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Univariate and Multivariate Outliers

A univariate outlier is a data point that consists of an extreme value on one variable.  A multivariate outlier is a combination of unusual scores on at least two variables.  Both types of outliers can influence the outcome of statistical analyses.  Outliers exist for four reasons.  Incorrect data entry can cause data to contain extreme cases.  A second reason for outliers can be failure to indicate codes for missing values in a dataset.  Another possibility is that the case did not come from the intended sample.  And finally, the distribution of the sample for specific variables may have a more extreme distribution than normal. 

In many parametric statistics, univariate and multivariate outliers must be removed from the dataset.  When looking for univariate outliers for continuous variables, standardized values (z scores) can be used.  If the statistical analysis to be performed does not contain a grouping variable, such as linear regression, canonical correlation, or SEM among others, then the data set should be assessed for outliers as a whole.  If the analysis to be conducted does contain a grouping variable, such as MANOVA, ANOVA, ANCOVA, or logistic regression, among others, then data should be assessed for outliers separately within each group.  For continuous variables, univariate outliers can be considered standardized cases that are outside the absolute value of 3.29.  However, caution must be taken with extremely large sample sizes, as outliers are expected in these datasets.  Once univariate outliers have been removed from a dataset, multivariate outliers can be assessed for and removed.  

Multivariate outliers can be identified with the use of Mahalanobis distance, which is the distance of a data point from the calculated centroid of the other cases where the centroid is calculated as the intersection of the mean of the variables being assessed.  Each point is recognized as an X, Y combination and multivariate outliers lie a given distance from the other cases.  The distances are interpreted using a p < .001 and the corresponding χ² value with the degrees of freedom equal to the number of variables.  Multivariate outliers can also be recognized using leverage, discrepancy, and influence.  Leverage is related to Mahalanobis distance but is measured on a different scale so that the χ² distribution does not apply.  Large scores indicate the case if further out however may still lie on the same line. Discrepancy assesses the extent that the case is in line with the other cases.  Influence is determined by leverage and discrepancy and assesses changes in coefficients when cases are removed.  Cases > 1.00 are likely to be considered outliers.

Dissertation Statistics

The dissertation is by far the most challenging aspect of a doctoral student’s career. The reason for this is because the dissertation is both lengthy and difficult to complete. There is no question that much time and energy needs to be devoted to the dissertation. One of the most difficult aspects of this dissertation is the dissertation statistics. Because dissertations rely on statistics, the dissertation statistics must be accurate, the dissertation statistics must be precise, the dissertation statistics must be performed according to certain methodologies, and the dissertation statistics must be valid. Thus, dissertation statistics are crucial to the dissertation as the dissertation statistics will encompass the entire dissertation.

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Because dissertation statistics play a crucial role in the dissertation, there are dissertation consultants trained to help students with the dissertation statistics. These dissertation consultants are expert statisticians and they can provide one-on-one help to any student needing help with dissertation statistics. And while most students might hesitate to acquire the help of a dissertation consultant to help with the dissertation statistics, once the student does actually hire the dissertation consultant, they will certainly be glad that they did! This is true because dissertation consultants provide many services to students.

Dissertation consultants can provide invaluable help to students throughout the entire dissertation process. Thus, dissertation consultants can provide help on things other than just the dissertation statistics. Dissertation consultants, then, can help from the very beginning of a project or dissertation as dissertation consultants can help a student decide upon a topic. Most students have a general idea of what they want to study, but most student need help narrowing-down that idea or making it statistically possible to study. Here again dissertation consultants can provide valuable feedback, advice, guidance and assistance. Dissertation consultants can also help students do the necessary research before the student decides on a topic. Because the dissertation must add new information to a field, proper dissertation research must be completed prior to the student starting their dissertation and conducting dissertation statistics.

Once the student chooses the topic with the help of a dissertation consultant, the dissertation consultant can help the student phrase the topic so it makes sense statistically. And because not all students are trained in statistics, not all students know how to phrase a topic so it is stated in statistical language. Once this is completed, the student and the dissertation consultant can get to work on the gathering of the data. Because the dissertation statistics will be based on this data, it is very important to get accurate data. Otherwise, the dissertation statistics will be skewed because the data is skewed. Proper procedures and methodologies are performed with the help of dissertation consultants in the data-gathering-stage, and the student can therefore acquire valid data.

Once the student (with the help of the dissertation consultant) has gathered valid and accurate data, the real work of dissertation statistics gets underway. Here, the dissertation statistics applies his or her statistical expertise to ensure that proper inferences and conclusions are drawn from the dissertation statistics. With the help of a dissertation consultant, then, the dissertation statistics becomes manageable and understandable. This is because a dissertation consultant explains every single thing to the student so that the student understands every single aspect of the dissertation statistics. Because the student must defend their own dissertation without the help of a dissertation consultant, the dissertation consultant will teach the student everything he or she needs to know about dissertation statistics. This is done along the way as the dissertation consultant helps the student step-by-step in the complex world of statistics. One of the most important things a dissertation consultant does, then, is to provide instruction. With the help of a dissertation consultant, the student will no-doubt have accurate dissertation statistics and will no-doubt succeed.