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Foundation Course On Research Methods Faculty : H.K DANGI RESEARCH METHODS Objective: The aim of the course is to create a background and awareness of the nature of research process and inquiry. It will expose the student to the methodological problems encountered in interdisciplinary research. The course will provide a comprehension of basic principles of research design and strategy, including an understanding of how to formulate and execute researchable problems. UNIT-1 Introduction Research – definition, scope and objective, types, approaches, significance; scientific investigation. The research process – the broad problem area, preliminary data collection, problem, selection and definition, theoretical framework, hypothesis development and elements of research design. Experimental design – the laboratory experiment, variables, validity, types of experimental designs. UNIT-2 Data measurement, collection, processing and analysis Measurement – measurement in research, operational definition, measurement scales, scaling, scaling techniques, reliability and validity. Data collection – sources of data; data collection methods: interviewing, questionnaires, other methods of data collection. Sampling: Introduction - Need and purpose of sampling, population and sample, population frame, sampling with and without replacement, population parameters. Sampling theory – sampling distributions, parameter estimation, hypothesis testing. Sampling designs – probability and non-probability sampling UNIT-3 Data processing and analysis – review of statistical data analysis, hypothesis formulation and testing , parametric and non parametric test UNIT-4 Interpretation and Report Writing Interpretation – meaning, need, technique. Report writing – the research proposal, the report, integral parts of the report, steps involved in report writing, types of reports, oral presentation, conclusions. Reading List Singleton.R.A.Jr, and Straits B. C. (1999). Approaches to Social Research. Oxford University Press, New York. Moore, D.S. (1999). The Basic Practice of Statistics. W.H. Freedman, N De Vaus, D.A. (1995). Surveys in Social Research. Allen & Unwin, Sydney, NSW, 1995. Foddy, W. (1994). Constructing Questions for Interviews and Questionnaires. Cambridge University Press, Cambridge,. Scarbrough E., E. Tanenbaum (1998) Research Strategies in the Social Sciences. Oxford University Press. Oxford. \ UNIT I INTRODUCTION TO RESEARCH METHODS Research can be defined as the systematic and objective identification, collection, analysis, and dissemination of information for the purpose of assisting management in decision making related to the identification and solution of problems (and opportunities) Identification: involves defining the research problem (or opportunity) and determining the information that is needed to address it. Collection: data must be obtained from relevant sources. Analysis: data are analyzed, interpreted, and inferences are drawn. Dissemination of information: the findings, implications, and recommendations are provided in a format that makes this information actionable and directly useful as an input into decision making. Types of research 1. Problem identification research. The goal is to identify existing or potential problems not apparent on the surface. Examples include market potential, market share, market characteristics, sales analysis, short-range forecasting, long-range forecasting, and business trends research. 2. Problem solution research. The goal is to solve specific marketing problems such as segmentation, product, pricing promotion, and distribution research. Steps for research process 1.Problem definition: defining the research problem to be addressed is the most important step because all other steps will be based on this definition. 2.Developing an approach to the problem: development of a broad specification of how the problem will be addressed allows the researcher to break the problem into salient issues and manageable pieces. 3.Research design formulation: a framework for conducting the research project that specifies the procedures necessary for obtaining the required information. It details the statistical methodology needed to solve the problem and thus the data requirements needed from data collection. 4.Fieldwork or data collection: a field force (personal interviewing, phone, mail, or electronic surveys) gathers project data. While seemingly trivial in nature, to obtain meaningful results field workers must be accurate and thorough in data collection. 5.Data preparation and analysis: the editing, coding, transcription, and verification of data allow researchers to derive meaning from the data. 6.Report preparation and presentation: the findings are communicated to the client. The report should address the specific research questions identified in the problem definition, describe the approach, the research design, data collection and the data analysis procedures adopted, and present The management decision problem asks what the DM needs to do, whereas the research hproblem entails determining what information is needed and how it can be obtained in the most feasible way. Management Decision ProblemResearch Problem1.Should the price be cut in response to a price-cut by a competitor?Determine the buyer- behavior at various price levels.2.Should the product ‘X’ be introduced in the market?Assess the probable market size and share for product ‘X’3.What should be done to increase therelative market share of product ‘Y’?Determine the strengths and weaknesses of ‘Y’ vis-à-vis those of the competitors. RESEARCH DESIGN Research design may be defined as a framework or blueprint for conducting the research project. It specifies the precise details of the procedures necessary for obtaining the required information. Finally, stress that it is important to have a