Request

To request a blog written on a specific topic, please email James@StatisticsSolutions.com with your suggestion. Thank you!

Tuesday, May 12, 2009

Dissertation Help

Writing a dissertation is the most significant part of a student’s academic life, and therefore every student wants to write an error and stress-free dissertation. However, this is very difficult, because it is nearly impossible for an inexperienced and busy student to overcome the doubts that always surround a dissertation. The very word “dissertation” is enough to strike fear in most students. This is because the process of writing a dissertation is very stressful. In these stressful times, students would benefit greatly from having some help that can take care of the queries surrounding the writing of the dissertation. Without this help, the unsuccessful search for solutions of queries gets magnified because students do not have access to their advisors when they need or want it. To avoid this confusion and stress, it is helpful for students to get assistance from Dissertation help.

For dissertation help, click here.

Dissertation help provides professionals who can help the student step-by-step as the student has questions about writing the dissertation. Experts from dissertation help get the correct methodology for the dissertation. In addition to the help in the collection of data, dissertation help workers help the student decide the most appropriate statistical test required to analyze the data. The choice of the statistical test is determined by the salient features of the student’s study and research design. Dissertation help and consultants are aware of the importance of the dissertation help. Consultants from dissertation help make sure that the student has the basic understanding of the study. They also make sure that the student knows the data and knows how to comprehend this data. This is very important as it is used to decide the most appropriate statistical test to answer the dissertation and research question. Much like computers, statistical tests are mathematical formulas that can easily be implemented with the help provided by dissertation help. Finally, the consultant from dissertation help can help the student in determining whether the used statistical tests are appropriate to the design of the student’s dissertation or research study.

Dissertation help assists a student in many ways:

-They give guidelines in developing a dissertation from the start.
-They write the method section of the student’s dissertation.
-They design, analyze, calculate and write the statistical portion of the student’s method section.
-They draft and develop the plan for data analysis.
-They perform power analysis for the required sample size.
-They analyze and transcribe the data.
-They help with the result section.
-They attend to the comments given by the advisors.
-They help the student build up a defense for the regular dissertation comments.

For dissertation help, click here.

Thus, dissertation help can explain the purpose and logic of the student’s dissertation. With the consultant sent by dissertation help, a student can practice the discussion of the student’s dissertation findings.


Hiring the help of dissertation help is very popular as dissertation help can offer the most sought after methods for students who are going through the difficult processes of dissertation statistics. While acquiring dissertation help, students should be mindful that the dissertation help is credible, available and that the dissertation help is well established. In this world where one often struggles to differentiate between what is fake and what is real, it is a very important task to decide on the proper dissertation statistics service provider. Despite the difficulty one might have in choosing the right dissertation statistics service, the service is very important and necessary to the process of writing a dissertation. Further, dissertation help can be very cost effective. This is true because there is much time saved by having the dissertation statistics service. Most services are very economical and worth it. Additionally, most statistics dissertation services provide the first consultation session free of charge, and this should also help in choosing the proper dissertation consulting service. With dissertation help, the student is guaranteed success.

Monday, May 11, 2009

Sign Test

There are non parametric tests or methods that are used in cases when the parametric test is not in use. One of the non parametric tests is the sign test. This non parametric test called the sign test is used to test the null hypothesis that is assumed and says that the median of the distribution is equal to a particular fixed value.

The sign test can be used in the place of parametric tests, like one sample t-test, or in the place of the paired sample t test. The sign test can be used to test that kind of data which is of ordered categorical type. The sign test is usually used in the kind of data where it is possible to rank the observations.

The researcher should keep in mind that the Wilcoxon Signed Rank Sum test is used in such situations, and is also more powerful than the sign test.

Let us discuss the procedure of carrying out the sign test. In the sign test, a sample consisting of ‘n’ number of observations is drawn. In the sign test, it is assumed that some s+ of the observations are greater than the population median. In the sign test, it is also assumed that some s- observations are smaller than the population median. In the sign test, the observations in the sample, which are absolutely equal to the population median, are ignored by the researcher. The value of the sum of s+ and s- are therefore less than the sample size ‘n’ in the sign test and therefore considered as ‘n/.’

