CHAPTER-6 RESEARCH METHODOLOGY, DATA ANALYSIS AND INTERPRETATION

Transcription

1 CHAPTER-6 RESEARCH METHODOLOGY, DATA ANALYSIS AND INTERPRETATION 6.1 Introduction Research methodology is a way to systematically solve the research problem. Research methods may be understood as all those methods/techniques that are used for conduction of research, thus refer to the methods the researchers use in performing research operations during course of studying the research problem. Research methodology has many dimensions and research methods do constitute a part of the research methodology. The various steps provides a useful procedural guideline regarding the research process are: (1) formulating the research problem;(2) extensive literature survey;(3) developing the hypothesis;(4) preparing the research design;(5) determining the sample design;(6) collecting the data; (7) execution of the project; (8) analysis of data; (9) hypothesis testing;(10) generalizations and interpretation and (11) preparation of the report of the results. The present changing scenario in the globalisation, an organisation cannot be run merely on investment and returns, but more on the quality of their products, services, human resource, productivity, timeliness, cost-reduction and its commitment to organisation s goals. The quality and productivity with commitment can be achieved only when there is a real change in the mindset of people at work in the way they look at the global; they look at the technology and the way they look at the organisations. This change can be made only by the proper implementation and utilisation of technology and human resource development practices. Therefore, the industrial productivity became the centre of attention as far as the research is concerned. In the present industrial scenario the organisation has to maintain good standard to stand in the highly competitive world of globalisation, for small continuous improvement in its quality. The research topic has been selected with reference to industrial productivity scenario and potentialities with an objective of identifying productivity and economy related problems specific to the area suggesting ways and means to reduce their ill effects. 6.2 Relevance of the study In the present age of cut-throat competition, it becomes highly necessary for an organisation to be dynamic in the globalisation era. This is possible only when the 156

2 employees, employers and organisations are capable enough to cope up with the changing world scenario. In the rapidly changing environment human being is the most important and valuable resource to play vital role in every organisation has in the form of its employees. A large number of studies have been carried out from time to time to examine, the changes in the productivity and its impact on economy, at the national level. Studied have also been carried out to analyse productivity trends in major manufacturing industries. Most of these studies are generic in nature and not necessarily area specific. Present study is to develop productivity enhance route programmes in the present context to the changed trends of education, technologies, collaborative partnership between institutions and industries of mutual benefit for all. Talent Management 93 : Talent is often cited as a key differentiator for competitive success. As more and more organisations realised that managing talent effectively is the key to business success; it is a topic of interest to both industry and academia. For many of the services organisations, it is more often than not an indication of the value of its human assets and other intangible assets. Talent is important to organisational performance; it is not just a human (capital) complementary issue. Human capital organisations not only have good talent, but are designed and managed from the board room to the front line in ways that optimise talent attraction, retention, and performance and is to source great talent to collective organisational capability. With the growth of the services in many countries including India, it would be of interest to work out how value creation happens within a human capital centric approach to talent management. 6.3 Objectives of the Study The primary objective of this research was to take the stock of existing situations and to assess the industrial performance in the context of the changing industrial scenario of the industrial units of the estate under consideration for this study. Another major focus of the study was to harvest if any means and measures were followed to keep pace with highly competitive situations for survival. 93 Edward E. Lawler III, Talent: Making people your competitive advantage, Vikalp, Volume 35, July- September, 2010, No.3, IIM, Ahmadabad, pp

3 The researcher wanted to study the possibility of effective means of utilisation of resources available and especially human wants and satisfaction leading to better performance and to study ills of the estate which are due to inadequate productivity levels and to study the possibilities for technological changes, potentialities, healthy industrial performance and scope for future developments. 6.4 Hypothesis of the study A hypothesis is an assumption about relations between variables. Hypothesis can be defined as proposition or generalisation, which needs to be tested to determine its validity. Thus, hypothesis is a tentative statement made by the researcher, which the researcher is going to prove or disprove. A hypothesis is a tentative statement asserting a relationship between certain facts. The generalised hypotheses are considered latter in this chapter covering all factors that govern the industrial performance considering all aspects, means measures and methods to enhance industrial productivity and to see the potentiality of allied and new industries in the areas were industrial productivity scenario and potentiality. 6.5 Research design Research design is the systematic arrangement of data collection and analysis in a manner that aims to combines relevance to the research purpose. It is a road map of the collection, measurement and analysis of data. For this research study both the primary and secondary sources of data were used. In the beginning of the research, an investigative work was carried out to identify status of industrial areas in Anand district of Gujarat state. For this purpose, secondary data were collected with the help of available records from District Industries Centres (DICs), Anand, V.U.Nagar GIDC office, Vitthal Udyognagar Industries Association (VUIA) and from their publications. It was observed that there are very few large-medium scale industries and majority of them are small-scale units and ancillary industries. There are quite high numbers of sick units either closed or about to close. Research methodology: The present study was conducted in industrial estates of Anand district, Gujarat. The estate was established in 1965.At present 1000 odd units working and around persons got jobs. The units were selected from the members directory published by Vitthal Udyognagar Industries Association (VUIA), out of which units were located for the study, Questionnaires were distributed / posted and interviews were conducted. 158

4 The basic methodology that followed was the questionnaire method. To serve the purposes the researcher has designed three questionnaires and one interview schedule. Each instrument was designed to gain the maximum relevant information from the cross sections of the organisation. Summary of total usable questionnaires received are listed in Table 6.1. A multifaceted method by incorporating both quantitative and qualitative technique was used. The questionnaires are presented in annexure I to IV Sampling design A sampling design is a definite plan for obtaining a sample from a given population. It is a pre-plan before actual survey is undertaken. It also decides techniques or the procedure a researcher adopts in selecting a sample and the sample size Universe (Area of study) Universe means the particular area from where the researcher collects the data by selecting sample from the total population of that area. Universe covers the whole defined field on which the study is based. The researcher has selected Vithal Udyognagar industrial estate and surrounding industries of six estates of Anand district of Gujarat state as the universe (area of study) The population Since, the study was related to the industries in the estates under consideration, especially Vitthal Udyognagar and to decide the target population which is one of the most important aspect of the study, the references were taken of the registered members unites with Vitthal Udyognagar Industries Association (VUIA) and District Industries Centre (DIC) at Anand. The members from registered units were considered as the population for this study Data collection Data: Statistical data can be broadly classified into two categories. The one is qualitative data, which signifies an attribute like level of satisfaction, gender, taste etc., which cannot be expressed on an interval scale or in some measured units. The second one is quantitative data, which signifies a measurement on an interval scale like body mass index, height, income of person etc. When study started it was decided to get responses from 100 industries. However, at the time of sending the questionnaires it was thought to put in all efforts and get as much as response possible. The study draws information from two sources- primary and secondary data: 159

5 Primary data sources: The data obtained directly from each unit in a survey is often known as primary data. The researcher has collected the needed data directly from the respondents for this study. Primary data were collected with the help of questionnaires designed from the top personnel, executive-staff, workers etc. Primary data is the first hand information and original source of data. Secondary data sources: The data from external sources like, some government and private agencies are involved in maintaining large databases, published materials or directly from computer media. The researcher has used published articles, reports, journals, library books, magazines, news papers, internets - websites, etc. as a secondary source of data, these references taken in the form of secondary data. The Instruments [Questionnaires]: Three questionnaires were designed as below: Questionnaire-1 (Main): A study of industrial productivity scenario and potentiality in the industrial estates under study. It includes both open ended and closed ended questions to be answered by the respondents. Questionnaire-2 (Executive, officers-staff): Through structured questionnaires for the middle level management- employees of the organisations respondents considering executives, officer-staff to study the industrial productivity scenario and potentiality in the industrial estates under study. Questionnaire-3 (Workers): Through structured questionnaires for the lower level staffs of the organisations and most important part of the work organisations are workers as respondents to study the industrial productivity scenario and potentiality in the industrial estates under study. Primary data was collected through structured questionnaire having closed-ended as well as a few open-ended questions/statements. In most of the cases five point Likert scale was used. The questionnaires are given as Annexure-I to III, from pages: Data preparation - The Respondents (Sample size) 94 After the research problem has been defined and a suitable approach developed, an appropriate research design formulated, and the fieldwork conducted, the important next steps are data preparation and analysis. 94 Malhotra, N.K, and Das S., Marketing Research - An applied Orientation, Pearson Education in South Asia, New Delhi, (2009), pp

6 Before the raw data contained in the questionnaires can be subjected to statistical analysis, they must be converted into a form suitable for analysis. The quality of statistical results depends on the care exercised in the data-preparation phase. Paying inadequate attention to data preparation can seriously compromise statistical results, leading to biased findings and incorrect interpretation. This includes data-collection process, which begins with checking the questionnaire for completeness. Questionnaire checking: The questionnaires were checked for incomplete, inconsistent, and ambiguous responses. Questionnaires with unsatisfactory responses were returned to the respondents and asked to reconsider the same. The questionnaires were discarded with large proportion of unsatisfactory responses and this has resulted in final sample sizes as shown in Table6.1. The data were cleaned by identifying out-of-range and logically inconsistent Table6.1: The sample sizes of the industrial units were considered for study Sr. No. Questionnaire Questionnaire distributed Questionnaire received 161 Questionnaire usable (Sample size) Percent 1. Main Executive-staff Workers These responses include primary data from small, medium and large scale units in operation. These responses were considered from usable questionnaires only and responses are ranging from 43.33% to 62.40% which are considered for this research study and analysis. Questionnaires editing: Editing is the review of the questionnaires with the objective of increasing accuracy and precision. Questionnaires were screened to identify illegible, incomplete, inconsistent, or ambiguous responses. Coding questions: It is a method of assigning a numeric value or a symbol to each level of the attribute under consideration. All the data for statistical analysis are required in quantitative form only. Even if the data is quantitative, it has to be coded before carrying out statistical analysis and latter decoded for interpretation. Coding of structured

