Statistical consulting is a major task in today’s world. It is required for many fields and offers extensive potentials to people in need of it. Conducting constructive analysis and research on certain topics is highly relevant because of the competition that exists in the contemporary world today. Statistical Consulting is therefore a necessary tool for obtaining the required and significant data in many fields and domains.
Statistical Consulting is necessary in the following areas:
· Science and Medicine
· Business and Commerce
· Social Sciences like Psychology and Sociology
· Government Bodies and Law
· Universities and Colleges for dissertations and theses
Statistical Consulting is very popular and is applied in almost every aspect of society because it ensures adequate and successful functioning of organizations. The activities that are associated with statistical consulting ranges, and can concern any topic. The task of the statistical consulting body varies from project to project. Statistical consulting involves the statistician acting as the problem solver because the consultant conducts analyses, researches and designs and implements the projects. In statistical consulting, the consultant also acts as a guide and advisor to the client.
Statistical consulting is very effective and accurate and is therefore a necessary entity in today’s day and age. A statistician should possess certain qualities that ensure his success. For a statistician, statistical consulting requires the following characteristics:
· Good Communication Skills: In statistical consulting, the statistician must possess good communication skills so that the consultant can interact with the client fluently and comfortably. Once the idea is made clear to the consultant (through healthy, professional conversations with the client) the statistical consultant is able to carry on with his work professionally as per the clients needs.
· Scientific Interest: The statistical consulting profession requires a keen and eager interest in the pursuits of science. Science forms the core root of statistics and is a fundamental feature in statistical consulting.
· Statistical Knowledge: Without proper training and education in statistics, one cannot engage in statistical consulting. One has to be able to understand the subject and to apply the required technical and specialized techniques and procedures of statistics.
· Computer Proficiency: Basic computer skills are essential in statistical consulting. The statistician must be able to utilize the computer while making use of the new and latest statistical software available in the market today.
Statistical consulting necessitates that the statistician perform research studies and experiments. It also includes designing the experiments needed for observations and interpretations. With statistical consulting at hand, organizations need not worry themselves with the problem of obtaining the needed information.
Statistical consulting is instrumental to small scale industries in particular. Small scale industries can gain profits through statistical consulting as the statistician gives the industry the opportunity to conduct proper researches as well as giving them a full length statistical analysis. Without this, the company would not have the resources or knowledge to carry on with the project. Thus, small scale industries benefit a great deal from statistical consulting.
Contemporary times offer a number of possibilities to people. The advent of statistics and statistical consulting has in many ways made things a lot easier for everyone. Statistical consulting has brought with it an endless number of solutions for research findings and data analysis. Information is an important need and statistics have various ways of finding that information so that it may be utilized to bring about advancement and evolution. Clearly, statistical consulting is of crucial importance today.
Click here for more information on statistical consulting services.
Wednesday, April 1, 2009
Dissertation Research
It’s that time of the year again! With the end of the semester drawing near, pressure mounts up on students in regards to their theses and dissertations. The quality, presentation and content of the dissertations are very important for the students, as that is the deciding factor as to whether or not the theses are going to be approved. Throughout the year, students are engaged in dissertation research for the successful completion of the paper. Dissertation research plays an essential part of this dissertation and thesis creating process.
Dissertation research can be a very tiring and tedious process. While it takes up most of your time and energy, it can also be stressful. Not everyone is equipped with the proper and required research skills and interest. While some may be low on confidence, some may not even be able to think of a topic. Dissertation research therefore, is not a one week or last minute event, but it should be well planned and thought of even before starting. Dissertation research first begins with a topic. Topics are very difficult to pick as the student can never be sure whether or not it shall be accepted by the concerned authorities. After having settled on a topic, the student has to go through the preparatory stage where information, data and material have to be collected. This involves a lot of work for the student. When the information is collected and compiled together, the student has to examine and investigate the topic chosen and its contents. A thorough study of the paper is required. This can be time consuming and exhausting. Dissertation research requires the student to also prepare questionnaires and surveys concerning the selected topic and then to pass them on for public opinion. Once the job is completed, the student is required to evaluate the questions and answers received on the questionnaires. The student is to analyze and scrutinize the results and formulate a conclusion based upon these questionnaires. The student can then come up with various findings, but to get to these findings, certain procedures and guidelines must be followed. Statistical knowledge and proficiency is also sometimes needed to validate the findings and results. The student may or may not be equipped with the required skill to perform such a task. Thus, more often than not, the student turns to professional help to carry the project through to its fruition.
