Dissertation Statistics Consulting

If you are stuck somewhere at the beginning, middle or end of your dissertation, dissertation statistics consulting is the best course of action for you. This is because dissertation statistics consulting can provide fast, easy, and accurate results for you as you complete the very difficult and very lengthy process of finishing your dissertation.

The dissertation is probably the hardest thing that you have done academically to date. This makes sense, however, as it is your last hurdle before you receive you doctoral degree. Thus, it is purposefully difficult and lengthy—as you must complete it in order to finish university with the prestigious title of “Doctor.” Dissertation statistics consulting can help you attain this prestigious title, as dissertation statistics consulting is designed to take you step-by-step through your dissertation.
Dissertation statistics consulting does exactly what its name suggests: it consults students as they aim to finish their dissertation. As such, dissertation statistics consulting can step into a project or dissertation at any stage. So, if you are just beginning your dissertation, dissertation statistics consulting can be extremely useful to you. Obviously, the sooner you acquire dissertation statistics consulting, the more help you can receive, and the easier it will be for you to complete your dissertation successfully. If you are half way through your dissertation and you are seeking help because you have perhaps taken a wrong turn somewhere, dissertation statistics consulting can also be a tremendous help. Dissertation statistics consulting will get you back on track and dissertation statistics consulting will make sure that you continue to travel in the right direction. This is extremely helpful because it can take someone months and months to figure out where he or she has gone wrong. This wasted time is not necessary with dissertation statistics consulting, however, as dissertation statistics consulting will spot the problem and help you correct it. Finally, if you are in the final stages of your dissertation, dissertation statistics consulting can also be of great help to you. This is true because dissertation statistics consulting can help you put the “finishing touches” on your dissertation. These “finishing touches” can actually slow a student down quite a bit, and dissertation statistics consulting can expedite the final processes of a dissertation. Thus, if you are close to finishing, dissertation statistics consulting will ensure that you finish quickly and successfully. Dissertation statistics consulting does this by checking every single aspect of your dissertation. In fact, dissertation statistics consulting will even edit your dissertation, so that you turn in a “clean” version of your dissertation—free of annoying typos and misspelled words. Thus, dissertation statistics consulting can help any student, regardless of where they are in the dissertation writing process.

Dissertation statistics consulting is most helpful on statistics. The statistics portion of the dissertation is by far the hardest and lengthiest aspect of the dissertation. Dissertation statistics consulting can change this, however, as dissertation statistics consulting can provide extremely precise information and help with statistical parts of a student’s dissertation. This includes providing hands-on help with the data collection part of statistics, the interpretation of that data and the incorporating of the interpretations into the dissertation. A mistake in the statistical part of the dissertation can derail the completion of a dissertation for months, if not years, and dissertation statistics consulting will make sure that a student does not fall into the many pitfalls involved in the statistical aspect of his or her dissertation.
Dissertation statistics consulting is the absolute best way to finish your dissertation. Thus, there is no reason for a student to struggle alone without the help of dissertation statistics consulting.

Independent and Dependent Variables

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Variables are defined as the properties or characteristics of some events that take on different values or amounts. There are basically two types of variables. They are as follows:

1. Independent variables
2. Dependent variables

Independent variables are those kinds of variables that are used for predicting the variation caused by the dependent variables in regression. Independent variables are also termed as predictors. Independent variables refer to the alternatives that are manipulated and are measured as well as compared. Independent variables are the type of variables that are not affected by any other variables, and are not changed by other variables abruptly. The concept of independent variables can be very well explained with the help of an example, like how the grades of a student can be affected by factors including how much time he devoted to studying, how many hours he slept, what his diet was, etc. These factors are independent variables as they are not at all affected by the grades of the students.

The second type of variable is the dependent variable. Like its name suggests, the dependent variables are always dependent on the independent variables. The variations caused by the dependent variables are generally explained by the independent variables in regression. The other name for dependent variables is predicted variables. The dependent variables are named the predicted variables because they are those types of variables that are predicted by the predictor variables or the independent variables. The other name for dependent variables is criterion variables. Considering the previous example, the score of the students, which are affected by several factors, is the dependent variable. Observing the relationship between the two things is used to find out what affects the dependent variable the most.