7 questions is relatively simple, because the response option is predetermined. The coding of unstructured or open-ended questions is more complex. Respondents verbatim responses are recorded on the questionnaire. 6.6 Limitations of the study The problems in data collection were many like: Non-availability of some secondary data. Responses with reservation caused limited co-operation from some of the respondents. Top level, middle level and lower-level officials, employees responded differently and might have added little or more bias. The postponements of the responses were time consuming and tiresome due to busy schedule or unwillingness to disclose certain information by the respondents. The investigator was thought to be industry - agent or government authority in spite of avowal was given, so extracting information was difficult initially, too much time was consumed in convincing them for the purpose of the study. The time factors, poor awareness of some respondents were other limitations. The supervisors and technicians were scared about the disclosing problems they are facing at workplace. Lower education, language problem and lack of freedom to disclose the facts were major constraints to the most of the workers. 6.7 Statistics associated with the various statistical analyses 95 Basic Analysis: Once the data have been prepared for analysis, the researcher should conduct some basic analysis such as frequency distribution, cross-tabulation, and hypothesis testing etc. Statistical analysis is a vital component in every aspect of contemporary research. Survey: One is by conducting a survey of the entire population in which the researcher is interested or by taking a sample of it. 95 Sharma, K.V.S., Statistics Made Simple, Prentice Hall of India, New Delhi (2006), pp

8 Sample: A sample is a set of items or individuals selected from a larger aggregate or population about which we wish quantitative information. Sample should be a true representative of the population. A poor representative naturally gives a poor show! Practitioners believe in thumb rules like taking 10% of the population as the sample. All those cases, which are included in the study from the population, will be the sample. The sample taken should be a random one so that the conclusions drawn will be free from bias. Sampling: is the process of drawing samples from a given population. Census: If all the individuals or units of a population are inspected for the study, it is called census or 100% inspection. In the context of quality control, census is called screening inspection, according to which every item is inspected with respect to some vital characteristics. Population: The population from which the sample has to be taken shall be examined carefully. If all the units were homogeneous, it would be enough to collect data through a simple random sample. If the population is not homogeneous with respect to one or more characteristics, then a method called stratified random sampling is recommended. It takes care of the groups (called strata) within the population and suggests a method of drawing the sample in such a way that the different groups will have proper representation in the sample. Parameters: If the measurements are obtained from the entire population, the values of mean, median, mode, standard deviation etc., would be exact and they are called the parameters. If relevant data is taken from each and every in the population, the average will be the true value and it is called the parameter. Estimates: When calculated values are based on a sample, the resulting statistics are called the estimates of the unknown parameters of the population. If it is not possible to take relevant data and the random sample is taken, this need not be the same as the true value. The result called an estimate of the true value. Statistic: A value like the mean obtained from the sample data is often called a statistic. Variable: Any aspect on which data is collected is called a variable. Usually all the independent questions in a survey are attached separate variables. It is necessary to determine whether a variable should be taken as a cont or measurement. Statistical inference: The theory of statistics has a special branch called statistical inference that deals with two major issues namely estimation and tests of hypothesis. 163

9 6.7.1 Inferential statistics 96 Apart from descriptive statistics, the major function of statistics is to help in drawing conclusions about the population parameters based on sample statistics. This is called inferential statistics and an important concept that is related to this branch is probability. Probability is basically the chance of happening or non-happening of an event. Inferential statistics deals with two major activities: i) Estimation of unknown parameters of a population. ii) Testing whether the sample data have sufficient evidence to support or reject a hypothesis about the population parameters. A researcher should be familiar with these two concepts. Every population is characterized like mean, median, standard deviation. Each parameter explains one aspect of the population. When we do not have prior knowledge about the value of the population parameter, we use the concept of estimation. A function of the sample observations, like the mean, is called a statistic. The statistic used to estimate the parameter is called the estimator. A good estimator is characterized by certain properties like unbiasedness or consistency. Depending on the sample size and the nature of population, this point estimate may deviate from the true parameter by some amount of unknown and variable error. The relationship between the statistic and the parameter is given by: Parameter = Statistic ± Error Statistical Tests Concerning Means: These tests are based on the assumptions that the sample data has come from a normal population with mean µ and variance σ 2. Knowledge about the population variance is an important factor for analysis. Z-Test: In case of a sample with size 30 or more (usually called large sample), the sample variance can be used in place of σ 2 and the area property of the normal distribution is used to test the null hypothesis. Such a test is often called the normal test or the Z-test. For these tests, the test statistic Z follows the standard normal distribution for which the mean is 0 and the standard deviation is 1. The Z-test is a univariate hypothesis test using the standard normal distribution. The z-test can be used for one sample or two independent samples as well. 96 Sharma, K.V.S., Statistics Made Simple, Prentice of Hall of India, New Delhi (2006), pp