good research design in order to ensure that the project is conducted effectively and efficiently. Exploratory research is used in situations where the problem may have to be defined more precisely, relevant courses of action identified, hypotheses formulated, or additional insights gained before an approach can be developed. Conclusive research would be used to test specific hypotheses, examine specific relationships, or make predictions. While both descriptive and causal researches are classified as conclusive research, they differ in terms of their objectives. Descriptive research is used to describe something, usually market characteristics or functions. Causal research is used to obtain evidence regarding cause-and-effect relationships. Exploratory research is typically used to provide structure and insight into the research problem. For example, using focus groups to determine key factors related to the use of your product.. Descriptive research, it begins with the structure already defined and proceeds to actual data collection in order to describe some market variable. For example, determining the average age of purchasers of your product. Causal research also proceeds from a pre-established structure but attempts to infer causal relationships between variables as opposed to describing variables. For example, determining if increased advertising spending has led to an increase in sales. Descriptive research is marked by the prior formulation of specific hypotheses, the design requires a clear specification of the six W’s of the research: 1.Who: who should be considered? 2.Where: where should the respondents be contacted to obtain the required information? 3.When: when should the information be obtained from the respondents? 4.What: what information should be obtained from the respondents? 5.Why: why are we obtaining information from the respondents? 6.Way: the way in which we are going to obtain information from the respondents Causal research is appropriate to use when the purposes are to understand which variables are the cause and which variables are the effect, and to determine the nature of the functional relationship between the causal variables and the effect to be predicted. Descriptive research can be classified into cross-sectional and longitudinal designs. Cross-sectional designs involve the collection of information from a sample population at a single point in time, whereas in a longitudinal design a fixed sample population is measured repeatedly over several points in time. Longitudinal data tend to be more informative than cross-sectional data because they measure changes in behavior, large amounts of data can be collected, and they are more accurate. Types and Characteristics of Exploratory Studies A Literature Search Conceptual literature Trade literature Published statistics Library homepage Analysis of Selected Cases Intensive study of related cases or past activities May be internal or external Can help provide clues as to how other units or companies have dealt with similar issues B Depth Interview One-on-one interviews that probe and elicit detailed answers to questions, often using nondirective techniques to uncover hidden motivations. Advantages No group pressure Respondent is focus of attention and feels important Respondent is highly aware and active Long time period encourages revealing new information Can probe to reveal feelings and motivations Discussion is flexible and can explore tangential issues Disadvantages Much more expensive than focus groups Do not get the same degree of client involvement; clients do not want to observe single interviews Are physically exhausting for the moderator…reduces the number of people that can be interviewed in a given time period. Moderators do not have other group members to help obtain reactions and to stimulate discussion. C. Focus Group Goal of focus group research: learn and understand what people have to say and why. Find out how participants feel about a product, concept, idea, organization, etc.; How it fit into their lives; Their emotional involvement with it May be conducted alone or as part of a broader project May be use to define issues or to confirm findings from survey research. Requirements for Focus Groups Good group of information-rich participants How many people? How many groups? Characteristics of participants Discussion guide and outline Ground rules Agenda Guiding questions Qualified Moderator Controls flow Stimulates discussion Analysis and Report Methods of Descriptive Research Secondary data analyzed in a quantitative as opposed to a qualitative manner Surveys Panels Observational and other data Experimental research design Independent variables are variables or alternatives that are manipulated and whose effects are measured and compared, e.g., price levels. Test units are individuals, organizations, or other entities whose response to the independent variables or treatments is being examined, e.g., consumers or stores. Dependent variables are the variables which measure the effect of the independent variables on the test units, e.g., sales, profits, and market shares. Extraneous variables are all variables other than the independent variables that affect the response of the test units, e.g., store size, store location, and competitive effort. Validity in ExperimentationInternal validity refers to whether the manipulation of the independent variables or treatments actually caused the observed effects on the dependent variables. Control of extraneous variables is a necessary condition for establishing internal validity. External validity refers to whether the cause-and-effect relationships found in the experiment can be generalized. To what populations, settings, times, independent variables and dependent variables can the results be projected? A Classification of Experimental Designs Pre-experimental designs do not employ randomization procedures to control for extraneous factors: the one-shot case study, the one-group pretest-posttest design, and the static-group. In true experimental designs, the researcher can randomly assign test units to experimental groups and treatments to experimental groups: the pretest-posttest control group design, the posttest-only control group design, and the Solomon four-group design. Quasi-experimental designs result when the researcher is unable to achieve full manipulation of scheduling or allocation of treatments to test units but can still apply part of the apparatus of true experimentation: time series and multiple time series designs. A statistical design is a series of basic experiments that allows for statistical control and analysis of external variables: randomized block design, Latin square design, and factorial designs. One-Shot Case Study X01 A single group of test units is exposed to a treatment X. A single measurement on the dependent variable is taken (01). There is no random assignment of test units. The one-shot case study is more appropriate for exploratory than for conclusive research. One-Group Pretest-Posttest Design 01 X02 A group of test units is measured twice. There is no control group. The treatment effect is computed as 02 – 01. The validity of this conclusion is questionable since extraneous variables are largely uncontrolled. Static Group Design EG:X 01 CG:02 A two-group experimental design. The experimental group (EG) is exposed to the treatment, and the control group (CG) is not. Measurements on both groups are made only after the treatment. Test units are not assigned at random. The treatment effect would be measured as 01 - 02. UNIT 2 Measurement and Scaling Measurement means assigning numbers or other symbols to characteristics of objects according to certain pre-specified rules. Scaling involves creating a continuum upon which measured objects are located. Primary Scales of Measurement Nominal Scale The numbers serve only as labels or tags for identifying and classifying objects. When used for identification, there is a strict one-to-one correspondence between the numbers and the objects. The numbers do not reflect the amount of the characteristic possessed by the objects. The only permissible operation on the numbers in a nominal scale is counting. Only a limited number of statistics, all of which are based on frequency counts, are permissible, e.g., percentages, and mode. Ordinal Scale A ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic. Can determine whether an object has more or less of a characteristic than some other object, but not how much more or less. Any series of numbers can be assigned that preserves the ordered relationships between the objects. In addition to the counting operation allowable for nominal scale data, ordinal scales permit the use of statistics based on centiles, e.g., percentile, quartile, median. Interval Scale Numerically equal distances on the scale represent equal values in the characteristic being measured. It permits comparison of the differences between objects. The location of the zero point is not fixed. Both the zero point and the units of measurement are arbitrary. Any positive linear transformation of the form y = a + bx will preserve the properties of the scale. It is not meaningful to take ratios of scale values. Statistical techniques that may be used include all of those that can be applied to nominal and ordinal data, and in addition the arithmetic mean, standard deviation, and other statistics commonly used in research. Ratio Scale Possesses all the properties of the nominal, ordinal, and interval scales. It has an absolute zero point. It is meaningful to compute ratios of scale values. Only proportionate transformations of the form y = bx, where b is a positive constant, are allowed. All statistical techniques can be applied to ratio data. A Classification of Scaling Techniques Comparative scales involve the direct comparison of stimulus objects. Comparative scale data must be interpreted in relative terms and have only ordinal or rank order properties. In noncomparative scales, each object is scaled independently of the others in the stimulus set. The resulting data are generally assumed to be interval or ratio scaled. Relative Advantages of Comparative Scales Small differences between stimulus objects can be detected. Same known reference points for all respondents. Easily understood and can be applied. Tend to reduce halo or carryover effects from one judgment to another. Relative Disadvantages of Comparative Scales Ordinal nature of the data Inability to generalize beyond the stimulus objects scaled. Paired Comparison Scaling A respondent is presented with two objects and asked to select one according to some criterion. The data obtained are ordinal in nature. Paired comparison scaling is the most widely used comparative scaling technique. With n objects , [n(n - 1) /2] paired comparisons are required Under the assumption of transitivity, it is possible to convert paired comparison data to a rank order. Rank order scaling: The respondents are required to rank various object on the basis of there preferences Constant Sum Scaling: Respondents allocate a constant sum of units, such as 100 points to attributes of a product to reflect their importance. If an attribute is unimportant, the respondent assigns it zero points. If an attribute is twice as important as some other attribute, it receives twice as many points. The sum of all the points is 100. Hence, the name of the scale. Noncomparative Scaling Techniques Respondents evaluate only one object at a time, and for this reason noncomparative scales are often referred to as monadic scales. Noncomparative techniques consist of continuous and itemized rating scales. Continuous Rating Scale: Respondents rate the objects by placing a mark at the appropriate position on