We shall now describe the dependent and the independent variables in the following cases:
For the case of the linear model, the general equation is described as the following:

So, in this model, the variable ‘Y’ is defined as the dependent variable, and the variable ‘X’ is defined as the independent variable.

In the regression model, the equation is given by the following:

The regressors called the βij (j=1, ,p) are defined as the independent variables, and the regressands Yi are defined as the dependent variables.

The independent variables are also called ‘ regressors’ and sometimes the independent variables are called the ‘control variables.’ This is because the independent variables are the ones that control the dependent variables. The other name for independent variables is ‘explanatory variables.’

Regression Analysis

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Regression analysis is a statistical technique that is widely used for research. Regression analysis is used to predict the behavior of the dependent variables, based on the set of independent variables. In regression analysis, dependent variables can be metric or non-metric and the independent variable can be metric, categorical, or both a combination of metric and categorical. These days, researchers are using regression analysis in two manners, for linear regression analysis and for non-linear regression analysis. Linear regression analysis is further divided into two types, simple linear regression analysis and multiple linear regression analysis. In simple linear regression analysis, there is a dependent variable and an independent variable. In multiple linear regressions analysis, there is a dependent variable and many independent variables. Non- linear regression analysis is also of two types, simple non-linear regression analysis and multiple non-linear regression analysis. When there is a non-liner relationship between the dependent and independent variables and there is a dependent and an independent variable, then it said to be simple non-liner regression analysis. When there is a dependent variable and two or more than two independent variables, then it said to be multiple non-linear regression.

There is a difference between linear and non-linear regression analysis. Linear regression analysis is based on assumptions. These assumptions are as follows:

1. There is normal distribution.
2. There is a linear relationship between the dependent and independent variable.
3. There is no multicollinearity between the independent variables or no exact correlation between the independent variable.
4. There is no autocorrelation.
5. The means lagged value of the regression variable does not affect the current value.
6. The homoscedasticity or variance between all the independent variables is equal.

However, in the non-linear regression analysis, there are no assumptions like autocorrelation, multicollinearity, homoscedasticity, etc. Non-linear regression is used when linear regression does not meet these assumptions. Logistic regression is an example of non-linear regression.

Most researchers use two methods to calculate the coefficient of the regression analysis. The first method is the OLS method, which stands for the ordinary least square method. The second method is the maximum likelihood method. The OLS method is used when there is a linear relationship between the dependent and independent variables. The maximum likelihood method can be used in non-linear relationships as well. When there is a non-linear relationship between the dependent and independent variables, most of the researchers transform the data in the linear form, and then they use the OLS method. The Maximum likelihood method is quite mathematical, and that is why many researchers prefer the OLS method in regression analysis. But these days, computers can solve this problem quite easily. Now the researchers are using the OLS and maximum likelihood method equally.

Regression analysis has two types of variables; one is the dependent and the other is the independent variable. The intercept term in regression analysis shows the common variance explained by all the independent variables, and the beta coefficient shows the rate of change. The Beta coefficient shows how the dependent variable alters when one unit of the independent variable increases. In regression analysis, R-square shows how much total variance is explained by the independent variable for the dependent variable. In regression analysis, the t-test is used to test the significance of the variable. In regression analysis, if the independent variable is categorical in nature, then the researcher must have to convert that independent variable into a dummy variable. For example, the male and female is converted into 0 and 1. When a dependent variable is categorical in nature, then a simple regression cannot be used. In such situations, logistic regression is used. When the dependent variable has two categories, then the binary logistic can be used to predict the probability of the dependent variable categories. But if the categories of the dependent variables are more than two, then multinomial logistic regression is used to predict the probability of the categories of the dependent variable. When dependent variable categories are ordinal in nature, then ordinal logistic regression is used to predict the probability of the dependent variable categories. In time series analysis, regression analysis is used very frequently. ARIMA, ARCH, VAR, and Co-integration are examples of regression analysis in time series analysis.