10 T-Test: When the sample size is small, the test statistic Z for comparing the means does not follow the standard normal distribution. The exact distribution is called the t- distribution after name of its inventor W.S. Gusset who published his results by the pen name Student. It is popularly known as Student s t-distribution and the tests based on it are known as t-tests. DF: Degree of freedom: The t-distribution is index by constants called the degree of freedom denoted by DF. The DF is the number of independent observations available for estimating the true parameter of the population. If the sample size is n, then the DF is (n - 1). Depending on the type of test, the DF is appropriately defined. The critical value of the test has to be read from tables of t- distribution corresponding to one critical corresponding to the DF at the desired number level of significance. The every constraint imposed on the data reduces one degree of freedom. The t-distribution possesses all the properties of the standard normal distribution, when the sample size becomes large. In such cases, the critical value for the test can be used either from the t-distribution tables or from the table of standard normal distribution. Hence, tests based on the t-distribution can be used for large samples without any difference. 1. The One - Sample Z-test for mean: The objective of this test is to investigate whether the difference between the hypothesized mean (µ 0 ) and the sample mean (x) is significant. The test is based on the assumption that the sample data has come from a normal population with mean µ and known variance σ 2.The null hypothesis is H 0 :µ = µ 0 and the alternative can be either two-sided or one sided. When the sample size is large but σ is not known (which is the case usually), the sample standard deviation can be used as an estimate of σ and the same Z-test can be used for testing the significance of the mean. 2. The One - Sample t-test for mean: The t-test is one of the popularly used tests for comparing the means. When the sample size is small and the population variance σ 2 is not known, the Z-test cannot be applied for testing the significance of the observed mean. However, when the sample has come from a normal distribution (at least with close approximation) we can use the theory of Student s t-distribution in place of the normal distribution used in the Z-test. The resulting test is called the t-test. 165

11 3. The Two - sample Z-test for means: The test is used for comparing the means of two independent populations is µ 1, µ 2 and variance σ 2,σ2 respectively. We wish to test whether the difference between these two means could be taken as zero (or some other constant). Random samples of size n 1 and n 2 from the two populations. The test depends on the difference between the sample means x 1 and x 2. The objective is to investigate whether the observed difference between the sample means is any evidence of a significance difference between the two population means. It follows standard normal distribution. As usual we reject the null hypothesis if the calculated value of Z is larger than the critical value at the fixed level α. We use Z-test when the sample size is large and the population variances are known. 4. The Two - sample t-test for means: This is a test for comparing the means of two populations based on the sample means. This is commonly known as the small sample test for means. The test procedure is similar to that of the Z-test except that the critical value is based on the t-distribution. The test is used when the researcher has belief (evidence) that the population variances are equal. The other one is used when the population variance are likely to be different. 5. F test is a statistical test of the equality of the variances of two populations. An F- test of sample variance may be performed if it is not known whether the two populations have equal variance. The F statistic is computed as the ratio of two sample variances. F distribution is a frequency distribution that depends upon two sets of degrees of freedom-the degrees of freedom in the numerator and the degree of freedom in the denominator. 1 Mean sumof squares( MS) between groups( s ) The F ratiois defined as, F = 2 Mean sumof squares( MS) within groups( s ) If the groups really have any significant effect, we can expect the F- ratio to be larger than the critical value. (If the F-ratio is less than 1, it is automatically insignificant and we need not compare it with the critical value).while using the t-test for comparing two means, we have assumed that the variances of the populations are equal. This 2 assumption can be verified by testing, the hypothesis, H0 : σ 1 = σ 2 2. This test is called 166