a line that runs from one extreme of the criterion variable to the other. The form of the continuous scale may vary considerably. Itemized Rating Scales: The respondents are provided with a scale that has a number or brief description associated with each category. The categories are ordered in terms of scale position, and the respondents are required to select the specified category that best describes the object being rated. The commonly used itemized rating scales are the Likert, semantic differential, and Stapel scales. Likert Scale: The Likert scale requires the respondents to indicate a degree of agreement or disagreement with each of a series of statements about the stimulus objects. Semantic differential is a seven-point rating scale with end points associated with bipolar labels that have semantic meaning. The Staple scale is a unipolar rating scale with ten categories numbered from -5 to +5, without a neutral point (zero). This scale is usually presented vertically. Measurement Accuracy The true score model provides a framework for understanding the accuracy of measurement. XO = XT + XS + XR Where XO = the observed score or measurement XT = the true score of the characteristic XS = systematic error XR = random error Reliability can be defined as the extent to which measures are free from random error, XR. If XR = 0, the measure is perfectly reliable. In test-retest reliability, respondents are administered identical sets of scale items at two different times and the degree of similarity between the two measurements is determined. In alternative-forms reliability, two equivalent forms of the scale are constructed and the same respondents are measured at two different times, with a different form being used each time. Internal consistency reliability determines the extent to which different parts of a summated scale are consistent in what they indicate about the characteristic being measured. In split-half reliability, the items on the scale are divided into two halves and the resulting half scores are correlated. The coefficient alpha, or Cronbach's alpha, is the average of all possible split-half coefficients resulting from different ways of splitting the scale items. This coefficient varies from 0 to 1, and a value of 0.6 or less generally indicates unsatisfactory internal consistency reliability. Validity: The validity of a scale may be defined as the extent to which differences in observed scale scores reflect true differences among objects on the characteristic being measured, rather than systematic or random error. Perfect validity requires that there be no measurement error (XO = XT, XR = 0, XS = 0).Content validity is a subjective but systematic evaluation of how well the content of a scale represents the measurement task at hand. Criterion validity reflects whether a scale performs as expected in relation to other variables selected (criterion variables) as meaningful criteria. Relationship between Reliability and Validity If a measure is perfectly valid, it is also perfectly reliable. In this case XO = XT, XR = 0, and XS = 0. If a measure is unreliable, it cannot be perfectly valid, since at a minimum XO = XT + XR. Furthermore, systematic error may also be present, i.e., XS≠0. Thus, unreliability implies invalidity. If a measure is perfectly reliable, it may or may not be perfectly valid, because systematic error may still be present (XO = XT + XS).Reliability is a necessary, but not sufficient, condition for validity. QUESTIONNAIRE DESIGN A questionnaire is a formalized set of questions for obtaining information from respondents. It must translate the information needed into a set of specific questions that the respondents can and will answer. A questionnaire must uplift, motivate, and encourage the respondent to become involved in the interview, to cooperate, and to complete the interview. A questionnaire should minimize response error. Is the Question Necessary: If there is no satisfactory use for the data resulting from a question, that question should be eliminated. Sometimes, several questions are needed to obtain the required information in an unambiguous manner. In situations where not all respondents are likely to be informed about the topic of interest, filter questions that measure familiarity and past experience should be asked before questions about the topics themselves. A “don't know” option appears to reduce uninformed responses without reducing the response rate. Unstructured questions are open-ended questions that respondents answer in their own words. What is your occupation? Who is your favorite actor? Structured questions specify the set of response alternatives and the response format. A structured question may be multiple-choice, dichotomous, or a scale. In multiple-choice questions, the researcher provides a choice of answers and respondents are asked to select one or more of the alternatives given A dichotomous question has only two response alternatives: yes or no, agree or disagree, and so on. Often, the two alternatives of interest are supplemented by a neutral alternative, such as “no opinion,” “don't know,” “both,” or “none.” A leading question is one that clues the respondent to what the answer should be, as in the following Pretesting refers to the testing of the questionnaire on a small sample of respondents to identify and eliminate potential problems. A questionnaire should not be used in the field survey without adequate pretesting. All aspects of the questionnaire should be tested, including question content, wording, sequence, form and layout, question difficulty, and instructions. The respondents for the pretest and for the actual survey should be drawn from the same population. Pretests are best done by personal interviews, even if the actual survey is to be conducted by mail, telephone, or electronic means, UNIT –III SAMPLING The target population is the collection