Dissertation research can be made simple with the help of dissertation research and statistical help. There are a number of firms and companies that offer such services to students. For those students who are unable to apply statistics to their paper, they may rely on dissertation research and statistics help. These experts who help in dissertation research and statistics not only assist the student with the statistics portion of the dissertation, but they also aid the student throughout. The statistician may even guide the student from the very beginning—they may even help in the selection of the topic. Dissertation research, however complex and unnerving, is a necessity for all students intending on acquiring their doctorate degrees.
Dissertation research is not so difficult today due to the various types of help made available to students. Dissertation research should be taken seriously as it decides the future of the student academically. Depending on the dissertation research completed by the student, the dissertation may either be rejected or accepted. The facts collected must hold true and valid arguments must be made to substantiate the facts.
Dissertation research is a process that all students pursuing a masters or doctorate program must undergo. The quality of the dissertation research should be complete and comprehensive, allowing no lapses or confusion. Dissertation research should be precise, accurate and factual. It should be a proven, bona-fide and original document authored appropriately. For help with your dissertation research, click here.
Dissertation research can be a very tiring and tedious process. While it takes up most of your time and energy, it can also be stressful. Not everyone is equipped with the proper and required research skills and interest. While some may be low on confidence, some may not even be able to think of a topic. Dissertation research therefore, is not a one week or last minute event, but it should be well planned and thought of even before starting. Dissertation research first begins with a topic. Topics are very difficult to pick as the student can never be sure whether or not it shall be accepted by the concerned authorities. After having settled on a topic, the student has to go through the preparatory stage where information, data and material have to be collected. This involves a lot of work for the student. When the information is collected and compiled together, the student has to examine and investigate the topic chosen and its contents. A thorough study of the paper is required. This can be time consuming and exhausting. Dissertation research requires the student to also prepare questionnaires and surveys concerning the selected topic and then to pass them on for public opinion. Once the job is completed, the student is required to evaluate the questions and answers received on the questionnaires. The student is to analyze and scrutinize the results and formulate a conclusion based upon these questionnaires. The student can then come up with various findings, but to get to these findings, certain procedures and guidelines must be followed. Statistical knowledge and proficiency is also sometimes needed to validate the findings and results. The student may or may not be equipped with the required skill to perform such a task. Thus, more often than not, the student turns to professional help to carry the project through to its fruition.
Dissertation research can be made simple with the help of dissertation research and statistical help. There are a number of firms and companies that offer such services to students. For those students who are unable to apply statistics to their paper, they may rely on dissertation research and statistics help. These experts who help in dissertation research and statistics not only assist the student with the statistics portion of the dissertation, but they also aid the student throughout. The statistician may even guide the student from the very beginning—they may even help in the selection of the topic. Dissertation research, however complex and unnerving, is a necessity for all students intending on acquiring their doctorate degrees.
Dissertation research is not so difficult today due to the various types of help made available to students. Dissertation research should be taken seriously as it decides the future of the student academically. Depending on the dissertation research completed by the student, the dissertation may either be rejected or accepted. The facts collected must hold true and valid arguments must be made to substantiate the facts.
Dissertation research is a process that all students pursuing a masters or doctorate program must undergo. The quality of the dissertation research should be complete and comprehensive, allowing no lapses or confusion. Dissertation research should be precise, accurate and factual. It should be a proven, bona-fide and original document authored appropriately. For help with your dissertation research, click here.