12 the variance ratio test. If n 1, n 2 denotes the sizes of the two samples respectively and S 2 1, S 2 2 denotes the corresponding estimates of the population variances based on the 2 two samples, then the F-statistic is given by F = S 1 / S 2 2. This statistic follows a distribution called the Snedecor s F- distribution with (n 1-1, n-2) Frequency distribution 97 Frequency: The fundamental requirement in data analysis is that of counting how many times each distinct value of a variable has occurred. The count or the tally of such values is called the frequency. When we arrange the values and their corresponding frequencies as a table, we get what is called a one-dimensional frequency table. This job is called tabulation and the variable for tabulation could be either numeric or categorical. A mathematical distribution whose objective is to obtain of the number of responses associated with different values of one variable and to express these counts in percentage terms. Frequency distribution and crosstabulations are basic techniques that provide rich insights into the data and lay the foundation for more advanced. The distribution of total frequency into different groups or classes is known as frequency distribution. To describe the frequency distribution of a variable in the form of a simple statistical graph called histogram. A frequency distribution is a convenient way of looking at different values of a variable. Cross tabulation: It is basically a job of summarizing the raw data into an understandable form. Tabulation can also be defined as a process of counting the number of cases falling in different categories of a variable. A statistical technique that describes two or more variables simultaneously and results in tables that reflect the joint distribution of two or more variables. Cross-tabulation is the merging of the frequency distribution of two or more variables in single table The Chi-Square (χ 2 ) Test 98 The chi-square test is a statistical test used to compare the observed frequencies with those, which are expected according to some theory or a hypothesis. There are two specific applications of the chi-square test namely: (a) Chi-square test for the goodness of fit, and (b) Chi-square test for the independence of attributes.: It assists us in determining whether a systematic association exists between the two 97 Malhotra, N.K, and Das S., Marketing Research - An applied Orientation, Pearson Education in South Asia, New Delhi, (2009), pp Sharma, K.V.S., Statistics Made Simple, Prentice of Hall of India, New Delhi (2006), pp

13 variables. The χ 2 statistic can also be used in goodness-of-fit tests to determine whether certain models fit the observed data. The chi-square statistic is used to test the statistical significance of the observed association in a cross-tabulation. It helps us to understand how one variable relates to another variable, statistics are available for examining the significance and strength of the association. Chi-square test for the goodness of fit: This test is used to compare the differences between the observed frequencies and the expected frequencies corresponding to n categories or classes. The expected frequencies could be obtained by using a statistical distribution like Binomial, Poisson, Normal or some other law. Now the problem is to verify whether the theory according to which these frequencies have been obtained fits well to the data. In other words, we may investigate whether the available data supports the theory or not. The procedure is to compare the observed and the expected values and investigate whether the discrepancy could be taken as zero. The null hypothesis is that the theory fits well to the data and the alternative is that the fit is not good. We conclude that the fit is good only if the p-value is less than the target of α =0.05 or The p-value is higher than 0.05 we accept the null hypothesis and conclude that the numbers of items are equally distributed. Thus the chi-square test can be used to test for the discrepancy between the observed and expected number of cases in a data. Chi-square test for Independence: Consider another application of chi-square test called the test of independence of attributes. Consider the cross-tabulation of some characteristic across two categorical variables. The resulting table is called a two-way frequency table or a contingency table. One characteristic or attribute is shown along the rows and the other is shown along the columns. Each cell of the table gives the count or the number of cases corresponding to that cell. If the χ 2 value exceeds the critical value, we reject the null hypothesis. The conclusion is that the two characteristics are not independent and they are associated with each other. Phi-Coefficient (φ): The phi-coefficient is used as a measure of the strength of association in the special case of a table with two rows and two columns. The phi coefficient is proportional to the square root of the chi-square statistic. When φ=0, there is no association, when the variables are perfectly associated, phi coefficient assumes the value of 1 and all observations fall just on major or minor diagonal. 168

14 Contingency Coefficient (C): Whereas the phi coefficient is specific to a 2x2 table, the contingency coefficient can be used to assess the strength of association in a table of any size. This index is also related to the chi-square. Cramer s (V): Cramer s V is a modified version of the phi correlation coefficient, and is used in tables larger than 2x2, it has no upper limit. A large value of V indicates a high degree of association. It does not indicate how the variables are associated. Lambda Coefficient (λ): Lambda assumes that the variables are measured on a nominal scale. Asymmetric lambda measures the percentage improvement in predicting the value of the dependent variable, given the value of the independent variable. A value of λ = 0 means no improvement in prediction. A value of λ= 1 indicates that the prediction can be made without error. This happens when each independent variable category is associated with a single category of the dependent variable. Symmetry lambda measures the overall improvement when prediction is done in both directions Testing of Hypotheses: 99&100 Formulae the hypotheses: The first step is to formulate null and alternate hypotheses. A null hypothesis is a statement of the status quo, one of no difference or no effect. If the null hypothesis is not rejected, no changes will be made. An alternate hypothesis is one in which some difference or effect is expected. Accepting the alternate hypothesis will lead to changes in opinions or actions. Thus, the alternate hypothesis is the opposite of the null hypothesis. The null hypothesis is always the hypothesis that is tested. A null hypothesis may be rejected, but it can never be accepted based on single test. A statistical test can have one of two outcomes. One is the null hypothesis is rejected and the alternate hypothesis accepted. The other outcome is that the null hypothesis is not rejected based on the evidence. However, it can be incorrect to conclude that because the null hypothesis is not rejected, it can be accepted as valid. In classical hypothesis testing, here is no way to determine whether the null hypothesis is true. 99 Sharma, K.V.S., Statistics Made Simple, Prentice of Hall of India, New Delhi (2006), pp Malhotra, N.K, and Das S., Marketing Research - An applied Orientation, Pearson Education in South Asia, New Delhi, (2009), pp