of elements or objects that possess the information sought by the researcher and about which inferences are to be made. The target population should be defined in terms of elements, sampling units, extent, and time. An element is the object about which or from which the information is desired, e.g., the respondent. A sampling unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process. Extent refers to the geographical boundaries. Time is the time period under consideration. Convenience Sampling Convenience sampling attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time. use of students, and members of social organizations mall intercept interviews without qualifying the respondents department stores using charge account lists “people on the street” interviews Judgmental sampling is a form of convenience sampling in which the population elements are selected based on the judgment of the researcher. test markets purchase engineers selected in industrial research bellwether precincts selected in voting behavior research expert witnesses used in court Quota sampling may be viewed as two-stage restricted judgmental sampling. The first stage consists of developing control categories, or quotas, of population elements. In the second stage, sample elements are selected based on convenience or judgment. Population SampleCharacteristicPercentagePercentageNumber Sex Male4848480 Female5252520____________1001001000 In snowball sampling, an initial group of respondents is selected, usually at random. After being interviewed, these respondents are asked to identify others who belong to the target population of interest. Subsequent respondents are selected based on the referrals. Simple Random Sampling Each element in the population has a known and equal probability of selection. Each possible sample of a given size (n) has a known and equal probability of being the sample actually selected. This implies that every element is selected independently of every other element. Systematic Sampling: The sample is chosen by selecting a random starting point and then picking every ith element in succession from the sampling frame. The sampling interval, i, is determined by dividing the population size N by the sample size n and rounding to the nearest integer. When the ordering of the elements is related to the characteristic of interest, systematic sampling increases the representativeness of the sample. If the ordering of the elements produces a cyclical pattern, systematic sampling may decrease the representativeness of the sample. For example, there are 100,000 elements in the population and a sample of 1,000 is desired. In this case the sampling interval, i, is 100. A random number between 1 and 100 is selected. If, for example, this number is 23, the sample consists of elements 23, 123, 223, 323, 423, 523, and so on. Stratified Sampling A two-step process in which the population is partitioned into subpopulations, or strata. The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted. Next, elements are selected from each stratum by a random procedure, usually SRS. A major objective of stratified sampling is to increase precision without increasing cost. The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible. The stratification variables should also be closely related to the characteristic of interest. Finally, the variables should decrease the cost of the stratification process by being easy to measure and apply. Cluster Sampling: The target population is first divided into mutually exclusive and collectively exhaustive subpopulations, or clusters. then a random sample of clusters is selected, based on a probability sampling technique such as SRS. For each selected cluster, either all the elements are included in the sample (one-stage) or a sample of elements is drawn probabilistically (two-stage). elements within a cluster should be as heterogeneous as possible, but clusters themselves should be as homogeneous as possible. Ideally, each cluster should be a small-scale representation of the population. In probability proportionate to size sampling, the clusters are sampled with probability proportional to size. In the second stage, the probability of selecting a sampling unit in a selected cluster varies inversely with the size of the cluster. Parameter: A parameter is a summary description of a fixed characteristic or measure of the target population. A parameter denotes the true value which would be obtained if a census rather than a sample was undertaken. Statistic: A statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter. Finite Population Correction: The finite population correction (fpc) is a correction for overestimation of the variance of a population parameter, e.g., a mean or proportion, when the sample size is 10% or more of the population size. Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter. Confidence interval: The confidence interval is the range into which the true population parameter will fall, assuming a given level of confidence. Confidence level: The confidence level is the probability that a confidence interval will include the population parameter. _____\s Determining the sample size UNIT III - DATA ANALYSIS In a frequency distribution, one variable is considered at a time. A frequency distribution for a variable produces a table of frequency counts, percentages, and cumulative percentages for all the values associated with that variable. Statistics Associated with Frequency Distribution Measures of Location The mean, or average value, is the most commonly used measure of central tendency. The mean, ,is given by Where, Xi = Observed values of the variable X n = Number of observations (sample size) The mode is the value that occurs most frequently. It represents the highest peak of the distribution. The mode is a good measure of location when the variable is inherently categorical or