According to the null hypothesis in the sign test, it is expected that half of the observations should be above the median and the other half of the observations should be below the median. Hence, under the null hypothesis in the sign test, both s+ and s- follow a binomial distribution with the probability of ‘0.5’ and the size n= n/.

The first step of conducting a sign test involves choosing the value of ‘s,’ which is nothing but the maximum value among the s+ and s- .

Then, the usage of the tables of the binomial distribution is done in the sign test. This table of binomial distribution is done in the sign test in order to find the probability of the value of ‘s’ or something higher than ‘s’ under the assumption that the probability is ‘0.5’ and the n= n/ .
If the sign test is two sided, then the probability obtained from the tables of binomial distribution is doubled.

The sign test can also be performed with the help of SPSS software. In SPSS software, the sign test can be performed by selecting “analyze” from the menu item. Then, the sign test is conducted in SPSS by clicking the “non parametric tests” in the analyze menu. From the non parametric tests, the researcher selects the “binomial test,” which is nothing but the sign test. Therefore, it should be noted by the researcher that due to the involvement of binomial distribution, the sign test is also called the binomial test.

In SPSS, after selecting the type of non parametric test, the researcher chooses the relevant variable, which is considered as the test variable on which the sign test is to be conducted.
In the case of a paired type of data in the sign test, the researcher specifies the null value of the paired data. The researcher also selects the cut point under “define dichotomy criteria” while conducting the sign test.After finishing all the specifications in SPSS, the researcher finally clicks on the “OK” button in order to the view the outcome obtained from the sign test.

Kruskal-Wallis Test

The Kruskal-Wallis test is one of the non parametric tests that is used as a generalized form of the Mann Whitney U test. The Kruskal-Wallis test is used to test the null hypothesis which states that ‘k’ number of samples has been drawn from the same population or the identical population with the same or identical median. If Sj is the population median for the jth group or sample in the Kruskal-Wallis test, then the null hypothesis in mathematical form can be written as S1 =S2= ….. = Sk. Obviously, the alternative hypothesis in the Kruskal-Wallis test would be that Si is not equal to Sj. This means that in the Kruskal-Wallis test, at least one pair of groups or samples has different pairs.

In order to apply the Kruskal-Wallis test, one has to write the data in a two way format in such a manner that each column represents each successive sample. In the computation of the Kruskal-Wallis test, each of the ‘N’ observations is replaced in the form of ranks. This means that in the Kruskal-Wallis test, all the values from the ‘k’ number of samples are combined together and are ranked in a single series.

The smallest in the Kruskal-Wallis test is replaced by the rank 1. The next smallest in the Kruskal-Wallis test is replaced by rank 2, and the largest in the Kruskal-Wallis test is replaced by ‘N.’ Here, ‘N’ in the Kruskal-Wallis test is denoted as the total number of the observations in the ‘k’ number of samples. After this, the sum of ranks in each sample or column is found in the Kruskal-Wallis test.

From the sum of the ranks, the researcher in the Kruskal-Wallis test computes the average rank for each sample or group. If the samples are from an identical population in the Kruskal-Wallis test, then the average rank should be about the same. On the other hand, if the samples in the Kruskal-Wallis test are from populations with different medians, then the average rank will differ.

The Kruskal-Wallis test assesses the differences against the average ranks in order to determine whether or not they are likely to have come from samples drawn from the same population.
If the ‘k’ samples in the Kruskal-Wallis test are actually drawn from a same population or an identical population, then the sampling distribution of the Kruskal-Wallis test statistic and the probability of observing the different values of the Kruskal-Wallis test can be tabled.

While conducting the Kruskal-Wallis test, the researcher should keep in mind that if the number of groups exceeds the value of three and if the number of the observations in each group exceeds the number five, then, in such cases, the sampling distribution of the Kruskal-Wallis test is well approximated by the chi square distribution. This approximation gets better in the Kruskal-Wallis test when both the number of groups and the number of the observations in each group gets increased.

There are certain assumptions in the Kruskal-Wallis test.
  • It is assumed in the Kruskal-Wallis test that the observations in the data set are independent of each other.
  • It is assumed in the Kruskal-Wallis test that the distribution of the population should not be necessarily normal and the variances should not be necessarily equal.
  • It is assumed in the Kruskal-Wallis test that the observations must be drawn from the population by the process of random sampling.