15 In research problem, the null hypothesis is formulated in such a way that its rejection leads to the acceptance of the desired conclusion. The alternate hypothesis represents the conclusion for which evidence is sought. In the light of the sample data, if the hypothesis is found false, we may have evidence to believe in this alternative hypothesis. For example, managerial decisions call for verification of statements on the basis of available information. Thus, a marketing manager may be interested in verifying the statement the brand X is performing as well as brand Y. He may verify this statement on the basis of average sales of X and average sales of Y, and by comparing these averages. Are the averages same or different? Whether the difference in averages is statistically significant or not? Similarly, a finance manager may be interested in testing the statistical significance of the difference between performances of his company vis-à-vis his competitor by measuring the performance in terms of average profits earned during the last five years. Numerous such situations are encountered by managers wherein they are interested in testing some Hypotheses and then take decisions that can be used for statistical testing of hypotheses. Simple Hypothesis: A hypothesis is said to be simple if it specifies the distribution of the population completely. For instance, in case of normal population with mean µ and standard deviation σ, a simple null hypothesis is of the form H 0: µ = µ 0, σ known, knowledge about µ would be enough to understand the entire distribution. Composite Hypothesis: If the hypothesis does not specify the distribution of the population completely, it is said to be a composite hypothesis. All these are composite because none of them specifies the distribution completely. Hence, for such a test the level of significance (LOS) is specified not as α but as at most α. Hypothesis Testing Related to Associations Null hypothesis (H 0 ): It is a hypothesis usually formulated in a way opposite to what we wish to prove. For instance, if we wish to prove that the teaching method A is better than B, we formulate the null hypothesis that there is no difference between the two methods. This is usually denoted by H 0. The null hypothesis (H o ) is a statement in which no difference or effect is expected. Alternate Hypothesis (H 1 ): A statement that some difference or effect is expected. Accepting the alternate hypothesis will lead to changes in opinions or actions. Thus, the 170

16 alternative hypothesis is the opposite of the null hypothesis. The alternative hypothesis represents the conclusion for which evidence is sought. Whenever we draw inferences about a population, there is risk that an incorrect conclusion will be reached. Alternate hypothesis means that whenever the null hypothesis is not true, one of the alternatives must be true. That is why H 0 and H 1 are mutually disjoint statements. Significance level: Significance level states, whether the means of two populations really differ or not. Let the following hypothesis be framed. H 0 : The population means are equal (µ 1 = µ 2 ), H 0 : The population means are not equal (µ 1 # µ 2) Type-I error: By looking at the sample means we may arrive at the conclusion that H 0 is wrong and hence support H 1. Suppose H 0 really true and the sample evidence is a chance occurrence, which has led to a wrong rejection of H 0. This is an error, called Type-I error. It is called the level of significance (LOS) denoted by the Greek letter α. The commonly used value of α is 0.05 or 0.01 which are understood as 5% and 1% levels respectively. The Type I error is controlled by establishing the tolerable level of risk of rejecting a true null hypothesis. Type-II error: There is another error that can be committed by an analyst while accepting the null hypothesis even though it is false. It is like accepting that the population means are different even when they do not really differ. This is called the Type-II error and the risk of committing this error is denoted by β and it is called the β-risk. The quantity (1-β) is called the power of the test and it is a measure of the discriminating power of the test between chance occurrence and true occurrence of the result under the given hypothesis. Type II error (β) occurs when, based on the sample a result, the null hypothesis is not rejected when it is in fact false. Critical Value: While testing for the difference between the means of two populations, our concern is whether the observed difference is too large to believe that it has occurred just by chance. But then the question is how much difference should be treated as too large? Based on the sampling distribution of means, it is possible to define a cut-off or threshold value such that if the difference exceeds this value, we say that it is not an occurrence by chance and hence there is sufficient evidence to claim that the means are different. Such a value is called the critical value and it is based on the level of significance. The critical value is based on the 171