Tuesday, March 31, 2009
Advantages of SEM over Regression
The proper selection of methodology is a crucial part of the research study. (Davis, 1996; Stevens, 2002). Structural Equation Modeling (SEM) is a second generation multivariate method that was used to assess the reliability and validity of the model measures. Each statistical technique has certain characteristics that determine applicability to a given problem. Understanding the techniques and their characteristics is essential for selecting the most appropriate approach to the data. This section will discuss why confirmatory factor analysis (CFA) was selected instead of multiple regression.
First generation multivariate methods, like multiple regression, are appropriate for evaluating constructs and relationships between constructs. The terms regression and correlation have been used interchangeably to label a regression analysis, however the intent of a regression analysis is prediction while the intent of a correlation is to assess the relationship between the dependent variable and the independent variables. (Tabachnick & Fidell, 2001, p. 111). Multiple regression is an excellent tool to predict variance in an interval dependent variable, based on linear combinations of interval, dichotomous or dummy independent variables. Interaction terms may be added to the model to measure the joint effect of two variables on a dependent variable, for example, the joint effect of PD*NA on PCTINT in the present model.
Parameter estimates in multiple regression are the unstandardized regression coefficients (β weights).
Where Y is the dependent variable, βo and β1 are parameter estimates, Xi is the value of the independent variable, X, for the i-th case and εi is the random error term associated with that particular value of Xi. The value β1 represents the amount the dependent variable Y changes when the independent variables changes by one unit while the other independent variables are held constant.
The powerful technique of matrix algebra is well suited for multivariate regression. Data are arranged such that each row represents one person's scores or responses on the independent variables. Each column represents the same variable for all subjects or cases. A (I*J) data matrix X consists of measurements of J independent variables on I subjects.
Multivariate regression estimates the same coefficients and standard errors as obtained using separate ordinary least squares (OLS) regressions. In addition, multivariate regression also estimates the between-equation covariances. This means that it is possible to test coefficients across equations. The matrix formula for multivariate regression is identical to the OLS formula. The solution for β that minimizes ε is
B = (X'X)-1X'Y
Where β is a column vector, X' is the transpose of S, and (X'X) (inverse) is the inverse of (X'X). Using the principle of least squares, the goal is to obtain a solution for β that will minimize ε, the residual error.
Tests of Significance. The proportion of the variance in the dependent variable explained by the independent variables in the model is the coefficient of multiple determination, or R2. R-squared can also be interpreted as the proportionate reduction in error in estimating the dependent variable from the independent variables (Pedhazur, 1982, p. 68). The F test is used to test the significance of R-squared. The "best model" can be determined by comparing the difference between two R-squares when an additional independent variable is added. Relative predictive importance of the independent variables is assessed by comparing the standardized regression coefficients (beta weights). Beta is the average amount the dependent variable changes when the independent variables increases one standard deviation and the other independent variables are held constant. To test the significance of the individual regression coefficients (unstandardized beta), t-tests may be used (but not for dummy variables).
Assumptions. The assumptions for multiple regression include proper specification of the model (omission of pertinent variables can substantially affect the parameter coefficients and the error), interval or near-interval data with unrestricted ranges, linear relationships, and homoscedasticity (the same level or relationship throughout the range of the independent variables).
Meeting the strict assumptions of multiple regression in the current research was not practical or possible, but the main reason for not choosing multiple regression in the current study is that simultaneous evaluation of model construct relationships is not possible; evaluation has to be performed in sequential steps. The introduction of software such as LISREL, AMOS, DEPATH, EQS and RAMONA have fueled the popularity of the methodology.
Second generation multivariate methods (Fornell, 1984; Chin, 1998) allow simultaneous analysis of all the variables in the model instead of separately. In addition, measurement error is not aggregated in a residual error term. Structural equation modeling (SEM) has been applied to a variety of research problems. Within the family of SEM techniques are many methodologies, including covariance-based and variance-based methods. Covariance analysis is also referred to as confirmatory factor analysis (CFA), causal modeling, causal analysis, simultaneous equation modeling, and analysis of covariance structures, path analysis or LISREL. Path analysis and confirmatory factor analysis are special types of SEM; LISREL is the name of a particular software program developed by Karl Jöreskog and Dag Sörbom (1989).
