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# BUS 308 - Paper

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Date Created: 11/06/15

Running Head Statistics Page 1 Cassandra Settlemyre What I ve learned about Statistics BUS 308 Statistics for Managers Instructor Jennifer Dale December 26 2015 What I ve learned about Statistics Page 2 Introduction The following paper seeks to provide basic knowledge in some specific areas of statistical data analysis While there are no hard and fast distinctions for analyzing statistical data ensuring that you have a methodical approach is vital to an accurate analysis The process of data analysis is that of turning data into significant information Data analysis is done to convert the raw data into meaningful information Statistics is all about this data analysis Before actually working on data analysis in real world it is important that the basic knowledge is possessed by everybody involved in this process Transforming data into statistical information and then communicating it accurately is a crucial dynamic of effective decision making Descriptive Statistics Descriptive statistics is the tool of statistics to analyse the data Descriptive statistics are distinguishing from the inferential statistics descriptive statistics aims to summarize the sample rather than use the data to learn about the population The analysis helps in determination of patterns that exist in the data Descriptive statistics simply describes the data but not present an analysis beyond the data One cannot make any conclusions about any hypothesis using this The data when presented to users is difficult to comprehend in its raw form Sometimes the sheer size and volume of data may render it impossible to understand what it represents Descriptive statistics helps in proper presentation of data such that it can be understood and analyzed by the user For example if we had the data about the returns from stocks of 100 companies then that data would make no sense as it would be difficult to comprehend But if that data is arranges classified industrywise an average is calculated for each industry and for all the stocks and What I ve learned about Statistics Page 3 then the interpretation would be simpler Here descriptive statistics comes as a savior Following are two most common types of statistics used to describe data Measures of central tendency these are measures which are at the central position of the frequency distribution and which are representative of the whole distribution Some of the measures of central tendency are mean mode and median Measures of dispersion these are measures that show how far the actual values are from the measure of central tendency For example the average return from all the 100 stocks may be 5 but individual stocks will not exactly earn 5 each Each stock will earn a different rate of return Measures of dispersion find out that variation in the actual returns and the average returns Range standard deviation quartiles absolute deviation and variance are some of the measures of dispersion The mean median and mode are all valid measures of central tendency but under different conditions some measures of central tendency become more appropriate to use than others In the following sections we will look at the mean mode and median and learn how to calculate them and under what conditions they are most appropriate to be used Lund amp Lund 2013 Inferential Statistics Inferential statistics infer from the sample to the population and determine probability of characteristics of population based on the characteristics of the sample Inferential statistics help assess strength of relationship between dependent and independent variable We use inferential statistics to test hypothesis and make estimation using sample data Normal Distribution One of the goals of inferential statistics is to start with a statistical sample and from there state a range of values for a corresponding population parameter To find the population mean we announce a process inference about the mean There are many What I ve learned about Statistics Page 4 different procedures and probability distributions that we can use for inference about the mean zscores tscores and bootstrapping Taylor 2014 The normal distribution or bell curve can be used in a number of settings for statistical inference Unfortunately most of these situations are rarely encountered in real life This is because in order to use the normal distribution of z scores for inference about the mean we need to know the value of the population standard deviation This is rarely the case in practice Often a person does not have access to the whole population needed for investigation For example an investor may want to know and compare the returns of all the securities in the United States stock exchange It will almost be impossible for the investor to do so hence using a sample of say 100 securities will be better which are representative of all the other securities This sample can be used to make generalizations about the whole population s parameters Inferential statistics makes available the techniques used for the same This means that the sample characteristics are used to infer about the population parameters So it is of utmost importance that the sample selected is an accurate representation of the population To ensure this sampling processes are used Hypothesis Development and Testing Inferential stats are closely tied to the logic of hypothesis testing In hypothesis testing the goal is usually to reject the null hypothesis The null hypothesis is the null condition no difference between means or no relationship between variables Data are collected that allow us to decide if we can reject the null hypothesis and do so with some confidence that we re not making a mistake Hypothesis testing is another way of drawing conclusions about a population parameter parameter is simply a number such as a mean that includes the full population and not just a sample With hypothesis testing one uses a test such as TTest ChiSquare or ANOVA to test whether a hypothesis about the mean is true or not Trochim 2006 What I ve learned about Statistics Page 5 When a quantitative research is conducted it means an attempt to answer a hypothesis