BSMS2209 Ch#1 Introduction To Statistics PDF

WHAT IS STATISTICS? Statistics is defined as the art and science of collecting, analyzing, presenting, and interpreting data. Dat...

WHAT IS STATISTICS? Statistics is defined as the art and science of collecting, analyzing, presenting, and interpreting data. Data means information in raw or unorganized form Source: Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2011). Statistics for Business and Economics. St. Paul, Cengage Learning, pp.3. Retrieved from : pdfdrive.net Statistical analysis: Why is it? Statistical analysis – used to manipulate summarize, and investigate data, to provide useful information for decision-making.  Role of Statistics in Business and Economics Data are used everywhere. Applied statistical analysis helps business managers and economic planners formulate management policy and make business decisions more effectively. Statistics is a key ingredient in understanding accounting, economics, finance, marketing, production, organizational behavior, and other business courses. Source: C.-F. Lee et al., Statistics for Business and Financial Economics, DOI 10.1007/978-1-4614-5897-5_1, # Springer Science+Business Media New York 2013, pp.3. Retrieved from pdfdrive.net  Applications of Statistics in Business and Economics Accounting Public accounting firms use statistical sampling procedures when conducting audits for their clients. (e.g. Accounts receivables of a large firms. the auditors selecting samples to draw a conclusion ). Finance Financial analysts use a variety of statistical information to guide their investment recommendations. (e.g. the analysts review a variety of financial data including price/earnings ratios and dividend yields. By comparing the information for an individual stock with information about the stock market averages, a financial analyst can begin to draw a conclusion as to whether an individual stock is over- or underpriced). Source: Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2011). Statistics for Business and Economics. St. Paul, Cengage Learning, pp3-4.. Retrieved from : pdfdrive.net  Marketing Electronic scanners at retail checkout counters collect data for a variety of marketing research applications. (e.g., data suppliers such as ACNielsen and Information Resources, Inc., purchase point-of-sale scanner data from grocery stores, process the data, and then sell statistical summaries of the data to manufacturers) Production Today’s emphasis on quality makes quality control an important application of statistics in production. A variety of statistical quality control charts are used to monitor the output of a production process. Source: Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2011). Statistics for Business and Economics. St. Paul, Cengage Learning,pp3-4.. Retrieved from : pdfdrive.net Economics Economists frequently provide forecasts about the future of the economy or some aspect of it. They use a variety of statistical information in making such forecasts. (Eg. Forecasting inflation rates, the unemployment rate).  TYPES OF STATISTICS There are two major divisions of statistics such as: Descriptive Statistics Inferential Statistics Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, PP.5.. Retrieved from: http://cnx.org/content/col11776/1.33  Descriptive statistics Descriptive statistics Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, PP.5.. Retrieved from: http://cnx.org/content/col11776/1.33 –  Inferential statistics Inferential statistics – The methods used to make conclusion about a population on the basis of a sample For example, Estimate the population average height using the sample average height Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, PP.5.. Retrieved from: http://cnx.org/content/col11776/1.33  POPULATION AND SAMPLE In general population means number of people but in statistics meaning of population is different Population –The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest Sample – A portion, or part, or a sub set of the population of interest Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University,PP.6.. Retrieved from: http://cnx.org/content/col11776/1.33  SAMPLING Sampling is the process of selecting sample participants from the population. A sample should have the same characteristics as the population it is representing. There are various sampling Sampling methods: Methods Probability Non-Probability Sampling Sampling 1.SimpleRandom 1.Convenience 2.Systematic 2.Quota 3.Stratified 3.Judgement 4.Cluster 4.Snowball Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.16-17. Retrieved from: http://cnx.org/content/col11776/1.33  SAMPLING METHODS Probability Sampling(Random Sampling): In probability sampling, every element of the population has an equal chance of being selected. Probability sampling gives us the best chance to create a sample that is truly representative of the population(unbiased). The easiest method to describe is called a simple random sample. Non-Probability Sampling(Non-Random Sampling): In non-probability sampling, all elements do not have an equal chance of being selected(biased). Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.16-17. Retrieved from: http://cnx.org/content/col11776/1.33  SAMPLING ERRORS Vs NON-SAMPLING ERRORS The actual process of sampling causes sampling errors. For example, the sample may not be large enough or representative of the population. Factors not related to the sampling process cause non-sampling errors. A defective counting device can cause a non-sampling error. Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.17-18.. Retrieved from: http://cnx.org/content/col11776/1.33  TYPES OF DATA Statistical data are usually obtained by counting or measuring items. Most data can be put into the following categories: Qualitative Data Quantitative Data Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.17-18.. Retrieved from: http://cnx.org/content/col11776/1.33  Qualitative Data Qualitative data are the result of categorizing or describing attributes of a population. Qualitative data are also often called categorical data. Qualitative data are generally described by words or letters. e.g., Gender, blood groups, hair colour etc. Many numerical techniques do not apply to the qualitative data. For example, it does not make sense to find an average hair color or blood type. Source:Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.8-9. Retrieved from: http://cnx.org/content/col11776/1.33  Quantitative Data Quantitative data are always numbers. Quantitative data are the result of counting or measuring attributes of a population. e.g. Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics Quantitative data can be separated into two subgroups: a. Discrete -data that are the result of counting is known as discrete data. (e.g. the number of students of a given ethnic group in a class, the number of books on a shelf) b. Continuous-Continuous data are often the results of measurements like lengths, weights, or times. (e.g.distance traveled, weight of luggage) Source:Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.8-9. Retrieved from: http://cnx.org/content/col11776/1.33  SOURCES OF DATA There are two sources of data: Primary Data Secondary Data  Primary Data Primary data are collected for first time specifically for the analysis desired. Methods are: Questionnaire Interview Observation Experiments Source: C.-F. Lee et al., Statistics for Business and Financial Economics, DOI 10.1007/978-1-4614-5897-5_1, # Springer Science+Business Media New York 2013, pp.16-17. Retrieved from pdfdrive.net  Secondary Data Secondary data have already been compiled and are available for further statistical analysis Documents Newspapers/ Magazine / journals Websites Source: C.-F. Lee et al., Statistics for Business and Financial Economics, DOI 10.1007/978-1-4614-5897-5_1, # Springer Science+Business Media New York 2013, pp.16-17. Retrieved from pdfdrive.net  MEASUREMENT SCALES The way a set of data is measured is called its level of measurement. Data can be classified into four levels of measurement/ measurement scales: Nominal scale Ordinal scale Interval scale Ratio scale Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.21. Retrieved from: http://cnx.org/content/col11776/1.33  Nominal scale Data that is measured using a nominal scale is qualitative (categorical). It refers to quality more than quantity. Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. A nominal level of measurement is simply a matter of distinguishing by name. e.g., 1 = male, 2 = female. e.g., Country Visited : 1-Singapore, 2-United States, 3- United Kingdom, 4-South Africa Even though we are using the numbers 1 and 2, they do not denote quantity. Nominal scale data cannot be used in calculations.  Ordinal scale Data that is measured using an ordinal scale is similar to nominal scale data but there is a big difference. Ordinal refers to the order in measurement. An ordinal scale indicates direction Examples: Taste of the Food : 3- Excellent/2-Good/1-Bad; Exam Performance : 3-High/2-Medium/1-Low; Ranking an experience as a ‘9’, on a scale of 1 to 10 indicates that it was higher than an experience ranked as a ‘6’, but lesser than the highest experience of rank ‘10’.  Interval scale Interval scales provide information about order, and also possess equal intervals. Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. Interval level data can be used in calculations, but one type of comparison cannot be done. E.g. The most popular example is the temperature in degrees Fahrenheit. The difference between a 100 degrees F and 90 degrees F is the same difference as between 60 degrees F and 70 degrees F. Time is also one of the most popular interval data examples measured on an interval scale where the values are constant, known, and measurable.  Ratio scale In addition to possessing the qualities of nominal, ordinal, and interval scales, a ratio scale has an absolute zero (a point where none of the quality being measured exists). Using a ratio scale permits comparisons E.g., four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The exams are machine-graded. The data can be put in order from lowest to highest: 20, 68, 80, 92. The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. The smallest score is 0. So 80 is four times 20. The score of 80 is four times better than the score of 20.  VARIABLES A variable is a characteristic or attribute that can assume different values. Variable is the term used to record a particular characteristic of the population we are studying. Example: Marks, Age, Gender, etc For example, if our population consists of pictures taken from Mars, we might use the following variables to capture various characteristics of our population: Quality of a picture Title of a picture Latitude and longitude of the center of a picture Date the picture was taken Source: Holmes, A., ILLOWSKY,B., Dean, S.,(2018). Introductory Business Statistics. OpenStax, Rice University, pp.6. Retrieved from: http://cnx.org/content/col11776/1.33  TYPES OF VARIABLES Variables can be categorized into two broad categories: Categorical Variables Numerical Variables  TYPES OF VARIABLES Categorical variables are variables that have a limited number of distinct values or categories. They are sometimes called discrete variables. Categorical variables again split up into two groups, ordinal and nominal variables. Ordinal variables represent categories with some intrinsic order (e.g., low, medium, high; or strongly agree, agree, disagree, strongly disagree). Ordinal variables could consist of numeric values that represent distinct categories (e.g., 1 = low, 2 = medium, 3 = high). These numbers are merely codes. Nominal variables represent categories with no intrinsic order (e.g., job category, company division, and race). Nominal variables could also consist of numeric values that represent distinct categories (e.g., 1 = male, 2 = female). Numeric variables refer to characteristics that have a numeric value. They are usually continuous variables, that is, all values in an interval are possible.