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advanced_statistics.pptxAdvanced Statistics
Unit 5
There are several related topics in this unit…
Types of Variables in Analysis
Univariate and Multivariate
Statistics Overview
Univariate Statistics
Multivariate Statistics
Independent Variables (IV)
This is the variable thought to influence or cause a change in the value of another variable.
For example, if you do not get enough sleep you will experience fatigue and drowsiness during work. Lack of sleep, then, is the independent variable thought to affect fatigue and drowsiness.
Dependent Variables (DV)
This is the variable that is thought to be changed or affected by another (independent) variable. Said another way, the value of the dependent variable is responsive to or determined by changes in the independent variable.
In the example above fatigue and drowsiness are the variables affected. We will experience more fatigue and drowsiness if we have less sleep.
Confounding Variables
This is a variable that confounds, or confuses, the relationship between the independent and dependent variables. Or we can think of it this way…something other than the independent variable is accounting for changes in the dependent variable.
For example, how engaging and interesting a meeting is (vs. boring) will affect whether or not you feel fatigue and drowsiness during the meeting. Thus, lack of sleep is not accounting for fatigue or drowsiness. Rather the nature of the meeting or a combination of lack of sleep and the nature of the meeting are causing fatigue and drowsiness.
Types of Variables in Analysis Statistics
Univariate and Multivariate Statistics Overview Statistics
We differentiate statistics as univariate or multivariate depending on the
number of dependent variables involved in the statistical analysis.
When there is a single dependent variable we use a univariate statistic.
When there is more than one dependent variable we use a multivariate statistic.
We also need to consider how both the dependent and independent variables
were measured in order to determine what statistic is appropriate. Remember
that we can measure numerically (interval and ratio level of measurement) or
we can measure simply by differentiating between types (nominal level of
measurement).
Univariate Statistics Statistics
There are two groups of univariate statistics we commonly use
when we have a single numerical dependent variable.
The first set are appropriate when we have a nominal/categorical
independent variable. This would include statistics that compare
categories or groups like men/women, highly
satisfied/dissatisfied employees, youth/seniors, etc.
These include…
t-test
ANOVA
ANCOVA
and Factorial Analysis of Variance
Univariate Statistics Statistics
We use the following statistics when we have a single numerical dependent
variable and we want to make…
t-test a simple comparison between two groups
ANOVA (a one-way analysis of variance)
a comparison between three or more groups
ANCOVA a comparison between three or more groups
while controlling for a confounding variable
In all these cases we have only a single independent variable, which may be
comprised of two, three, or more groups. However, when we have more than
one independent variable we need to use a factorial analysis of variance.
Factorial Analysis of Variance Statistics
A factorial analysis of variance involves a comparison of scores
on a single, numerical dependent variable — the value of which
is determined by several nominal or categorical independent
variables.
Factorial analyses of variance are prefaced with a numerical
string or statement that indicates:
the number of independent variables (designated by the total
number of numbers in the string, not the values of the numbers)
and the number of levels of each independent variable (designated by the actual values of each number in the string)
Factorial Analysis of Variance Statistics
So for example, a 3x2x3 factorial analysis of variance has…
3 independent variables,
the first with 3 levels,
the second with 2 levels,
and the third with 3 levels.
Similarly, a 4x2 factorial analysis of variance has…
two independent variables,
the first with four levels
and the second with two.
This could be a comparison that examines
student achievement (A, B, C, and D students)
and sex (male, female).
Univariate Statistics Statistics
When we attempt to determine if variables are related and both the
independent and dependent variables have been measured numerically we use
one of the following univariate statistics…
Correlation simply assessing the relationship between
independent and dependent variables
Regression assessing the ability of the independent variable to predict the value of the dependent variable
Multiple assessing the predictive ability of several
Regression independent variables on a single dependent variable
Univariate Statistics Statistics
The chart below helps to clarify how the common univariate statistical procedures relate
and differ from one another. Being univariate all the statistics below have a single dependent
variable that is numerical (measured at the interval or ratio level of measurement).
t-test (2 groups) Correlation (relating)
ANOVA (3+ groups) Regression (predicting)
ANCOVA (while controlling) Multiple Regression
Factorial Analysis (with more than 1 IV)
of Variance (with more than 1 IV)
The family of statistics in the left-hand column have nominal/categorical independent variables
(abbreviated in the chart as IV) and therefore involve comparisons between groups.
The family of statistics in the right-hand column have numerical independent variables and thus
involve assessing relationships between variables (versus groups).
Multivariate Statistics Statistics
Multivariate statistics are appropriate when we have more than one
dependent variable. It is helpful to think of them as an extension of the two
previous groups discussed.
When we compare groups and we have more than one dependent variable we
move from an ANOVA to a…
MANOVA compares groups in terms of more than one
dependent variable
Or from an ANCOVA to a…
MANCOVA compares groups in terms of more than one dependent variable while controlling for a confounding variable
Multivariate Statistics Statistics
Similarly, we can move from a multiple regression (which
considers how several numerical independent variables predict a
single numerical dependent variable) to a…
Canonical examines the relationship between multiple
Correlation independent and multiple dependent variables all of which are numerical
or, said another way, examines the relationship between a group of
numerical independent and a group of
numerical dependent variables
Multivariate Statistics Statistics
The chart below serves to clarify how the common multivariate statistical procedures
relate and differ from one another. As multivariate statistics all of those listed below
have multiple dependent variables (abbreviated as DV in the chart) that are numerical
in nature.
MANOVA (more than 1 DV) Canonical Correlation
MANCOVA (while controlling) (comparing two sets of variables)
As with the univariate families of statistics, the family of statistics in the left-hand
column have nominal/categorical independent variables and therefore involve
comparisons between groups.
The family of statistics in the right-hand column have numerical independent variables
and thus involve assessing relationships between variables (versus groups).
Uni- and Multivariate Statistics Statistics
Finally, the chart below puts both the univariate and multivariate statistics together.
You can see then how the univariate statistics link to the multivariate statistics.
Univariate Statistics (Single Dependent Variable)
t-test (2 groups) Correlation (relating)
ANOVA (3+ groups) Regression (predicting)
ANCOVA (while controlling) Multiple Regression
Factorial Analysis (with more than 1 IV)
of Variance (with more than 1 IV)
Multivariate Statistics (More Than One Dependent Variable)
MANOVA (more than 1 DV) Canonical Correlation
MANCOVA (while controlling) (comparing two sets of variables)