Survey Research

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The concept of survey research is defined as the research that focuses upon those surveys that are performed on the basis of advanced scientific knowledge.

Survey research basically provides knowledge about quantitative description of a few aspects of study.

The analysis that is carried out by the process of survey research is entirely concerned, either with the association between the variables, or with the findings of the project in a descriptive manner. The concept of survey research is that it is basically a kind of quantitative method that needs standardized kinds of information about the subjects under study. The subjects whom are being studied in survey research generally include individuals, groups, organizations or communities.

The second characteristic of survey research involves the extraction of knowledge by questioning structured and predefined questions by the people participating in the study. The responses that are given by the respondents in survey research consist of the data that is being analyzed.

The third characteristic of survey research is generally extracted by considering only a fraction of the study population. For example, this is done with service or manufacturing organizations, etc. Generally, the sample in survey research is quiet large and can allow the researcher to perform extensive statistical analyses.

The nature of survey research can be easily and comfortably understood by comparing two methods, namely case study methods and laboratory experiments.

Case studies in survey research refer to the examination of the phenomenon in its natural setting. In survey research, the researcher cannot control the occurrence of that particular phenomenon. But the researcher can definitely control the scope and the time of the examination. The researcher in survey research might or might not have already defined independent variables and dependent variables.

In case studies, which are important for the researcher in survey research, mainly involve the relationship between the context and the phenomenon of interest. In survey research, the researcher conducts the manipulation of the independent variables and then observes their corresponding effects on the dependent variables.

Laboratory experiments in survey research are the ones that are well matched with the research projects, and that involve comparatively limited and well defined strategies and propositions. These experiments in survey research involve few individuals, or a small group of people.

The researcher in survey research has direct control over laboratory conditions and manipulation of the independent variables.

The process of survey research is applicable when the researcher is primarily interested in knowing about the event, in knowing the reason behind the manner the event has occurred, and in knowing the reason behind the occurrence of an event. The process of survey research is quite useful in answering many types of questions. In fact, survey research is carried out to answer many types of questions.

The process of survey research is also applicable and useful in cases where the control of the independent and dependent variables is not possible and is not desirable. The process of survey research is also applicable in cases where the phenomenon of interest on which the survey research is carried out has occurred in the present time or in the recent past. The process of survey research is applicable in cases where the phenomenon of interest should be in its natural settings.

The inappropriateness of the survey research must also be kept in mind. Survey research is inappropriate in cases when detailed understanding of the context and history of the given computing phenomena is desired.

Statistical Power

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Data acquired and accumulated through research and observations can be inferred and interpreted with the help of statistics. Statistical analysis is the most reliable and dependable method of procuring the best and most accurate results on any given topic. This is where statistical power enters the arena.

Statistical power has established itself as a crucial element in the present day. To eliminate and deal with Type II errors that may prove to be menacing and potentially dangerous, (especially in pharmaceutical research) statistical power is crucial.

There are two types of errors that exist in statistical research, and they are type I and type II errors. Type I errors are those errors when a researcher rejects a true hypothesis as true, and type II errors are the exact opposite. To control the occurrence of type II errors, statistical power has been created. Statistical power was specifically designed to prevent null hypotheses from getting accepted as true. Since the offset of statistical power against type II errors, such errors have been controlled and prevented. Statistical power has been a very useful tool in researches and experiments.

Given the growing need for evidence-based practices in the world today, statistical power has done much in the world. Instead of accepting as true what is actually a null hypothesis, statistical power helps the researcher to identify the difference. Considering the dangers of taking a null hypothesis as true, statistical power acts as the probability (1-β) of rejecting null hypothesis when it is false. Statistical power ensures that the null hypothesis is rejected so it allows the researcher to avoid type II errors. Statistical power must be kept correspondingly high. The more the statistical power, the less the chance of having type II errors.