The sample sizes in the Kruskal-Wallis test should be as equal as possible, but some differences are allowed.The Kruskal-Wallis test also has one limitation. If the researcher does not find a significant difference in his data while conducting the Kruskal-Wallis test, then he cannot say that the samples are the same.

Dissertation Statistics Help

One of the most time consuming aspects of the dissertation is the statistics part of the dissertation. Because statistics are needed for the dissertation, and because a dissertation is needed for a student to receive his/her doctoral degree, the statistics part of the dissertation is essentially the most important part of the dissertation.

There is help, however, and this help comes in the form of dissertation statistics help. Dissertation statistics help can help with every single statistical issue in a dissertation. Dissertation statistics help can guide the student step-by-step through the statistics, and dissertation statistics help can be an invaluable resource for all students pursuing their doctoral degree.

Dissertation statistics help is invaluable because dissertation statistics help can answer all questions a student might have. While students can certainly ask their advisor these questions, oftentimes a student’s advisor is unavailable. Dissertation statistics help, however, is always available and dissertation statistics help is there only to help the student. Thus, dissertation statistics help is like a permanent advisor for the student.

And just like an advisor, dissertation statistics help guides and assists the students who are seeking their doctoral degree. Dissertation statistics help provides all of the information necessary for the student to do the work. Because dissertation statistics help offers this information and guidance, students are able to learn the material for themselves, with the help of dissertation statistics help. In other words, dissertation statistics help ensures that the student is actually learning—not just hiring someone to do the work. Therefore, dissertation statistics help can be an invaluable learning tool for students.

Additionally, dissertation statistics help can save the student much time and energy. There are many, many, many rules and regulations guiding statistics (it is, after all a science—and just like all science, it has rules, regulations, procedures, etc. that need to be followed). Dissertation statistics help can explain these rules and procedures and dissertation statistics help can make sure that students are traveling in the right direction. Improper statistics lead to inaccurate results and therefore dissertation statistics help will ensure that students who seek dissertation statistics help do not get improper results.

Dissertation statistics help will also create a timeline for students to follow. This timeline provided by dissertation statistics helps allows students to know exactly what needs to be done, when it needs to be done and how it needs to be done. Without this timeline provided by dissertation statistics help, students are often at a loss at how to proceed and where to even begin. The timeline provided by dissertation statistics help organizes students and helps them stay on-target and on-task.

Dissertation statistics help should be sought by the student and it should come from experts in the field. These experts, above all, must be trained in statistics. They must also have comprehensive knowledge of computers and the statistical programs that work on computers (SPSS, for example). Additionally, dissertation statistics help should be sought from people who are easily and readily available. Finally, dissertation statistics help should be acquired from people who know how to effectively communicate with students and their clients. Because proper communication is essential for any project to get done, people who offer dissertation statistics help should be good communicators. There is no question that dissertation statistics help is the most invaluable, essential and helpful tool available for all students needing to successfully complete their dissertations. Dissertation statistics help can make the difficult chore of completing the dissertation possible, and dissertation statistics consultants can allow students to complete this chore on-time. Finally, dissertation statistics consultants will not stop until their student earns his/her degree in the most successful way possible.

Friday, May 8, 2009

Statistics Consulting

Statistics consulting is a valuable tool for anyone in need of help with statistics. Statistics involves the very precise accumulation of data and the very precise interpretation of this data. Because statistics is a science, it can be very difficult to obtain accurate statistics without the help of statistics consulting. Statistics consulting, then, provides all of the information, guidance and assistance one would need to acquire accurate statistics.

Statistics consulting came about because not everyone who needs to use statistics is trained in the various methodologies of statistics. Statistics consulting helps individuals who are in this predicament.