References
Chin, W. (1998). The partial least squares approach for structural equation modeling. In G. A. Marcoulides (Ed.), Modern methods for business research. Mahwah, NJ: Lawrence Erlbaum Associates, 295-336.
Chin, W.W. & Newsted, P.R. (1999). Structural equation modeling analysis with small samples using partial least squares. In R.H Hoyle, Statistical strategies for small sample research. Ca: Sage Publications, 307-341.
Davis, D. (1996). Business research for decision making. Belmont, CA: Duxbury Press.
Fornell, c. (1984). A second generation of multivariate analysis: classification of methods and implications for marketing research.
Pedhazur, E.J. (1982). Multiple regression in behavioral research (2nd ed.). New York: Holt, Rinehart and Winston.
Jöreskog, K.G. and Sörbom, D. (1989). LISREL7: A Guide to the Program and Applications. Chicago: SPSS inc.
Stevens, J. P. (2002). Applied multivariate statistics for the social sciences, Mahwah, New Jersey: Lawrence Erlbaum Associates.
Tabachnick, B.G., Fidell, L.S. (2001). Using multivariate statistics. 4th ed. Needham Heights, MA: Allyn & Bacon.
First generation multivariate methods, like multiple regression, are appropriate for evaluating constructs and relationships between constructs. The terms regression and correlation have been used interchangeably to label a regression analysis, however the intent of a regression analysis is prediction while the intent of a correlation is to assess the relationship between the dependent variable and the independent variables. (Tabachnick & Fidell, 2001, p. 111). Multiple regression is an excellent tool to predict variance in an interval dependent variable, based on linear combinations of interval, dichotomous or dummy independent variables. Interaction terms may be added to the model to measure the joint effect of two variables on a dependent variable, for example, the joint effect of PD*NA on PCTINT in the present model.
Parameter estimates in multiple regression are the unstandardized regression coefficients (β weights).
Where Y is the dependent variable, βo and β1 are parameter estimates, Xi is the value of the independent variable, X, for the i-th case and εi is the random error term associated with that particular value of Xi. The value β1 represents the amount the dependent variable Y changes when the independent variables changes by one unit while the other independent variables are held constant.
The powerful technique of matrix algebra is well suited for multivariate regression. Data are arranged such that each row represents one person's scores or responses on the independent variables. Each column represents the same variable for all subjects or cases. A (I*J) data matrix X consists of measurements of J independent variables on I subjects.
Multivariate regression estimates the same coefficients and standard errors as obtained using separate ordinary least squares (OLS) regressions. In addition, multivariate regression also estimates the between-equation covariances. This means that it is possible to test coefficients across equations. The matrix formula for multivariate regression is identical to the OLS formula. The solution for β that minimizes ε is
B = (X'X)-1X'Y
Where β is a column vector, X' is the transpose of S, and (X'X) (inverse) is the inverse of (X'X). Using the principle of least squares, the goal is to obtain a solution for β that will minimize ε, the residual error.
Tests of Significance. The proportion of the variance in the dependent variable explained by the independent variables in the model is the coefficient of multiple determination, or R2. R-squared can also be interpreted as the proportionate reduction in error in estimating the dependent variable from the independent variables (Pedhazur, 1982, p. 68). The F test is used to test the significance of R-squared. The "best model" can be determined by comparing the difference between two R-squares when an additional independent variable is added. Relative predictive importance of the independent variables is assessed by comparing the standardized regression coefficients (beta weights). Beta is the average amount the dependent variable changes when the independent variables increases one standard deviation and the other independent variables are held constant. To test the significance of the individual regression coefficients (unstandardized beta), t-tests may be used (but not for dummy variables).