The analysis on Statistical Power is called Power Analysis. To analyze statistical power through power analysis, an analysis can be done both on data collected prior and post. Statistical power usually depends upon the desired power level and the desired level of significance in the test. Here, statistical power particularly identifies the level or possibility of preventing a type II error. On most occasions, the researcher takes the power level at 0.80, or 80% chance of not making the error. The level of significance signifies that a sample is probably about to get linked with the population. For instance, if the level of significance is 5%, then the sample drawn should have at least 5% characteristics of the population from where it has been drawn in statistical power. Statistical power is also decided by the strength of association or the effect size in the population. In statistical power, the effect size or the strength of association generally refers to the strength of association between the two variables. Hence, the greater the effect size, the more the statistical power. A greater effect size accentuates a greater Statistical power. The sensitivity of the data and the size of the sample also determine statistical power. In statistical power, sensitivity refers to the number of true positives out of the total of true positives and false negatives. In layman terminology, sensitivity relates only to data which is totally correct. This in turn implies that high sensitivity will give way to good data and finally a high statistical power. With high statistical power, there is access to data which has fewer type II errors.

The determination of the sample size of past data is very important in statistical power. This sample size keeps the significance of statistical power high, thereby denoting a larger sample size. With greater statistical power, errors (like type II errors) can be slowly prevented and controlled.

Methodology

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In statistics, methodology is a very important and useful tool. Given the mounting need of evidence-based practices in today’s world of challenging competition, statistics is very important.

Methodology in statistics forms the core foundation for various statistical tests and examinations.

In the field of psychology, where experimental testing is carried out, statistics is crucial. Psychology students conduct tests like personality tests (MMPI), IQ tests (Wechsler) and many different tests that require methodology and specific techniques. For execution of the methodology, questionnaires, surveys and tests are designed and conducted. A specific methodology is also utilized while determining the existence of certain pathological diseases or symptoms within the individual or a group of individuals. Questionnaires are very popular modes of methodology in statistics.

Psychology requires a certain mode, tactic, or methodology, by which the psychologist reaches his conclusion. Methodology in statistics is crucial as hypotheses and theories are drawn-out and validated with the help of the questionnaires or surveys. For instance, if an IQ test needed to be conducted between two schools – ‘A’ and ‘B’—, the psychologist can do that with the use of a methodology. The psychologist first prepares the questionnaires in which questions relating to general awareness are asked. Then he/she distributes it to the students. Through the results, with the help of methodology, the answers to questions may be attained. Methodology is crucial in psychology as it charts the line of action for the statistician so that he/she may attain a comprehensive and clear conclusion.

In science and medicine, methodology plays a significant role. For conducting medical research like bio-statistics, clinical trials, survival analysis, tests of hypothesis in statistical inference, etc., methodology is required. With methodology, public health and problems are analyzed. This includes studying bio-statistics, ensuring safety of data through clinical trials, and attaining knowledge of the population at any given time through survival analysis. In survival analysis, methodology determines the population that may have existed at a certain time in the past. Mathematically, this methodology can be observed as the likelihood of a persons death at time ‘T,’ which would be much later than time ‘t.’ As age increase, this methodology is presupposed to touch zero. In determining medical errors and risks of improper and uncalculated dosages of a particular drug, the test of hypothesis is conducted. This methodology helps in removing type II errors, which may occur with improper dosage of drugs.

Methodology should be strictly adhered to by the practitioner or nurse. Methodology allows researchers to utilize software like SAS for analyzing the data. For achieving accurate and precise results, methodology is binding on the researchers. There is a specific methodology for each of the tests and each of these tests achieves specific objectives.

Business is another such field where methodology is highly valued. Financial analysis, marketing researches, econometrics, auditing and production (and operations including services improvement), all require methodology and statistics. Methodology in the lines of commerce and business involves financial modeling. The financial modeling methodology is usually carried out by the financial analysts who write reports and provide information illustrating the company’s prospects. With a certain methodology, financial analysts develop certain models like Discounted Cash Flow model, binomial prizing model, etc. that help analyze the annual report. Technical analysts follow the time series modeling methodology to predict forecasts and price values of commodities. Through this methodology, they also analyze and predict the Sensex. Econometrics methodology is another instrument of statistics in business. It is a mixture of both economics and mathematical statistics and the methodology that it abides by involves statistical models like regression, binomial prizing model, etc.