Students looking to acquire their doctorate degree are often in need of statistics consulting. This is because, again, students are not always trained in statistics. And yet, these students need to use statistics in order to get accurate information from which to write a dissertation. Statistics consulting, however, can guide a student step-by-step through the process and procedures of statistics, as statistics consulting will provide valuable assistance to any student. Statistics consulting helps students break-down what needs to be done to get accurate statistics. The first thing that needs to be done, of course, is gathering data or information. This, however, is not easy as there are many rules and regulations surrounding the gathering of information. Statistics consulting explains these rules and statistics consulting can take the student through each and every step of the gathering of data and information. Once this data is gathered and acquired, statistics consulting helps students analyze and interpret the results. Here again, this is not easy. Students not trained in statistics often do not know how to accurately interpret the results, but statistics consulting provides all of the information necessary to accurately interpret the results. Finally, statistics consulting helps students to “put it all together.” In other words, statistics consulting helps students finalize their dissertations as statistics consulting ensures that all of the statistics acquired are not only accurate, but pertain to the actual topic of the dissertation.

Statistics consulting can also provide invaluable help to businesses. This is particularly true for very small businesses as statistics consulting can provide these small businesses with everything they need to be successful. This is true because oftentimes small businesses do not have the expertise, know-how or experience to get useful statistics. And useful statistics are invaluable in market research—which, of course is invaluable in knowing which products will work where, and at what price, etc. Statistics consulting, then, does all of this research for the business and statistics consulting provides all of the results necessary to help a small business. Small businesses can take the information received from statistics consulting and apply it to their business model. Without the help of statistics consulting, small businesses are often left struggling as they try their product on the market without proper market research, and only learn from experience (and much money lost) that their product will not work in that particular market. Statistics consulting can clearly save a business both time and money.
Because statistics consulting can be so helpful both to organizations and businesses, it is important to seek statistics consulting from experts in the field. Statistics consulting is widely available and a simple on-line search will yield many search results for statistics consulting. Not all statistics consulting firms are as good as others, however. Thus, before deciding upon a particular statistics consulting firm, it is important to do adequate research on that statistics consulting firm. Once that research is completed, and once a statistics consulting firm is hired to help, there is no-doubt that the people seeking that help will benefit greatly from statistics consulting.

Thursday, May 7, 2009

Autocorrelation

In cross sectional studies, data often involves households (in a consumption function analysis) or firms (in an investment study analysis), so if by chance an error term of a particular household or firm gets correlated with some other household or firm, then such correlations are termed as autocorrelation. Autocorrelation also occurs in the case of time series data. In the case of time series data, if the observations exhibit intercorrelations, especially when the time interval between the successive observations are short, then those intercorrelations are nothing but autocorrelation.

So, the term autocorrelation is defined as the correlation between the members of the series of the observations that are ordered with respect to time. Let us discuss two cases based on cross sectional and time series data to explain autocorrelation in a much better manner. In the case of cross sectional data, if a change in the income of a particular person affects the consumption expenditure of another household (other than his), then autocorrelation is present in the data. In the case of time series data, if an output is low in one quarter due to a labor strike, and if the data shows low output continues in the next quarter as well, then autocorrelation is present in the data.

Autocorrelation can be defined as the lag correlation of a given series with itself, lagged by a number of time units. On the other hand, serial autocorrelation defines the lag correlation between the two series in time series data.

There are certain patterns of autocorrelation, thus autocorrelation comes with various patterns. One example would be showing a discernible pattern among the residual errors. Autocorrelation exists when the residual error shows a cyclical pattern or an upward or downward trend in the disturbances, etc.

One of the major reasons for autocorrelation is the inertia or sluggishness caused in the time series data. The usage of an incorrect functional form also becomes a reason for an autocorrelation to occur.

The manipulation involving the extrapolation and the interpolation in the data also becomes a reason for autocorrelation. In this, the time series data is averaged so that smoothness occurs in the data, and this smoothness in the data exhibits a systematic pattern which in turn, introduces autocorrelation in the data.

A non stationarity property in the time series data also gives rise to the phenomenon of autocorrelation. Therefore, in order to make the time series free of autocorrelation, the researcher should make the data stationary.

Researchers should know that autocorrelation can be positive as well as negative. Economic time series generally exhibits positive autocorrelation as the series move in an upward or downward pattern. If the series move in a constant upward and downward movement, then autocorrelation is negative.

The major consequence of using ordinary least square (OLS) in the presence of autocorrelation is that it simply makes the estimator inefficient. As a result, the hypothesis testing procedures will give inaccurate results due to the presence of autocorrelation.