17 theoretical distribution of the test statistic under consideration. The following rule would help in reading the critical values from the tables: If α = 0.05 and the test is two-sided, read the critical value under α = If α = 0.05 and the test is one-sided, read the critical value under α/2 = The test statistic: Whenever a test is conducted we accept the null hypothesis if the calculated value of the test statistic is less or equal to the critical value; otherwise it is not accepted. The p-value of a test: The observed significance level is a criterion that can be computed from a sample data. It is the probability of obtaining a test value as large as the observed one, when the null hypothesis was really true. This is called the p-value of a test and commonly shown in every computer output associated with a problem of testing. Symbolically, the p-value is simply P (Z Cal >= ZCri). Therefore, the p-value is the probability of wrongly rejecting the null hypothesis. If p < 0.05, we say that the test result is significant at 5% level. We then reject the null hypothesis with a high confidence. When the p-value is given along with the test result, there is no need to specify the critical value. Hypothesis-testing procedures are classified as tests of associations or tests of differences based on one or two samples. These findings are often displayed using tables and graphs. Compare the probability (Critical Value) and make the decision: If the probability associated with the calculated or observed value of test statistic (TS CAL ) is less than the level of significance (α), null hypothesis is rejected. If the calculated value of the test statistic (TS CAL ) is greater than the critical value the test (TS CR ), the null hypothesis is rejected. If probability of TS CAL < significance level (α), then reject H 0, but If probability TS CAL > TS CR, then reject H 0. Research Conclusion: The conclusion reached by hypothesis testing must be expressed in terms of the research problem. The hypotheses testing can be related to either an examination of association or an examination of differences. 172

18 In tests of associations, the null hypothesis is that there is no association between the variables ( H 0 :..is NOT related to ). In tests of associations, the null hypothesis is that there is no difference (H 0:..is NOT different from ). Hypothesis Testing Related to Differences Tests of differences could relate to distribution, means, proportions, medians, or rankings. Hypothesis-testing procedures can be broadly classified as parametric or nonparametric, based on the measurement scale of the variables involved. Independent samples: Two samples that are not experimentally related. The measurement of one sample has no effect on the values of the second sample. Independent samples are drawn randomly from different populations. 101 & Analysis of Variance (ANOVA) Analysis of Variance is used as a test of means for two or more populations. In its simplest form, analysis must have a dependent variable that is metric, (measured using an interval or ratio scale). There must also be one or more independent variables. ANOVA is a statistical technique for examining the differences among means for two or more populations. ANOVA is thus an important inferential tool in statistics. Statistical data analysis can be broadly divided into two categories as follows: i) Univariate analysis: This aspect deals with one variable at a time. Study of descriptive statistics like mean, and standard deviation of one single variable at a time, belong to this category. ii) Multivariate analysis: This aspect deals with more than one variable and addresses the problems of inter-relationships among several variables, extraction of hidden factors, problems of classification, etc. This is a statistical test for comparing the means of more than two populations or groups. With two means, we use t-test or the Z-test but when there are three or more groups for comparison, we have to use procedure called analysis of means of simply ANOVA. 101 Malhotra, N.K, and Das S., Marketing Research - An applied Orientation, Pearson Education in South Asia, New Delhi, (2009), pp Sharma, K.V.S., Statistics Made Simple, Prentice of Hall of India, New Delhi (2006), p

19 It gives an overall comparison of means and investigates whether the population means are likely to be same or different. If they are found to be different then there are other tests to verify which pair of means has a significant difference. There are forms: i) One way ANOVA: When the data is classified into groups according to only one characteristic or factor, ANOVA is called the one- way ANOVA. ii) Two way ANOVA with replication: When the data classified according to two characteristics or factors, like age group and gender we call it a two-way classified data and the corresponding ANOVA is called the two-way ANOVA. When there are replications, it is possible to estimate the interaction or the joint effect of the two factors on the response being studied. With only two groups, the one-way ANOVA and the Student s t-test will give the same decision. It can be shown that the square of the t-statistic follows F distribution. Hence, we can use either t- test or ANOVA for comparing two means Discriminant Analysis 103 Basic Concept of Discriminant Analysis: It is a technique for analyzing data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature. Discriminant analysis is a useful way to answer the questions Are the groups different? On what variables are they most different. Can I predict which group a person belongs to using these variables? Statistics Associated with Discriminant Analysis Canonical correlation: Canonical correlation measures the extent of association between the discriminant scores and groups. It is a measure of association between the single discriminant function and the set of dummy variables that define the group. Centroid: The centroid is the mean values for the discriminant scores for a particular group. There are as many centroids as there are groups, because there is one for each group. The means for a group on the functions are the group centroids. Classification matrix: Sometimes also called confusion or prediction matrix, the classification matrix contains the number of correctly and incorrectly classified cases. The correctly classified cases appear on the diagonal, because the predicted and actual groups are the same. The off-diagonal elements represent cases that have been 103 Malhotra, N.K, and Das S., Marketing Research - An applied Orientation, Pearson Education in South Asia, New Delhi, (2009), pp