In such technical fields, methodology is of the essence. In today’s world where evidence-based practices are required, methodology is necessary in most fields— particularly those fields where facts and figures are needed.

SPSS

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Initially, SPSS stood for Statistical Package for Social Sciences, and it was developed in the 1960’s by the by Chairman of the Board, Norman H. Nie in collaboration with C. Hadlai Hull and Dale Bent. When it was invented, SPSS was used in psychology research to analyze social research data. Today, however, SPSS is usually used in psychology, business, and medical or university research.

SPSS is preferred by the researcher as it is user-friendly because of its “point-and-click” interface. Most of the other statistical packages are based on programming languages. Some statistical packages that are “point-and-click” menu based do not have all the features that a researcher requires. SPSS, however, is the complete package because it is based on the “point-and-click” interface and is full of features. That is why most researchers, either in psychology, medicine or business, prefer to analyze data on SPSS.

In SPSS, the researcher can enter any type of data easily using the “import” function from the file menu. SPSS has two windows called the “data window” and the “viewer window.” In the SPSS data window, we can manually enter the data and change the data. In research, either psychology research, medical research or business research, data must be manipulated. In the SPSS data window, we cannot assign variable names that are more than eight characters, but from the viewer window, we can assign a label as long as we want. Additionally, from the viewer window of SPSS, we can fix missing values or other operations. In psychology, most of the researchers use SPSS to calculate the descriptive statistics, to help with significance testing and basic inferential tests, to find the analyses of the variance, to help with more advanced correlation and regression techniques, and to manage data.

A psychology researcher can easily calculate descriptive statistics in SPSS. They do this from the “analysis” menu where selecting “descriptive statistics” is required. In psychology research, many researchers want to compare two independent samples or two related samples. By using SPSS, a psychology researcher can easily compare two groups. Sometimes, when a sample does not meet the assumption of normal distribution, then a researcher can use a “non-parametric test” option available from the SPSS analysis menu. In psychology research, many times groups of the independent variables are more than two and the researcher needs to use advanced techniques like ANOVA, MANOVA, ANCOVA and MANCOVA. SPSS performs this analysis very easily and accurately. In psychology, the researcher needs to be advanced in regression techniques like multiple regression, logistic regression and SEM analysis. All regression techniques are available in the “SPSS regression” option, but for SEM analysis SPSS has an add-on module that performs this analysis very easily.

In medical or business research, most of the techniques used by the researchers are the same, but they use these techniques for different purposes. For example, in medicine, T-test, Chi-square, Analysis of variance, etc. techniques are used to test whether a particular drug can cure the illness. Regression technique is used to predict the long term impact of a drug.

In SPSS, all procedures are the same for all techniques but the uses are different. In business, T-test in SPSS is used to compare the mean of two samples. Samples may be output of workers, sales of two regions, etc. In business, the regression technique is used to predict average behavior of the dependent variable based on independent variables. For example, it can be used if business researchers want to predict sales for next year. If a credit card company wants to predict the risk of a credit card, he can use these tests to predict the risks. In SPSS, “logistic regression,” “discriminate analysis” and “CHAID” options are used to predict the risk. In SPSS, there are other options that make analysis very easy. For example, in SPSS, the “transform” option gives the flexibility to compute new variables or to change the existing variable. The SPSS “compute” option performs all the mathematical operations to make the changes in the data. In SPSS, the “graph” provides a high quality chart. With help, everyone can use SPSS. Samples and case studies are given in SPSS help. Step-by-step, these case studies are solved in SPSS and the results are interpreted.

Factor Analysis

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Factor analysis is a class of procedures that allow the researcher to observe a group of variables that tend to be correlated to each other and identify the underlying dimensions that explain these correlations. In other words, factor analysis is a class of procedures that are primarily used for data reduction and data summarization.

There are many statistical methods that are used to study the relationship between independent variables and dependent variables, but factor analysis is used to understand the patterns of relationships among many dependent variables while simultaneously discovering the nature of the independent variables that affect them.

