true) is calculated. The smaller the p-value is, the more significant the results are. If the p-value is less than the specified α, the null hypothesis is rejected and the alternative hypothesis is correct (Collings & Christiansen, 2001). References Read More