There is a popular test called the Durbin Watson test that detects the presence of autocorrelation. This test is conducted under the null hypothesis that there is no autocorrelation in the data. A test statistic called‘d’ is computed. “d” is defined as the ratio between the sum of the square of the difference in the residuals with ith and (i-1) time and the square of the residual in ith time. If the upper critical value of the test comes out to be less than the value of ‘d,’ then there is no autocorrelation. If the lower critical value of the test is more than the value of ‘d’ then there is autocorrelation.If one detects autocorrelation in the data, then the first thing a researcher should do is to try to find whether or not the autocorrelation is pure. If it is pure autocorrelation, then one can transform it into the original model, which is free from pure autocorrelation.

Wednesday, May 6, 2009

Time Series Analysis

Time series analysis is that type of analysis that deals with time series data. The time series data in time series analysis usually involves price data of certain commodities, or stock exchanges, like the Bombay Stock Exchange (BSE) and the New York Stock Exchange (NYSE).
There are many concepts used in time series analysis. One such process is a random process or a stochastic process in time series analysis. This is a collection of random variables that are ordered with respect to the time. For example, if Y is a random variable, in the case of continuous nature, it will be denoted as Y(t), and in the case of its discreet nature, it will be denoted as Yt in time series analysis.

In time series analysis, it is very important for the analyst to know that before conducting time series analysis, the stochastic process should be made stationary. A stationary process in time series analysis is said to be stationary only if the mean and variance is constant over the time, and if the value of the covariance between the two time periods mainly depends upon the distance between the two time periods. It is important for the analyst to know the reason behind stationary stochastic process in time series analysis. The reason is that it is not practically possible to compute mean and variance for every time period in time series analysis. If the time series is not stationary, then it will give the value of mean and variance for that particular time series.

A stochastic process in time series analysis is said to be purely random only if it has the mean as zero and the variance as constant. Additionally, it must be serially uncorrelated.
Differencing is one of the methods in time series analysis that helps in making the volatile time series into a stationary one. There are different orders of differencing in time series analysis. Suppose, for example, that the volatility is not reduced from the data after first order differencing. In this case, the analyst can make a second order differencing, in order to achieve stationarity in data in time series analysis.

In time series analysis, the exponential smoothing method predicts the next period value on the basis of the past value and the current value. In time series analysis, this method is used to make short term predictions about the commodities or the stock exchanges. Alpha, Gamma, Phi, and Delta are the parameters that are used to estimate the effect of the time series data in time series analysis. In time series analysis, alpha is used when seasonality is not present in the data. In time series analysis, Gamma is used when the series exhibits certain trends in the data. Delta is used in time series analysis when seasonality cycles are present in data. In time series analysis, the various models are applied according to the exhibition of the pattern in the data.
The major goal of time series analysis is to fit the data to the appropriate model under consideration.

There are certain assumptions made in time series analysis. These assumptions are as follows:
In time series analysis, the first assumption is that the series should be stationary. In other words, it means that in time series analysis, the series are normally distributed and the mean and variance is constant over that period of time.

In time series analysis, it is assumed that the error term is randomly distributed and the mean and the variance are constant over a time period. The errors in time series analysis are assumed to be uncorrelated to each other.

In time series analysis, it is assumed that no outlier is present in the series. The presence of outliers affects the inference of the data in time series analysis and thus leads to inaccurate results. If shocks are present in the time series analysis, they are assumed to be randomly distributed with a mean zero and a constant variance.

Chi Square Test

The idea behind the parametric tests that involve parameters is to test the statistical significance of the observations under study. Chi square test is one of the parametric tests.
Chi square test involves different types of chi square tests, like chi square test for cross tabulation, chi square test for goodness of fit, likelihood ratio chi square test, etc.


The statistic in chi square test is used to test the statistical significance of the observed relationship in the cross tabulation of two variables. The statistic used in chi square test helps the researcher to determine whether or not an appropriate relationship exists between the two variables.