Factor analysis is an interdependence technique because factor analysis involves the examination of interdependence relationships.

Factor analysis involves factors that are the underlying dimensions that define the correlations among the set of variables.

In the field of psychology, researchers can utilize factor analysis to understand the psychographic profile of a person by studying his lifestyle statements.

Factor analysis is widely used in the business field. In market research, factor analysis can be used in market segmentation in order to identify the underlying variables upon which the consumers are being grouped. Factor analysis is then used to segment the customers into categories like economically sensitive, convenience sensitive, comfort sensitive, performance sensitive, etc.

There are two approaches of factor analysis. One of the approaches of factor analysis is common factor analysis. Common factor analysis, as the name suggests, involves the estimation of the factors based only on the common variance. On the other hand, in principal component factor analysis, the total variance of the data is considered.

There are certain statistics that are associated with factor analysis.

The Bartlett’s test of sphericity in factor analysis is a test statistic that is used to examine the null hypothesis that is assumed. This says that the variables are uncorrelated in the population.

The correlation matrix in factor analysis is used to show that there exists some correlation between all the pairs of variables that are being included in the analysis.

The Kaiser – Meyer- Olkin (KMO) measures of sampling adequacy in factor analysis is an index that is used to examine the appropriateness of factor analysis. Therefore, the researcher should keep in mind that if the value of this index is between 0.5 and 1, then factor analysis is appropriate. And if the values are below 0.5, then factor analysis is an inappropriate technique for that study.

Factor loadings in factor analysis are nothing but the simple correlation between the variables and the factors under study.

A factor matrix in factor analysis consists of the factor loadings of all the variables on all the factors being extracted.

The factor scores in factor analysis are the combined scores estimated for each respondent on the derived factors.

As in all analysis, the first task of factor analysis is to formulate the problem. The next task is to construct the correlation matrix in factor analysis. Then, the researcher determines the method or an approach of the factor analysis. After determining the approach of factor analysis, the researcher determines the number of factors. The next task is to rotate the factors and interpret the factors by either calculating the factor scores or selecting the surrogate variables in factor analysis. After this, the researcher determines the model being fit in factor analysis.

F-Test

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An F-test is conducted on the basis of F statistic. F statistic is defined as the ratio between the two independent chi square variates divided by their respective degree of freedom. F-test follows Snedecor’s F- distribution.

The F-test has some applications in statistical theory. This document will discuss the applications of F-test in detail.

F-test can be used to test the equality of two population variances. Suppose a researcher wants to test whether or not two independent samples have been drawn from normal populations with the same variability. In this case, the researcher uses the F-test to do this study. The F-test can also be used to know whether there is any homogeneity between the two independent estimates of the population variance.

A practical example can show the above case in which the F-test is applied. Suppose two sets of pumpkins were grown under two different experimental conditions. Then, a random sample of size 9 and 11 were taken from the two different conditions. Those samples indicate that the standard deviations of their weights are 0.6 and 0.8 respectively. On making an assumption that the distribution of their weights is normal, the researcher conducts an F-test to test the hypothesis of whether or not the true variances are equal.

F-test can be used to test the significance of an observed multiple correlation coefficient. F-test can also be used to test the significance of an observed sample correlation ratio. The term sample correlation ratio is a measure of relationship between the statistical dispersion between the categories within the sample and the sample as a whole. Its significance is tested by the researcher using the F-test. F-test can also be used to test for the linearity in the regression model.

The most popular usage of F-test is that of Analysis of Variance (ANOVA) which plays a very important and fundamental role in Design of Experiments in Agricultural Statistics. In analysis of variance (ANOVA), F-test is carried out to test the equality of several means.

There is a relationship between t and F distributions, as in the F-test. This relationship states that if a statistic t follows Student’s t distribution with ‘n’ degrees of freedom, then the square of this statistic will follow Snedecor’s F distribution, as in F-test with 1 and n degrees of freedom.

There is also a relationship between F-test and chi square distribution. This relationship states that if the degree of freedom and the second chi square variate goes to infinity, then the F distribution (as in F-test) will follow the chi square distribution.