Assumptions. The assumptions for multiple regression include proper specification of the model (omission of pertinent variables can substantially affect the parameter coefficients and the error), interval or near-interval data with unrestricted ranges, linear relationships, and homoscedasticity (the same level or relationship throughout the range of the independent variables).
Meeting the strict assumptions of multiple regression in the current research was not practical or possible, but the main reason for not choosing multiple regression in the current study is that simultaneous evaluation of model construct relationships is not possible; evaluation has to be performed in sequential steps. The introduction of software such as LISREL, AMOS, DEPATH, EQS and RAMONA have fueled the popularity of the methodology.
Second generation multivariate methods (Fornell, 1984; Chin, 1998) allow simultaneous analysis of all the variables in the model instead of separately. In addition, measurement error is not aggregated in a residual error term. Structural equation modeling (SEM) has been applied to a variety of research problems. Within the family of SEM techniques are many methodologies, including covariance-based and variance-based methods. Covariance analysis is also referred to as confirmatory factor analysis (CFA), causal modeling, causal analysis, simultaneous equation modeling, and analysis of covariance structures, path analysis or LISREL. Path analysis and confirmatory factor analysis are special types of SEM; LISREL is the name of a particular software program developed by Karl Jöreskog and Dag Sörbom (1989).
References
Chin, W. (1998). The partial least squares approach for structural equation modeling. In G. A. Marcoulides (Ed.), Modern methods for business research. Mahwah, NJ: Lawrence Erlbaum Associates, 295-336.
Chin, W.W. & Newsted, P.R. (1999). Structural equation modeling analysis with small samples using partial least squares. In R.H Hoyle, Statistical strategies for small sample research. Ca: Sage Publications, 307-341.
Davis, D. (1996). Business research for decision making. Belmont, CA: Duxbury Press.
Fornell, c. (1984). A second generation of multivariate analysis: classification of methods and implications for marketing research.
Pedhazur, E.J. (1982). Multiple regression in behavioral research (2nd ed.). New York: Holt, Rinehart and Winston.
Jöreskog, K.G. and Sörbom, D. (1989). LISREL7: A Guide to the Program and Applications. Chicago: SPSS inc.
Stevens, J. P. (2002). Applied multivariate statistics for the social sciences, Mahwah, New Jersey: Lawrence Erlbaum Associates.
Tabachnick, B.G., Fidell, L.S. (2001). Using multivariate statistics. 4th ed. Needham Heights, MA: Allyn & Bacon.
Thursday, March 26, 2009
Dissertation Help
Today’s world of statistical science ushers in a new mode of learning for students and aspirants. While dissertations and theses are mandatory for students pursuing post graduation studies, dissertation help and assistance is the new trend. A dissertation is a lengthy, formal discourse written by a student in a university and it covers any given topic. A dissertation generally requires a lot of effort and hard work on the part of the student. While the student may be qualified in a particular field, statistical skills may be beyond his/her capabilities. Hence, dissertation help and assistance, which requires statistical knowledge and competence by the person who is helping with the dissertation, is being developed and is widely popular.
Dissertation help is provided by statistical consultants, statisticians and experts and these experts cater to the students’ needs. Dissertation help can provide much assistance in making sure that dissertations or theses get accepted and approved. Before a dissertation or thesis can be approved, however, much work must be put into the actual dissertation or thesis itself. The dissertation writing process is a long and tedious one and follows an extensive process where the candidate is required to first come up with a proposal. This involves finding a topic, assessing the writing, noting the problem, and developing research questions, hypothesis and design. This is then followed by many steps and tasks, including researching and preparing the data for the analysis, entering and screening the data, performing the statistical analyses, deciphering and interpreting results, discussing these results and forming conclusions. Dissertation writing is indeed a lengthy process. Dissertation help is therefore made available to provide much-needed assistance and support to students.
Dissertation help is provided by experts like professors, statistical consultants and statisticians. These professionals help the students in a multitude of ways. They can help students with the entire project from the very first step of choosing a topic. They can also help in designing a dissertation study and preparing a dissertation proposal. Finally, they can also assist students with more complex activities throughout the process, like statistical examination, interpretation and the entering of the dissertation findings.
