Transcript Document

ALL ABOUT ANOVA ANACOVA and other
BEAUTIES
Tristram Jones, Ph. D.
Kaplan University PS512, Unit VIII
Naturally, all studies of beauty must
begin with VISUAL ANALYSIS!
 Visual Analysis
is the
most basic form of data
evaluation, but it has its
obvious shortcomings, the
most obvious being high
subjectivity!
 Interobserver reliability is
often used to reduce
subjectivity.
Visual Analysis often Formative as
well as Summative.
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Summative analysis is collecting and
presenting information that is necessary to
make final statements and judgments about
the value of an activity, usually at the end of
the activity's implementation.
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Formative analysis is the continuous
monitoring of short-term results and
procedures to provide ongoing information
to improve student achievement.
APPLYING VISUAL ANALYSIS
 To
inspect data
points within a
phase—you need
enough to tell
whether perceived
progress represents
the impact of the IV
on the DV. This is
especially important
with exhibited
behavior.
 When
VARIABILITY IN
PERFORMANCE
there is less variability in performance, as
in a flat or consistently trending data path, there
will be less need for multiple data points. When
variability is high, it is necessary to track it
within phases.
 When behavior is individually exhibited, like
the number of time a Tourettes sufferer raps his
forehead with his fist, you will want more data
points! Of course you can use interval reporting
with extremely rapid behaviors!
Level of behavior can also be
analyzed visually.

JUMPS IN THE DATA PATH within a
BEAUTIFUL!
phase are plotted by various
methods
 OBTAINING THE MEAN, the
MEDIAN, or the RANGE.
 And we all know what they are,
right? The "mean" is the "average."
The "median" is the "middle" value
in the list of numbers. The "mode" is
the value that occurs most often. If
no number is repeated, then there is
no mode for the list. The "range" is
just the difference between the
largest and smallest values.
The GRAPHIC chart
And CELERATION CHARTS! 
Celeration=deceleration without the de, get it?
“A measure of the rate of learning over time”
Of course, TRENDS are important, too!
 TRENDS
can be flat,
increasing, or
decreasing. Visual
analysis is possible
when trends are
relatively obvious.
When they are less
obvious and varied, a
split middle line is often
used to plot them!
IN EXCEL you can do this:

Trendlines are used for revealing patterns or trends in your data. We use them in our XY
charts, and they can be plotted on EXCEL:
1. Select the series you wish to use to create the trendline.
2. Go to Chart Tools, select the Layout tab and click Trendlines.
3. You’ll need to specify the type of relationship you are expecting the
data to reveal, your typical choice would be Linear.
4. Right-click the newly created trendline and select Format Trendline.
Use the Line Color, Line Style and Shadow sections to modify the look
of the trendline.
5. Click Close.
Advantages to visual analysis
 Upholds
the principle of
SOCIAL VALIDITY
better than options.
 Allows for almost total
flexibility
 Requires less technical
formulations and “keeps
it real!”
And visual disadvantages:

Not as reliable as
statistical analysis for
the most part!
 Guidelines are not
codified or stringent.
 Studies show that even
as many as 30
observers do not rate
with as much interater
acuity as statistics can
render!
SO WHAT ABOUT
STATISTICS?
Why bother with statistics???
 Because
visual inspection often does not
allow as clear an analysis of whether the
intervention was effective as does stats
analysis.
 Equivocal results can be demonstrated to
be significant or not significant by stats
whereas visual analysis will be
problematic.
 Stats can most efficiently determine a
significant effect in between settings
designs.
So what kind of statistics should we
use?
THEY’RE
ALL
GREAT!!!!
 DESCRIPTIVE
means, medians,
modes, frequencies,
(not used to
demonstrate
significance) and…
 INFERENTIAL
ANOVA
t-tests
Randomization
We’ll start with a t-test! ?
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T-tests are the most basic type of
statistical test! In usual inferential
stats they are used to compare the
means of two groups to test an
hypothesis of difference! Often this
will be an experimental group and
a control group. All you do is find
the averages of the measures of
both groups’ DVs
and then do this:
(it’s really
easy!)
Since this is a probability test, you
start with a NULL HYPOTHESIS
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You take your t score and relate it to a pvalue that expresses the probability that the
null hypothesis is wrong. If you’re lucky, it
will be wrong beyond the likelihood of mere
chance, and you’ll be showing statistical
significance! That’s a good thing!
How the heck can you do that with
single subject research, you ask?
Good question!
You do it by
comparing data
between phases,
and you get your
means by
aggregating the
measures within
each phase, see?
Simple!
What if you have more than two
means you want to compare?

You can do an ANOVA!
It’s easier than doing a
bunch of t-tests! An
ANOVA is an analysis
of variance—invented
by Sir Ronald Fisher
(seen at left). The
ANOVA is designed to
determine whether a
significant
(nonchance) difference
exists among several
sample means.
And then of course there’s
ANCOVA
(analysis of covariance)
a variation on the
analysis of variance
procedure that allows for
the statistical control of
one or more extraneous
(irrelevant) variables. Ex:
when studying effects of
reading programs for
diff. aged children, the
effects of the children's
IQ level can be
statistically controlled
through the use of
ANCOVA.
And while we’re not on the subject,
what are type one and type two
errors?
 TYPE
ONE ERROR: You
incorrectly reject the null
hypothesis!
 TYPE
TWO ERROR:
You incorrectly accept
the null hypothesis
So what’s the latest and the coolest?
QUALITATIVE ANALYSIS, MAN!
QUALITATIVE RESEARCHERS
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Strive to interpret events by finding meaning and
context! Qualitative research is used to gain insight
into people's attitudes, behaviors, value systems,
concerns, motivations, aspirations, culture, politics or
lifestyles. It is essentially postmodern and narrative!
Qualitative Assumptions:
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MULTIPLE REALITIES (ontologies) cause us to
seek the reality of the person of concern
EPISTIMOLOGICALLY the realities of all
concerned in the study are intertwined and must
be understood dynamically.
GENERALIZATION occurs, but is better
understood theoretically than statistically
CAUSALITY can only be understood in terms of
multiple realities in combination and at odds.
PROPER CONTROL for bias results from proper
understanding of the dynamic (AXIOLOGY or
value theory).
Qualitative
Quantitative
The aim is a complete, detailed
description.
The aim is to classify features, count
them, and construct statistical models in
an attempt to explain what is observed.
Researcher may only know roughly in
advance what he/she is looking for.
Researcher knows clearly in advance
what he/she is looking for.
Recommended during earlier phases of
research projects.
Recommended during latter phases of
research projects.
The design emerges as the study unfolds.
All aspects of the study are carefully
designed before data is collected.
Researcher is the data gathering
instrument.
Researcher uses tools, such as
questionnaires or equipment to collect
numerical data.
Data is in the form of words, pictures or
objects.
Data is in the form of numbers and
statistics.
Subjective - individuals interpretation of
events is important ,e.g., uses
participant observation, in-depth
interviews etc.
Objective � seeks precise measurement
& analysis of target concepts, e.g., uses
surveys, questionnaires etc.
Qualitative data is more 'rich', time
consuming, and less able to be
generalized.
Quantitative data is more efficient, able
to test hypotheses, but may miss
contextual detail.
Researcher tends to become subjectively
immersed in the subject matter.
Researcher tends to remain objectively
separated from the subject matter.
So how should we proceed?
Objectively or Postmodernistically?