Due to such relationships, the F-test has many properties, much like the chi square test. The F-values in F-test are all non negative. The F-distribution (as in F-test) is always non symmetrically distributed. The mean in F-distribution (as in F-test) is approximately one. There are two independent degrees of freedom in F distribution, one is the numerator and the other is the denominator. There are many different F distributions (as in F-test), one for every pair of degrees of freedom.

F-test is a parameteric test that helps the researcher draw an inference about the data that is being drawn from a particular population. F-test is called a parameteric test because of the presence of parameters in the F- test. These parameters in F-test are mean and variance. The mode of F-test, i.e. the value that is most frequently in a data set, is always less than unity. According to the Karl Pearson’s coefficient of skewness, F-test is highly positively skewed. The probability distribution of F increases steadily before reaching the peak, and then again it starts decreasing in order to become tangential at infinity. Thus, we can say that the axis of F is asymptote to the right tail.

Heteroscedasticity

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One of the major assumptions of a classical linear regression model is that the disturbances occurring in the model should be homogeneous in nature. If this assumption is not fulfilled, then the researcher can say that heteroscedasticity is in the model.

Let us illustrate one example in order to describe heteroscedasticity. Let us consider an income saving model where the income of a person is the independent variable, and the savings made by the person is a dependent variable for heteroscedasticity. So, if the income of a person increases, then the savings will also simultaneously increase.

However, if heteroscedasticity is present in the data, then the graph for the savings of the person will remain constant when the income of the person will increase. This also states the major difference between heteroscedasticity and homoscedasticity. Heteroscedasticity results from the presence of outlier, which is nothing but an observation that is either small or large with respect to the other observations present in the sample.

Heteroscedasticity can occur if an important variable is omitted from the model. Suppose in the income saving model that one deletes the variable based on the income of the person. In this case, the researcher would not be able to interpret anything from the model. Heteroscedasticity can also occur due to the symmetrical or the assymeterical patterns of the regressors included in the model. Heteroscedasticity also arises due to incorrect data transformation, incorrect functional form (for example: comparing a linear model with a log linear model), etc.

It should be noted by the researcher that heteroscedasticity is more common in the case of cross sectional data than in time series data. If the researcher performs an ordinary least squares (OLS) method by taking heteroscedasticity into account, then the researcher will not be able to establish the confidence intervals and the tests of hypotheses. It is because of heteroscedasticity that the variance obtained will be less than the variance of the best linear unbiased estimator (BLUE). And due to this, the results obtained through the significant tests will be inaccurate due to heteroscedasticity.

A researcher can detect the presence of heteroscedasticity in the data because there are certain informal methods that illustrate the presence of heteroscedasticity.

Quite often, the nature of the case suggests that heteroscedasticity is likely to be involved. For example, in cross sectional data analysis, suppose a small, medium and large sized firm are sampled together. In this case, heteroscedasticity is usually expected.

There is a graphical method that can help the researcher to detect heteroscedasticity. If the researcher performs some regression analysis by assuming that there is no heteroscedasticity, then the estimated residuals will exhibit certain patterns that will indicate the presence of heteroscedasticity in the data.

There are, however, some informal tests to detect the presence of heteroscedasticity.

A formal test called Spearman’s rank correlation test is used by the researcher to detect the presence of heteroscedasticity.

This test can be used in the following way:

Suppose the researcher assumes a simple linear model (say) Yi = β0 + β1Xi + ui to detect heteroscedasticity. Then the researcher fits the model to the data by obtaining the absolute value of the residual and then ranking them in ascending or descending order to detect heteroscedasticity. After this, the researcher computes the spearman’s rank correlation for heteroscedasticity. Then, moving on to the heteroscedasticity detection process, the population rank correlation coefficient is assumed at 0, and the size of the sample is assumed to be greater than 8. A significance test is carried out to detect the heteroscedasticity. If the computed value of t is more than the tabulated value, then the researcher assumes that heteroscedasticity is present in the data. Otherwise heteroscedasticity is not present in the data.