20 incorrectly classified. The sum of the diagonal elements divided by the total number of cases represents the hit ratio. Eigen value: For each disriminant function, the Eigen value is the ratio of betweengroup to within- group sums of squares. Large Eigen values imply superior functions. Structure correlations: Also referred to as discriminant loadings, the structure correlations represent the simple correlations between the predictors and the discriminant function. Mahalanobis Procedure: The selection of the stepwise procedure is based on the optimising criterion adopted. The Mahalanobis Procedure is based on maximising a generalised measure of the distance between the two closest groups. This procedure allows researchers to make maximum use of the available information Factor Analysis 104 Basic Concept: Factor Analysis is a general name denoting a class of procedure primarily used for data reduction and summarisation. In research survey, there may be a large number of variables, most of which are correlated and which must be reduced to a manageable level. Relationships among sets of many interrelated variables are examined and represented in terms of a few underlying factors. Factor analysis seeks to identify a set of dimensions that is not readily observed in a large set of variables. The analysis summarizes a majority of the information in the data set in terms of relatively new few categories, known as factors. A factor is an underlying dimension that explains the correlations among a set of variables is called factor (variable). Factor analysis allows us to look at groups of variables that tend to be correlated to each other and identify underlying dimension that explain these correlations. Two basic reasons for using factor analysis are: 1. To simplify a set of data by reducing a large number of measures ( in which some may be interrelated causing multicollinearity ) for a set of respondents to a smaller manageable number of factors(which are not interrelated) that still retain most of the information found in the original data set. 104 Malhotra, N.K, and Das S., Marketing Research - An applied Orientation, Pearson Education in South Asia, New Delhi, (2009), pp

21 2. To identify the underlying structure of the data in which a large number of variables may be really be measuring a small number of basic characteristics of the sample. According to Naresh K. Malhotra and S. Dass, factor analysis is used in the following circumstances are; 1) To identify underlying dimensions, or factors, that explains the correlations among a set of variables, 2) To identify a new, smaller set of uncorrelated variables to replace the original set of correlated variables in subsequent multivariate analysis, regression or discriminate analysis, 3) To identify a smaller set of salient variables from a larger set for use. For the current factor analysis is used to reduce the number of factors/features that are used to measure the satisfaction level of respondents. Respondents were asked to give their level of satisfaction. The five points Likert scale was used (1:Highly dissatisfied to 5:Highly satisfied) for the factors considered to study industrial productivity scenario and potentiality in Vitthal Udyognagar G.I.D.C., Anand district of Gujarat state for various questionnaires statements(variables). Relationships among sets of many interrelated variables are examined and represented in terms of a few underlying factors. For these features, factor analysis was performed in this study. Statistics associated with factor analysis Raw data were converted into suitable form using especially Excel, SPSS statistical tools. For this purpose data codification is carried out first, and then transferred from questionnaires to the computer. Once the data are transferred properly, statistical analysis can be initiated. Different data analysis techniques were used to get the useful and meaningful outcome from the data obtained against different questions of the questionnaires. One of the most widely used interdependency techniques for data reduction is factor analysis. The key statistics associated factor analyses are: Bartlett s test of sphericity: It is a test statistic used to examine the hypothesis that the variables are uncorrelated in the population. In other words, the population correlation matrix is an identity matrix; each variable correlates perfectly (r = 1) with itself but has no correlation (r = 0) with the other variables under study. Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is a measure of sampling adequacy, an index used to examine the appropriateness of factor analysis. 176

22 The KMO value varies from 0 to 1. High values (between 0.5 and 1.0) indicate factor analysis is appropriate. Values below 0.5 imply that factor analysis may not be appropriate. Small values of the KMO statistic indicate that the correlation between pair of variables cannot be explained by other variables, and hence factor analysis may not appropriate. Generally, a KMO > 0.5 is desirable. Communality: The amount of variance shares with and portion of variance explained by common factors referred to as communality. Communality is the amount of variance a variable can explain with all the factors being considered. This is also the percentage of total variance explained by the common factors. The communalities can be found mathematically by squaring the factor loading of all factors and then summing these figures. This term may be interpreted as a measure of uniqueness. A low communalities figure indicates that the variable is statistically independent and cannot be combined with other variables. The extracted communalities greater than 0.5, are acceptable for the variables. Variance explained: It is required that the scale constructed and the components extracted should be able to explain maximum variance in the data. For this, an analysis of the Eigen values is required, which represents the total variance explained by each factor. Percentage of variance is the total variance attributed to each factor. Residuals: Residuals are the difference between the observed correlations, as given in the input correlation matrix, and the reproduced correlations, as estimated from the factor matrix. A scree plot is a plot of the Eigen values against the number of factors in order of extraction. It helps to decide the number of factors to be considered. Interpret Factors: Interpretation is facilitated by identifying the variables that have large loadings on the same factor. That factor can then be interpreted in terms of the variables that load high on it. Another useful aid in interpretation is to plot the variables using the factor loadings as coordinates. Variables at the end of axis have high loadings and hence describe the factor. Variables near the origin have small loadings on both the factors. Variables that are not near any of the axes are related to both the factors. If a factor cannot be defined in terms of the original variables, it should be labelled as on undefined or a general factor. 177