has otherwise been grouped into categories. The median of a sample is the middle value when the data are arranged in ascending or descending order. If the number of data points is even, the median is usually estimated as the midpoint between the two middle values – by adding the two middle values and dividing their sum by 2. The median is the 50th percentile The range measures the spread of the data. It is simply the difference between the largest and smallest values in the sample. Range = Largest – Smallest. The interquartile range is the difference between the 75th and 25th percentile. For a set of data points arranged in order of magnitude, the pth percentile is the value that has p% of the data points below it and (100 - p)% above it. The variance is the mean squared deviation from the mean. The variance can never be negative. The standard deviation is the square root of the variance. The coefficient of variation is the ratio of the standard deviation to the mean expressed as a percentage, and is a unit less measure of relative variability. Skewness. The tendency of the deviations from the mean to be larger in one direction than in the other. It can be thought of as the tendency for one tail of the distribution to be heavier than the other. Kurtosis is a measure of the relative peakedness or flatness of the curve defined by the frequency distribution. The kurtosis of a normal distribution is zero. If the kurtosis is positive, then the distribution is more eaked than a normal distribution. A negative value means that the distribution is flatter than a Normal distribution . Parametric tests assume that the variables of interest are measured on at least an interval scale. Nonparametric tests assume that the variables are measured on a nominal or ordinal scale. These tests can be further classified based on whether one or two or more samples are involved. the samples are independent if they are drawn randomly from different populations. For the purpose of analysis, data pertaining to different groups of respondents, e.g., males and females, are generally treated as independent samples. The samples are paired when the data for the two samples relate to the same group of respondents. Classification of Hypothesis Testing Procedures for Examining Differences Z-Test : The mean life of sample of 400 fluorescent light bulb produced by a company is found to be 1600 hours with a S.D of 150 hrs .Test the hypotheses mean life of bulb in general is higher than mean life of 1570 hours at 0.01 level of significance Z= 30/7.5 = 4 CV = 1570+2.337x7.5= 1587 Since Sample mean > CV null hypotheses rejected The t statistic assumes that the variable is normally distributed and the mean is known (or assumed to be known) and the population variance is estimated from the sample. Assume that the random variable X is normally distributed, with mean and unknown population variance that is estimated by the sample variance s 2. Then, t distributed with n - 1 degrees of freedom. The t distribution is similar to the normal distribution in appearance. Both distributions are bell-shaped and symmetric. As the number of degrees of freedom increases, the t distribution approaches the normal Founder WS Gosset Wrote under the pseudonym “Student”Mostly worked in tea (t) time? Hence known as Student's t test. Preferable when the n < 60Certainly if n < 30 When you have scores from a particular group of people and you want to estimate what the variance would be for people in general who are like the ones you have scores from, use (n -1).To calculate the variance of a sample, when estimating the variance of its population, use (n -1) in order to provide an unbiased estimate of the population variance. Degrees of Freedom : The number you divide by (the number of scores minus 1) to get the estimated population variance is called the degrees of freedom.The degrees of freedom is the number of scores in a sample that are “free to vary”. Imagine a very simple situation in which the individual scores that make up a distribution are 3, 4, 5, 6, and 7.If you are asked to tell what the first score is without having seen it, the best you could do is a wild guess, because the first score could be any number.If you are told the first score (3) and then asked to give the second, it too could be any number. The same is true of the third and fourth scores – each of them has complete “freedom” to vary.But if you know those first four scores (3, 4, 5, and 6) and you know the mean of the distribution (5), then the last score can only be 7.If, instead of the mean and 3, 4, 5, and 6, you were given the mean and 3, 5, 6, and 7, the missing score could only be 4. the t test, because the known sample mean is used to replace the unknown population mean in calculating the estimated standard deviation, one degree of freedom is lost.For each parameter you estimate, you lose one degree of freedom. Degrees of freedom is a measure of how much precision an estimate of variation has. A general rule is that the degrees of freedom decrease when you have to estimate more parameters. Type I Error occurs when the sample results lead to the rejection of the null hypothesis when it is in fact true. The probability of type I error is also called the level of significance. Type II Error occurs when, based on the sample results, the null hypothesis is not rejected when it is in fact false. The probability of type II error is denoted by Unlike, which is specified by the researcher, the magnitude of b depends on the actual value of the population parameter (proportion). The power of a test is the probability (1 – alpha) ejecting the null hypothesis when it is false and should be rejected. Although is unknown, it is related to . An extremely low value of (e.g., = 0.001) will result in intolerably high errors. So it is necessary to balance the two types of errors. Example: Odometers measure automobile mileage. How