Analysis of Univariate and Multivariate Statistics: Applications

This essay provides a detailed comparison of univariate and multivariate statistics. Univariate statistics, which deal with single-variable data, are defined and their applications in transportation (data fitting) and metabolic studies are discussed, highlighting the usefulness of parametric and non-parametric tests in hypothesis testing and data analysis. Multivariate statistics, used for analyzing multiple variables, are then explored, with examples in bioprocessing activities such as root cause analysis and process monitoring. The essay further contrasts the usefulness of parametric and non-parametric multivariate statistics, noting the advantages of non-parametric tests in handling non-normally distributed and ordinal data, as well as their robustness against outliers. The document is available on Desklib, a platform offering a wide range of study resources for students.

Running head: STATISTICS 1
Multivariate Statistics and Univariate Statistics
Student’s Name
Course
Institution
Date of Submission

STATISTICS 2
Definition of Univariate Statistics
Univariate refers to the term used commonly in statistics to explain or describe a data
type that is made up of observations on a single attribute or characteristics (Groppe, and Urbach,
2018). An example of univariate statistics is the worker's salaries in industry. It is possible to
visualize univariate data by use of images or graphs after the data has been reported, collected,
measured and analyzed (Groppe, 2018).
Applicability.
One technique that is commonly used in transportation application is known as data
fitting (Urbach, 2018). In this case, it involves the determination of the distribution that fit the
data best. A technique used to determine how a distribution fits the data is to carry out the
goodness of fit. A goodness of fit test statistics shows how distribution can produce a given
random sample. Another simple form is applied in metabolic studies. In this scenario, univariate
analysis, at a time, involves a variable that is used in the initial stages of biomarker discovery
and biology research. There are different methods of univariate statistics that are used
commonly in metabolomics such as Mann-Whitney U-test and Student’s t-test(Asamura, 2012).
The student’s t-test is widely used because it provides the probability that two sets of samples are
distinguishable. The test, however, does not assume that data are distributed normally, which in
the data sets of metabolomics may not be the case.
Usefulness
Parametric statistics are capable of testing the extent to which sample structures can be
reflected in the whole population. Some statistics, for example, test the differences between two
groups while other statistics test the differences that involve many groups. These statistics test
2

STATISTICS 3
the major or main effects, which is the effect of one variable on another — moreover, the
processes of statistical action test differences of the group only one time. The parametric tests
are used since they are considered to be the most robust inferential statistics (Asamura, 2012).
Parametric statistics are normally based on parametric, distribution tests applicable to the
variables only (Asamura, 2012). Another usefulness of parametric statistics is that one does not
need data that can be changed in some format or order of ranks. The conversation process is
something that occurs in rank and regularly uses parametric test results in a precision loss.
The test of hypothesis with non-parametric statistics is useful in several ways. Test of the
hypothesis that is more concern of a single value for a particular data. Test of a hypothesis
involves no difference among sets such as Rank, Fisher-Irwin test and two-sample sign test
(Asamura, 2012). Parametric statistics are important when testing a hypothesis of an association
among variables such as coefficient of concordance or Rank correlation. Also, they are
important when testing hypothesis that concerns a variation in the data given, for instance
ANOVA. Besides, it can be used to test randomness of a given sample based on runs theory or
runs test of one sample (Noris, M. J. (2016). Also, it is important to determine when categorical
data reveals dependency or if two categories are independent. The non-parametric statistics are
also important when making comparison between actual data and theoretical populations when
categories are employed.
Definition of Multivariate Statistics
Multivariate statistics are employed to analyses the behavior of at least one variable (Var, 2018).
There is various range of multivariate methods available. These include matrix plot, discriminant
3

STATISTICS 4
analysis, radar plot, correlation analysis, cluster analysis and principal component and factor
analysis (Var, 2018).
Application
Multivariate Data Analysis can be employed in supporting main activities needed for
appropriate bioprocessing. Such activities involve root cause analysis, fault diagnosis, process
monitoring, process scale-up and process characterization (Var, I. (2018). Multivariate statistics
in root cause analysis is used for identification of parameter interactions and scale-up differences
that impact the process performance of the cell culture. Modelling and multivariate data analysis
can be carried out by use of data from commercial-scale, pilot scale and small scale batches. The
parameters that can be examined include seed inocula, raw materials, ammonium, lactate, and
glucose. The output parameters can be osmolality, cell viability, viable cell density, product titer
and product attributes. Multivariate data analysis is a tool that can be used to identify the
experimental conditions and the root cause to correct and demonstrate it (Lohnes, 2017). The
multivariate statistics can be used to identify the interactions of process parameters that affect the
product attributes and cell culture performance (Lohnes, 2017). It can be used an efficient tool
for enhancing process understanding as well as collating process knowledge (Lohnes, P. R.
(2017).
Usefulness of Non Parametric and Parametric Multivariate Statistics
Multivariate Parametric tests can produce reliable results when continuous data is not
distributed normally. Also, Multivariate Parametric statistics such as ANOVA and 2 sample t-
test, makes it possible to analyses those groups having unequal variances (Lohnes, 2017). One
don’t have to worry concerning groups that have different volume of variability when using
4

STATISTICS 5
parametric statistics. Non-parametric tests offer an advantage since they assess median instead of
mean. The mean for a sample is not the most appropriate measure of central tendency (Lohnes,
2017). Even though one can carry out the analysis of parametric on skewed data, it does not
make it a most appropriate tool. For instance this can be described by use of salaries distribution
In most cases, salaries are right-skewed distribution. Most wages cluster or gather around
the median, the point at which half are below, and half are above. Nevertheless, there exists a
long tail stretching into the ranges of higher salary. The tail pulls the average or means away
from the median value (Martin and Maes, 2019). . Another advantage of the multivariate
nonparametric statistic is that it can analyses ranked and ordinal data, and not affected by outliers
(Martin, 2019). Outliers can be removed legitimately from the dataset in case they are
representing strange conditions. Outliers sometimes are the true part of distributions for an area
of study, and it is not recommended to remove them. Multivariate nonparametric statistics can be
used when the sample is not large or significant to satisfy certain conditions (Martin, 2019). In
some instances, one cannot be sure that the data is following the normal distribution. Small
sample sizes can have little power to produce results that are useful when testing for normality.
5

STATISTICS 6
References
Asamura, H., (2012). Bronchopleural fistulas associated with lung cancer operations. Univariate
and multivariate analysis of risk factors, management, and outcome. The Journal of
thoracic and cardiovascular surgery, 104(5), 1456-1464.
Groppe, D. M., Urbach, T. P. (2018). Mass univariate analysis of event‐related brain
potentials/fields I: A critical tutorial review. Psychophysiology, 48(12), 1711-1725.
Lohnes, P. R. (2017). Multivariate data analysis. J. Wiley.
Martin, N., & Maes, H. (2019). Multivariate analysis. London: Academic press.
Noris, M. J. (2016). SPSS 14.0 guide to data analysis. Upper Saddle River, NJ: Prentice Hall.
Var, I. (2018). Multivariate data analysis. Vectors, 8(2), 125-136.
6

STATISTICS 7
7