The Institute of Chartered Accountants of Sri Lanka Postgraduate Diploma in Business Finance and Strategy Quantitative Methods for Business Studies Handout 01: Basic Statistics What is Statistics? Statistics is a discipline which is concerned with: Designing experiments and data collection, Summarizing information to aid understanding, drawing conclusions from data, and Estimating the present or predicting the future. Today, statistics has become an important tool in the work of many academic disciplines such as medicine, psychology, education, sociology, engineering and physics, just to name a few. Statistics is also important in many aspects of society such as business, industry and government. Because of the increasing use of statistics in so many areas of our lives, it has become very desirable to understand and practice statistical thinking. Data vs Information Raw facts gathered about a condition, event, idea, entity or anything else which is bare and random, is called data. Information refers to facts concerning a particular event or subject, which are refined by processing data.
Descriptive vs Inferential Statistics. Descriptive statistics can be defined as those methods involving the collection, presentation, and characterization of a set of data in order to describe the various features of that set of data properly. Inferential statistics can be defined as those methods that make possible the estimation of a characteristic of a population or the making of a decision concerning a population based only on sample data. Types of variables Statisticians develop surveys to deal with a variety of phenomena or characteristics. These phenomena or characteristics are called random variables. The data which are observed outcomes of these random variables, undoubtedly differ from response to response. Categorical random variables yield categorical responses, such as yes or no answers. Numerical random variables yield numerical responses such as a person s height in inches. There are two types of numerical variables: discrete and continuous. Discrete random variables produce numerical responses that arise from a counting process. The number of students present in a class is an example of discrete numerical variables. Continuous random variables produce numerical responses that arise from a measuring process. The height of a person is an example of continuous numerical variable, because the response takes on any value within a range, depending in the precision of the measuring instrument. Levels of measurement and types of measuring scales Nominal scale A nominal scale classifies data into various distinct categories in which no ordering is implied. Nominal scaling is the weakest form of measurement because no attempt is made to account for
the differences within a particular category or to specify any ordering or direction across the various categories. Examples of nominal scaling are: Categorical variable Categories Gender Male Female Automobile ownership Yes No Ordinal scale An ordinal scale classifies data into distinct categories in which ordering is implied. Ordinal scaling is a somewhat stronger form of measurement, because an observed value classified into one category is said to possess more of a property being scaled than does an observed value classified into another category. Categorical variable Ordered categories Student grades A B C D F Restaurant rankings ***** **** *** ** * Facilities offered in college excellent fair disappointing unacceptable Interval Scale An interval scale is an ordered scale in which the difference between measurements is a meaningful quantity that does not involve a true zero. By implication, data measured on an interval scale have an arbitrary zero point. That is, the person designing the scale arbitrarily decides where to locate the zero. To qualify as an interval scale, the distance between numerical values needs only be definable. A good example of interval data is temperature measured in degrees Fahrenheit, and Celsius. Each scale uses a different zero point. Each of these scales constitutes an interval scale since the distance between any two numerical values can be precisely specified, and each scale has an arbitrary point defined to be zero.
Ratio Scale Ratio scale consists of numerical measurements where the distance between numbers is of a known, constant size; in addition there is a non-arbitrary zero point. Examples of measurements in ratio scales are height, weight, age and salary. Definitions of terms A population (or universe) is the totality of items or things under consideration. A sample is the portion of the population that is selected for analysis. A parameter is a summary measure that is computed to describe a characteristic of an entire population. A statistic is a summary measure that is computed to describe a characteristic from only a sample of a population. Sources of Data Primary data refers to the data originated for the first time for a specific purpose. Primary data collection sources include surveys, observations, experiments, questionnaire, personal interviews, etc. Secondary data is the already existing data, collected by other investigators or organisations earlier. Secondary data collection sources are government publications, websites, books, journal articles, internal records etc. Collecting Data Data can be collected based on a sample or from the whole population. A population census is where data is collected from the entire population. As this is difficult in many situations, studies are mostly conducted based on sample data.
Types of Studies conducted to collect data Observational Study - The data collector observes the subjects and measures variables, but does not influence in any way or attempt to intervene in the study. Designed Experimental Study - Unlike an observational study, an experimental study involves purposely attempting to influence the results. The goal is to determine what effect a particular treatment has on the outcome. Surveys are one form of an observational study, no influence is made on the outcomes. A survey may focus on opinions or factual information depending upon the purpose of the study. Surveys may involve answering a questionnaire or being interviewed. Data collection instruments. The quantitative data gathering strategies include: Interviews Questionnaires Interviews Face -to -face interviews have a distinct advantage of enabling the investigator to establish rapport with potential participants and therefore gain their cooperation. These interviews yield highest response rates in survey research. Telephone interviews are less time consuming and less expensive and the data collector has ready access to anyone who has a telephone. Computer Assisted Personal Interviewing (CAPI) is a form of personal interviewing, but instead of completing a questionnaire, the interviewer brings along a laptop or hand-held computer to enter the information directly into the database. This method saves time involved in processing the data, as well as saving the interviewer from carrying around hundreds of questionnaires.
However, this type of data collection method can be expensive to set up and requires that interviewers have computers and typing skills. Questionnaires Paper-pencil-questionnaires can be sent to a large number of people and saves time and money. Web based questionnaires are sent through e-mail on which respondent would click on an address that would direct the respondent to a secure web-site to fill in a questionnaire. Exercises: 1. For each of the following examples of data, determine the type of data and level of measurement. i. Amount of time taken to assemble a simple puzzle. ii. Rating of a newly elected politician (excellent, good, fair, poor) iii. Province in which a person lives iv. Colour of a car entering a parking lot. v. Weight of newspapers recovered for recycling on a single day. 2. Categories the following sources of data as primary or secondary sources: Diaries, Letters, Biographies, book about a specific subject, interview findings. 3. Discuss the advantages and disadvantages of conducting a population census and sample investigations. 4. Identify the types of studies conducted in the following examples. i. A study took random sample of adults and asked them about their bedtime habits. The data showed that people who drank a cup of tea before bedtime were more likely to go to sleep earlier than those who didn't drink tea. ii. iii. Another study took a group of adults and randomly divided them into two groups. One group was told to drink tea every night for a week, while the other group was told not to drink tea that week. Researchers then compared when each group fell asleep. A study was conducted to identify the factors affecting the consumer loyalty towards mobile telecommunication service providers. Data was collected using a questionnaire from 300 people who use cellular.