The null hypothesis assumed in chi square test assumes that there exists absolutely no correlation between the two variables being observed under the study. The chi square test is conducted by computing the cell frequencies which consist of the expected frequencies, if there is no correlation between the variables. The expected frequency in chi square test is then compared to the actual observed frequencies found in cross tabulation to calculate the chi square statistic in chi square test. The expected frequency in chi square test is calculated as the product of the total number of observations in the row and the column divided by the total size of the sample. The chi square statistic in chi square test is then calculated as the sum of the square of the deviation between the observed and the expected frequency, which is divided by the expected frequency.


The researcher should know that the greater the difference between the observed and expected cell frequency, the larger the value of the chi square statistic in chi square test.
In order to determine the association between the two variables, the probability of obtaining a value of chi square should be larger than the one obtained from chi square test of cross tabulation.


There is one more popular test called the chi square test for goodness of fit. This type of chi square test, called the chi square test for goodness of fit, helps the researcher to understand whether or not the sample drawn from a certain population has a specific distribution that actually belongs to that specified distribution. This type of chi square test can be applicable to only discrete types of distributions, like poisson, binomial, etc. This type of chi square test is an alternative test for the non parametric test and it is called the Kolmogorov Smrinov goodness of fit test.


The null hypothesis assumed by the researcher in this type of chi square test is that the data drawn from the population follows the specified distribution. The chi square statistic in this chi square test is defined in a similar manner as defined in the above type of test. One of the important points to be noted by the researcher is that the expected number of frequencies in this type of chi square test should be at least five. This means that the chi square test will not be valid for those whose expected cell frequency is less than five.


As discussed in the above chi square test, the probability of obtaining a value of chi square should be larger than the one obtained from chi square test for goodness of fit.

There are certain assumptions in a chi square test. The assumptions are as follows:

  • In a chi square test, random sampling of the data is assumed.
  • In a chi square test, a sample with a sufficiently large size is assumed. If a chi square test is conducted on a sample with a smaller size, then the chi square test will yield an inaccurate inference. The researcher, by using chi square test on small samples, might end up committing a Type II error.
  • In a chi square test, the observations are always assumed to be independent of each other.
  • In a chi square test, the observations must have the same fundamental distribution.

Tuesday, May 5, 2009

APA Bibliography

APA citation is a method of formatting a scientific paper or dissertation. APA stands for the American Psychological Association, and there are APA rules and guidelines that govern every single aspect of the dissertation. Oftentimes, APA citation can be divided into two separate parts: APA citation within the text and APA citation after the text. The APA citation after the text refers, essentially, to the APA bibliography. The APA bibliography must adhere to very precise rules and regulations in order to be acceptable. In other words, the APA bibliography must be formatted correctly, using proper APA bibliography standards if the dissertation is to be accepted.

The purpose of the APA bibliography is to document all of the sources that a student uses throughout his or her dissertation. Thus, the APA bibliography provides all of the information on the outside information that a student cites within his or her dissertation. (APA rules also govern how those citations are formatted within the text, as well as governing the rules of the APA bibliography.) Because dissertations must be checked in order to assess their validity, it is important to carefully document all sources used within the dissertation and within the APA bibliography. A well written and properly formatted APA bibliography will allow advisors, professors and those parties who authorize the dissertation to check all of the sources that the student has listed in the APA bibliography. Further, a standard method of formatting for the APA bibliography page saves valuable time for these people who want to double check all the sources.

The APA bibliography, therefore, lists all of the sources used in the dissertation. Examples of sources that can be found in the dissertation and in the APA bibliography include journal articles, books, web documents on university web-sites, stand alone web documents, journal articles from databases, abstracts from secondary databases, articles in edited books, etc. Because the list of possible sources is extensive, it is important to make sure that much time is spent researching what, exactly, needs to be written in the APA bibliography. In other words, because there are so many different kinds of sources that one can use and document in the APA bibliography, it is important to get accurate and precise information regarding what rules govern the APA bibliography.