Dissertation help ensures customized reports and the consultants guarantee prompt and thorough assistance to the clients. The dissertation help and support is personalized and has proven to be very effective and useful for clients. In this way, dissertation help can greatly lighten the load or the burden the client faces.
Dissertation help generally assists clients with performing the statistics, interpreting results, organizing the findings and revising and editing the material. The format, style and grammar are also crucially important, and dissertation help cross-checks the entire document for the clients. Dissertation help ensures that the thesis or dissertation is approved by the concerned authority, and that it meets the specified requirements and conditions.
With stiff competition prevalent among clients, dissertation help ensures success with their dissertation. Without dissertation help, most clients may not be able to furnish their findings as expertly as they could with a consultant or statistician. With access to dissertation help, clients have the opportunity to successfully complete their dissertations with the assistance of expert opinions and skilled techniques. Professional expertise is always an added advantage in the completion of dissertations and theses. Dissertation help provides clients with guidance and support by connoisseurs proficient in the field. Dissertation help meets the needs of the clients as clients who have depended on dissertation help to conclude their projects have a higher chance of getting their dissertations and thesis approved than those who do not get professional help. Cost, budget, expenses and deadlines are also to be taken into account and should be as per the client’s requirements.
Dissertation help is indeed a significant part of today’s world. It provides convenience and ease to the clients seeking help as it offers reliable and prompt delivery of services. Dissertation help places heavy emphasis on quality and value in the services that they provide.
Monday, March 16, 2009
Stat
The process of analyzing a complex problem of smaller sections and then analyzing those smaller sections individually is done by statistical analysis. When this analysis is over, the outcome is co-related in relation to the entire process and is used to solve the problem. Statistical analysis helps companies check their costs and enhance their quality thus increasing their profits. It also makes them consider all possible options to increase the effectiveness of their research.
Statistical analysis helps organizations carry out their business operations in a well directed manner. Statistical analysis help provided by statistical consultants can be a huge asset in terms of providing companies innovative ideas that expand a company’s already existing knowledge. Statistical analysis help provides both guidance and assistance to an organization, and can be beneficial in carrying out statistical operations like probabilistic risk assessment, expert systems, data analysis, data mining, decision support, etc. Statistical analysis is useful for both the office staff and the statistical consultant as both parties are able to exchange information that will help execute the organization carry out its business plan. Statistical analysis helps in extracting the useful and critical information from the existing programs and data of an organization. Statistical analysis is beneficial as it makes a company run optimally. In other words, the company gains higher profits by executing the outcome of the statistical analysis.
Statistical analysis help provides good suggestions and advice to organizations and these suggestions translate into success for the organization. Organizations that have hired statistical analysis help are known to be able to work more efficiently, and thus they have better results and gain higher profits. Along with higher profits, organizations have the satisfaction of achieving the intended objectives and targets. The outcome provided by the statistical analysis help is unique and comes in handy for increasing the growth rate of the organization. It also enhances an organization’s efficiency and improves the outlook of the company. The organizations should be aware, however, that the suggestions provided by the statistical analysis help may differ according to the nature of the business.
There are several statistical analysis firms that provide statistical analysis help. They have trained professionals who provide expert advice and great ideas that are both practical and able to be executed. Even small scale industries can hire these professionals as the firms are very economical and cost effective. Statistical analysis help is in high demand, as it is very useful to organizations in terms of performing at the highest level and rectifying any defects of the organization. While hiring the statistical analysis help, the organizations should keep in mind that the firms should be responsible, honest and should have skilled expertise in the required field. Statisticians should keep in mind that they should not have a biased approach to their employer’s company and they should apply a practical approach to the problems and work accordingly.
Today, statistical analysis help is required in many fields. For example, a company may need to introduce a product in the market, but they may first want to research that market. In order to do this, the company will need statistical analysis, and a person who is trained in calculating the results of various surveys. Additionally, students need statistical analysis help while writing their dissertations or while doing their projects. Manufacturers also require statistics analysis while launching their product so that they may see the demand of their product. Thus, statistical analysis help is very important in almost every field.
