Time Series Analysis
Although (according to your instructor),
visual graphs are seldom sufficient in
analyzing single-case data, a time series
analysis should ALWAYS begin with visual
inspection of the data.
Visual analysis is typically based on three
features.
1.level,
2.trend,
3.variability
You can quantify the level, by simply
calculating the mean score for each phase.
For example, if the sample data in the
single-case statistical analysis program
represented baseline, treatment, and
follow-up phases, the levels would be:
Baseline = 4.12
Treatment = 8.00
Follow-up = 6.37
http://www.unlv.edu/faculty/pjones/singlecase/scsastat.htm
The trend in the data is evaluated by two
features:
1. slope (going up or going down),
2. magnitude (how rapidly going up or
going down)
You can quantify the variability, by simply
calculating the standard deviation of scores
within each phase.
For example, if the sample data in the
single-case statistical analysis program
represented baseline, treatment, and
follow-up phases, the variability would be:
Baseline = 1.246
Treatment = .925
Follow-up = 1.597
Of the three features: level, trend, and
variability, determining level and variability
can be readily seen on the graph and
quantitative descriptors are easily
calculated.
It is often also not difficult to assess the
slope of a trend with visual analysis alone.
The complication comes with determining
the magnitude of the trend.
There are many statistical techniques
available to assist in evaluating the
magnitude of a trend but by far the easiest
to use is the C statistic featured in the
single case statistical analysis program.
There are few assumptions for its use
regarding the form of the data (for example,
test scores, teacher or self ratings,
absentee counts, etc.) can be used and it
fits easily into a clinical practice.
There will, however, be times when visual
analysis may be your only choice.
Some examples would be:
1. When you were unable to obtain the
minimum of 8 data points per phase.
2. When you were unable to obtain a stable
baseline.
There is also a nonparametric time series
analysis procedure based on the chi square
statistic.
We'll explore that option later.
Because the C statistic does not require a
special form of data, it will usually be a
better choice for time series analysis.
Time Series Analysis with the
C Statistic
All investigations do (or should) consider
whether there was significant change after
treatment is introduced.
The answer requires definition of the term
significant.
At least three types of significance warrant
consideration:
1.practical,
2.theoretical,
3.statistical
Practical significance deals whether there
was sufficient change to make a difference
in a person's life;
Theoretical significance relates to whether
the change came in a form consistent with
a particular theory.
Statistical significance is about whether the
observed change would be likely to have
occurred by chance alone.
In actual practice settings, the most useful
tool for the clinical scientist to assess
statistical significance in single-case design
is often a simplified form of time series
analysis based on Young's C statistic.
The C statistic is easily computed, makes
few assumptions about the form of the data,
and fits readily into the data gathering
process in clinical practice.
The number of required data points for use
of the C statistic is significantly less than
the number needed for more sophisticated
time series analysis tools.
Time series analysis with the C statistic
identifies whether a trend, defined as any
systematic departure from random
variation, is evident in the set of data.
The null hypothesis for the C statistic is that
there is no trend.
For example, there is no indication of
significant departure from randomness in
the sequence: 5-5-5-5-4-5-4-5. The C
statistic would be evaluated as not
statistically significant; the null hypothesis
would not be rejected.
In contrast, the sequence: 1-2-3-4-5-6-7-8
is a departure from random fluctuation; the
C statistic is evaluated as statistically
significant; the null hypothesis is rejected.
The formula to calculate the C statistic is:
n-1
S (Xi - Xi+1) 2
i=1
________________
C=1n
2 S (Xi - Mx) 2
i=1
but, I think you would prefer to go here:
http://www.unlv.edu/faculty/pjones/singlecase/scsastat.htm
The more sophisticated forms of time series
analysis require 50 to 100 data points in
each phase.
But, the C statistic can be used when there
are at least 8 measures in each phase.
The logic of the C statistic with actual
practice data is to continue baseline
measures until there is no evident random
variation, until in effect the baseline is
horizontally stable with no evident trend.
Then, treatment begins; measurement
continues, and the treatment data are
appended to the baseline data to assess
whether a trend, a departure from random
variation, becomes evident.
With the time series analysis, you can
investigate:
1.whether a trend was evident even before
treatment began,
2.whether a trend is evident within the
treatment itself,
3.whether the addition of the treatment
created change greater than would be
expected from random variation, and
4.what happens after the treatment stops.
Baseline:
C = .206, z = .668, p > .05.
Treatment:
C = .215, z = .697, p > .05.
Follow-up:
C = .009, z = .029, p > .05.
B + T:
C = .540, z = 2.306, p < .05.
B + F:
C = .509, z = 2.174, p < .05.
T + F:
C = .045, z = .192, p > .05.
What do these results mean?
Are they a desired outcome?