While the rules of APA citation and the APA bibliography are not necessarily hard to follow, it is time consuming to look up all of these rules and regulations regarding APA citation and the APA bibliography. Additionally, many students wait until the last minute to format their paper and their APA bibliography. They wait until the last minute because students do not realize how long it can take to transform everything (including the APA bibliography) into proper APA format. Add to this the pressure and stress that a student feels at the end of his or her dissertation, and this is a certain recipe for disaster. The disaster occurs when students rush through APA citation and take shortcuts on their APA bibliography. A dissertation cannot be approved, however, unless the document itself and the APA bibliography are formatted correctly. And while a student may think that his or her APA formatting within the text and his or her APA bibliography are “close enough,” the dissertation advisors and the dissertation acceptance committees are very well informed on proper APA citation. Thus, a student will not have their dissertation accepted or approved if it is not in proper APA format.

Students struggling with APA format and the APA bibliography should look for help. Oftentimes their advisors are too busy to worry about APA format and the APA bibliography. APA formatting help is available, however, and students should turn to consultants who have extensive expertise in APA formatting and the APA bibliography.

Monday, May 4, 2009

Analysis of covariance (ANCOVA)

Analysis of covariance (ANCOVA) is used in examining the differences in the mean values of the dependent variables that are related to the effect of the controlled independent variables while taking into account the influence of the uncontrolled independent variables.

The Analysis of covariance (ANCOVA) is used in the field of business. This document will detail the usability of Analysis of covariance (ANCOVA) in market research.

Analysis of covariance (ANCOVA) can be used to determine the variation in the intention of the consumer to buy a particular brand with respect to different levels of price and the consumer’s attitude towards that brand.

Analysis of covariance (ANCOVA) can be used to determine how a change in the price level of a particular commodity will affect the consumption of that commodity by the consumers.

Analysis of covariance (ANCOVA) consists of at least one categorical independent variable and at least one interval natured independent variable. In Analysis of covariance (ANCOVA), the categorical independent variable is termed as a factor, whereas the interval natured independent variable is termed as a covariate. The task of the covariate in Analysis of covariance (ANCOVA) is to remove the extraneous variation from the dependent variable. This is done because the effects of the factors are of major concern in Analysis of covariance (ANCOVA).
Analysis of covariance (ANCOVA) is most useful in those cases where the covariate is linearly related to the dependent variables and is not related to the factors.

Similar to Analysis of variance (ANOVA), Analysis of covariance (ANCOVA) also assumes similar assumptions. The following are the assumptions of Analysis of Covariance (ANCOVA):
The variance in Analysis of covariance (ANCOVA) that is being analyzed must be independent.
In the case of more than one independent variable, the variance in Analysis of covariance (ANCOVA) must be homogeneous in nature within each cell that is formed by the categorical independent variables.

The data should be drawn from the population by means of random sampling in Analysis of covariance (ANCOVA). Analysis of covariance (ANCOVA) assumes that the adjusted treatment means those that are being computed or estimated are based on the fact that the variables obtained due to the interaction of covariate are negligible.

The Analysis of covariance (ANCOVA) is done by using linear regression. This means that Analysis of covariance (ANCOVA) assumes that the relationship between the independent variable and the dependent variable must be linear in nature.

In Analysis of covariance (ANCOVA), the different types of the independent variables are assumed to be drawn from the normal population having a mean of zero.

The Analysis of covariance (ANCOVA) assumes that the regression coefficients in every group of the independent variable must be homogeneous in nature.

Analysis of covariance (ANCOVA) is applied when an independent variable has a powerful correlation with the dependent variable. But, it is important to remember that the independent variables in Analysis of covariance (ANCOVA) do not interact with other independent variables while predicting the value of the dependent variable. Analysis of covariance (ANCOVA) is generally applied to balance the effect of comparatively more powerful non interacting variables. It is necessary to balance the effect of interaction in Analysis of covariance (ANCOVA) in order to avoid uncertainty among the independent variables.

Analysis of covariance (ANCOVA) is applied only in those cases where the balanced independent variable is measured on a continuous scale.

Let us assume a researcher wants to determine the effect of an in-store promotion on sales revenue. In this case, Analysis of covariance (ANCOVA) is an appropriate technique because the change in the attitude of the consumer towards the store will automatically affect the sales revenue of the store in Analysis of covariance (ANCOVA). Therefore, in Analysis of covariance (ANCOVA), the dependent variable will be the sales revenue of the store. And the independent variable will be the attitude of the consumer in Analysis of covariance (ANCOVA).