close to the truth is the number that is registered? Suppose 12 cars travel exactly 10 miles (measured beforehand) and the following mileage figures were recorded by the odometers: 9.8, 10.1, 10.3, 10.2, 9.9, 10.4, 10.0, 9.9, 10.3, 10.0, 10.1, 10.2 Using the .01 level of significance, determine if you can trust your odometer. State the research question. Are odometers accurate? State the statistical hypotheses. Decide if result is significant. Fail to reject H0, 1.67<3.106 Interpret result as it relates to your research question. The mileage your odometer records is not significantly different from the actual mileage your car travels. You can estimate a population mean based on confidence intervals rather than statistical hypothesis tests. A confidence interval is an interval of a certain width, which we feel “confident” will contain the population mean. You are not determining whether the sample mean differs significantly from the population mean. Instead, you are estimating the population mean based on knowing the sample mean. If the primary concern is whether an effect is present, use a hypothesis test. You should consider using a confidence interval whenever a hypothesis test leads you to reject the null hypothesis, in order to determine the possible size of the effect. The t Test for Dependent Samples The t test for a single sample is for when you know the population mean but not its variance, and where we have a single sample of scores. In most research, you do not even know the population’s mean. and, in most research situations, we have not one set, but two sets of scores Chi-Square Test for Independence In one large factory, 100 employees were judged to be highly successful and another 100 marginally successful. All workers were asked, “Which do you find more important to you personally, the money you are able to take home or the satisfaction you feel from doing the job?” In the first group, 49% found the money more important, but in the second group 53% responded that way. Test the null hypothesis that job performance and job motivation are independent using the .01 level of significance. State the research hypothesis. Are job performance and job motivation independent? State the statistical hypotheses. Set the decision rule Decide if your result is significant. Retain H0, 0.32<6.64 Interpret your results. Job performance and job motivation are independent Goodness of Fit: Asks whether the relative frequencies observed in the categories of a sample frequency distribution are in agreement with the relative frequencies hypothesized to be true in the population. The road accident in a country vary from day to day .In a sample following information was obtained UNIT IV REPORT WRITING Readers. A report should be written for a specific reader or readers: the marketing managers who will use the results. Easy to follow. The report should be easy to follow. It should be structured logically and written clearly. Presentable and professional appearance. The looks of a report are important. Objective. Objectivity is a virtue that should guide report writing. The rule is, \"
Tell it like it is.\"
 Reinforce text with tables and graphs. It is important to reinforce key information in the text with tables, graphs, pictures, maps, and other visual devices. Terse. A report should be terse and concise. Yet, brevity should not be achieved at the expense of completeness. Guidelines for Graphs Round or Pie Charts In pie chart, the area of each section, as a percentage of the total area of the circle, reflects the percentage associated with the value of a specific variable. A pie chart is not useful for displaying relationships over time or relationships among several variables. As a general guideline, a pie chart should not require more than seven sections. Guidelines for Graphs -Line Charts A line chart connects a series of data points using continuous lines. This is an attractive way of illustrating trends and changes over time. Several series can be compared on the same chart, and forecasts, interpolations, and extrapolations can be shown. A stratum chart is a set of line charts in which the data are successively aggregated over the series. Areas between the line charts display the magnitudes of the relevant variables. Guidelines for Graphs Pictographs A pictograph uses small pictures or symbols to display the data. Pictographs do not depict results precisely. Hence, caution should be exercised when using them. A bar chart displays data in various bars that may be positioned horizontally or vertically. The histogram is a vertical bar chart and in which the height of the bars represents the relative or cumulative frequency of occurrence of a specific variable. Oral Presentation The key to an effective presentation is preparation. A written script or detailed outline should be prepared following the format of the written report. The presentation must be geared to the audience. The presentation should be rehearsed several times before it is made to the management. Visual aids, such as tables and graphs, should be displayed with a variety of media. It is important to maintain eye contact and interact with the audience during the presentation. Reading the Research Report Interpretation and Conclusions – The interpretation of the basic results should be differentiated from the results per se. Any conclusions or recommendations made without a specification of the underlying assumptions or limitations should be treated cautiously by the reader. Generalizability – It is the responsibility of the researcher to provide evidence regarding the reliability, validity, and generalizability of the findings. Disclosure – The reader should carefully examine whether the spirit in which the report was written indicates an honest and complete disclosure of the research procedures and results.

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