that is set A hypothesis simply means a claim Before starting a quantitative research a researcher makes a claim and through research she tries to prove the validity of that claim Following are the steps in conducting a hypothesis test 1 Define the hypothesis for the research and set the parameters for the same 2 Specify the null and alternate hypothesis 3 Explain how the operationalizing will be done 4 Define the significance level 5 Define whether the test will be one or two tailed 6 Define the type of distribution whether normal distribution or some other types say Poisson 7 Select a statistical test to be used 8 Run the statistical tests on the data and interpret the results 9 Either accept or reject the null hypothesis For example a hypothesis may be first set that the returns from all the stocks of the market average at 3 Then research may be conducted and tools may be used to confirm the validity of this hypothesis Selection of Appropriate Statistical Tests Selection of appropriate statistical test is very important for analysis of research data Wrong statistical tests can be seen in many conditions like use of paired test for unpaired data or use of parametric statistical tests for the data which does not follow the normal distribution or incompatibility of statistical tests with the type of data etc Parikh et al 2010 There are various statistical tests which can be used to conduct the research Selection of appropriate What I ve learned about Statistics Page 6 statistical tests depends upon the kind of data dealt with whether the data follows normal distribution and the aim of the study Usually data is in one of the following four categories Nominal data Ordinal data Interval data and Ratio data If one knows what type of distribution is followed then the selection of the statistical test becomes very easy Parametric statistical tests are used if the data follows normal distribution else nonparametric tests Nominal Data In these kinds of data observations are given a particular name Like a person is observed to be 39male39 or 39female39 or Name of drug as generic or brand etc Nominal data cannot be measured or ordered but can be counted These types of data are considered as categorical data but the order of the categories is meaningless Parikh et al 2010 Ordinal Data Ordinal data is also a type of categorical data but in this categories are ordered logically These data can be ranked in order of magnitude One can say definitely that one measurement is equal to less than or greater than another Many of the scores and scales are used in research fall under the ordinal data For example rating score scale for the color taste smell ease of application of products etc Parikh et al 2010 Interval Data Interval data has a meaningful order and also has the quality that equal intervals between measurements represent equal changes in the quantity of whatever is being measured But these types of data have no natural zero Example is Celsius scale of temperature In the Celsius scale there is no natural zero so we cannot say that 70 C is double than 35 C In interval scale zero point can be chosen arbitrarily IQ Test is also interval data as it has no natural zero Parikh et al 2010 Ratio Data Ratio data has all the qualities of interval data natural order equal intervals plus a natural zero point This type of data is observed to be used most frequently Example of ration data is height weight length etc In this type of data it can be said meaningfully that 10 m of length is double than 5 m This ratio hold true regardless of which scale the object is being measured in e g meters or yards Reason for this is the presence of natural zero Parikh et al 2010 Evaluation of Statistical Results After selecting the appropriate test for the sample this is main thing of the whole testing procedure when we test there is a test statistics we will calculated the test statistics from the sample based on the data under the null hypothesis also we will get the critical test statistics value which we will get from the given chart or table We will reject or accept the null hypothesis based on the critical value of the test statistics and on the alternative hypothesis Statistical analysis is a quantitative method to find probabilities between sets or results of data This data can come from the natural or social sciences Statistical analysis helps elaborate on What I ve learned about Statistics Page 7 trends or patterns found Within the research of a topic When evaluating statistical results following components should be given due importance the source of research and the source of funding the researchers Who had a link and contact With the participants the sample selection method the exact nature of questions asked in the research the extraneous differences among the groups Which are compared and the magnitude of any claim effects or differences Conclusion In conclusion I have learned that statistics is used by not only the researchers and academicians it is used in our daily lives also Thus every person must be familiar With the basics of statistics and its applications For researchers it becomes all the more important to understand each aspect of the data analysis process thoroughly so as to properly conduct the research and accurately interpret the results References 1 Hoffman Roald 1981 The Same and Not the Same Retrieved from httpWWWphysicscsbsjuedustatsdescriptive2html 2 Lund Adam Lund Mark 2013 Laerd Statistics A Research Tool Retrieved from httpsstatisticslaerdcom 3 Parikh MN Hazra A Mukherjee J Gogtay N editors Research methodology simplified Every clinician a researcher New Delhi J aypee Brothers 2010 Hypothesis testing and What I ve learned about Statistics Page 8 choice of statistical tests pp 121 8 Retrieved from httpWWWncbinlmnihgovpmcarticlesPMC31 16565 4 Tanner D E amp Youssef Morgan C M 2013 Statistics for Managers San Diego CA Bridgepoint Education Inc 5 Taylor Courtney 2014 Different Methods for Inference about the Mean Retrieved from httpstatisticsaboutcornodInferentialStatisticsaDifferentMethodsFor InferenceAboutTheMeanhtml 6 Trochim William MK 2006 Inferential Statistics Research Methods Knowledge Base Retrieved from httpcsiufsaczaresresfilesTrochimpdf

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