Apart from the firms, statistical analysis help can also be obtained from readymade software. For example, there is Plethora, which is readymade statistical analysis software that can perform the statistical analysis on the websites. Companies can purchase this software in order to determine the performance of their websites. Also ‘Google’ has released a number of analytical tools, which make statistical analysis easier and which are useful for the organizations as well as the web masters.
Statistical analysis can help an organization, company, firm or student be the best in one’s field. The only thing that one should keep in mind is that this help has to be implemented very practically and accurately. Clearly statistical analysis help is a valuable asset as it can help organizations and the like gain higher profits, spur new growth and attain success.
Friday, January 23, 2009
ANOVA
Analysis of variance (ANOVA) is a parametric statistical technique used to compare datasets. This technique was invented by R. A. Fisher, and is thus often referred to as Fisher’s ANOVA as well. It is similar in application to techniques such as t-test and z-test, in that it is used to compare means and the relative variance between them, although ANOVA is best applied where more than 2 populations or samples are meant to be compared.
Using ANOVA over other methods such as multiple t-tests offers significant advantages such as:
· A larger sample size and a larger number of samples can be compared using ANOVA.
· ANOVA can be used to evaluate much larger and more complex problems, using multiple variables and datasets, using both different types of ANOVA as well as its extensions.
ANOVA can be leveraged in a number of ways depending on the number of samples, variables or datasets in question, as well as how many variables are to be tested at once.
· One way between groups
The simplest form of ANOVA; it involves measuring the differences in the observations between two or more different groups, to determine if there is statistically significant difference between them.
· One way repeated measures
This is similar to one-way ANOVA except for the fact that the same variable is tested again and again to measure the results over say a period of time or multiple iterations of a treatment.
· Two way between groups
This is used where the impact of two independent variables need to be measured in a single instance. For instance, a researcher can look at performance by the impact of two different factors (independent variables) such as health (good and bad) and worker efficiency (high vs. low).
· Two way repeated measures
Again, this is the same as a two-way ANOVA, except for the fact that the analysis is done on multiple observations of the same variables.
Rather than types of ANOVA, extensions such as MANOVA and ANCOVA are also used where the need exists. MANOVA or Multiple analysis of variance is typically used where two-way ANOVA limits the need to have multiple (more than 2) independent variables whose impact needs to be measured.
The use of ANOVA involves certain key assumptions, including the following:
· Normality: being a parametric test, the use of ANOVA as a statistical technique requires that the dataset(s) in question be normally distributed, and if they aren’t they must be normalized. In order to determine normality of the dataset(s), tests such as the Kolmogorov Smirnov and Shapiro-Wilk test, in addition to examining the congruence of the mean, median and mode can be used.
· Homogeneity
While using ANOVA, sample variances are expected to be equal. In other words, the error terms in the samples should be the same and should not exhibit too much volatility. If this is not the case, the samples will not satisfy the said assumption and will be considered heterogeneous. Homogeneity can be measured using Durbin-Watson, Bartlett and/or other tests. In case of heterogeneity, first difference will be taken.
· Independence
ANOVA requires case independence, which means that each of the observations in each variable is independent of each other. It’s important to remember however, that this does not mean that the variables themselves have to be independent of each other, as in a repeat-measure experiment, where ANOVA is widely used.
Like any other statistical and scientific technique, ANOVA has it’s drawbacks. The most important ones to remember while using it are:
· Given the need for data normality while using ANOVA, it is relatively difficult to find a real world sample or population which is truly normal. The need for normality is usually fulfilled by transformation of the data with logs.
· ANOVA can be fairly ineffective as a technique for measuring variance, if the error time is not consistent throughout the samples. This problem of heteroscedasity implies that unless the variance between each of the samples in question is ‘equal’, ANOVA’s results may or may not be reliable. For instance, ANOVA may suggest statistical significance where there is none.
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