# meta

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```					               The Big Idea
• More studies are better
than less studies.
question.

meta.ppt
Northwest CLD

Dave told us that some research
studies are more powerful than
others. I was wondering if there
is any procedure in education
that examines collections of
studies?

meta.ppt
question. There is a
procedure for ‘aggregating*’
data from a variety of
Meta-Analysis
studies. It is called meta-
analysis.

*Aggregate: To gather into a mass or whole.

meta.ppt
In meta-analysis, a researcher examines many studies on a particular
strategy and derives a numerical indicator of the relative effectiveness
of the strategy, averaged across all studies. This indicator is called an
2
effect size (ES).
Such an analysis of research not only provides a numerical indicator of
the relative effect of a particular intervention, but the effect size also
allows comparison with other approaches used in special education or
related services.

Thanks NWCLD presenters. We ARE getting
a lot of great evidence based practices from
a research-summary procedure called
meta-analysis. Check out what Steve
1      Forness and his buddies wrote in Teaching
Exceptional Children…

this ‘ES’ in another special
education class. Could you
review how this works.
3
meta.ppt
I’d love to. Let’s begin with what you know
about the ‘normal bell-shaped curve since it is
at the heart of summarizing studies.
First, what does the curve look like?

meta.ppt
I hope I get the right answer: “It
looks like a bell.”

meta.ppt
Let’s talk about a normal distribution – the
bell-shaped curve. The peak of the
distribution, which occurs at the ‘mean’ (the
average of all the numbers)..

meta.ppt
Cite examples. Math performance, IQ, shoe size.
Each side of the curve has inflection points
where the curve makes shifts in direction.

meta.ppt
Each side of the curve has inflection points
where the curve makes shifts in direction.

meta.ppt
Inflection points occur at very specific
places.

Mean

meta.ppt
The first inflection point to the right of the
mean occurs one ‘standard deviation’
(SD) above the mean.

1
SD

Mean Mean
+
1 SD
Below                    Above
meta.ppt
The second inflection point to the right of
the mean occurs two standard deviations
above the mean.

Mean Mean Mean
+    +
1 SD 2 SD
Below                    Above
meta.ppt
Inflection points below the mean also
occur at one and two standard deviations
below the mean.

Mean Mean Mean Mean Mean
-    -         +    +
2 SD 1 SD      1 SD 2 SD
Below                     Above
meta.ppt
Because all points are in reference to the
mean, we will indicate the differences with
the mean implied.

-2   -1 Mean +1    +2
SD   SD      SD    SD

Below                           Above
meta.ppt
One of the most useful aspects of the
normal curve is that there are specific
areas under each part of the curve.

-2   -1 Mean +1    +2
SD   SD      SD    SD

meta.ppt
As we can see, 50% of the data (Math
scores, IQs, shoe sizes) fall on each side
of the mean.
50%                 50%

-2     -1 Mean +1      +2
SD     SD      SD      SD

meta.ppt
Of this 50%, 34% falls between the mean
and one standard deviation above and
one standard deviation below the mean.
50%                 50%

34%   34%

-2     -1 Mean +1      +2
SD     SD      SD      SD

Below                               Above
meta.ppt
The area between one and two standard
deviations from the mean holds 14% of
the distribution.
50%                 50%

34%   34%

14%                 14%

-2     -1 Mean +1          +2
SD     SD      SD          SD

Below                                   Above
meta.ppt
Since the total area on each side must
total 50%, we know there is 2% of the
distribution beyond two standard
deviations (SD) in each direction.
50%                 50%

34%   34%

14%                 14%
2%                               2%

-2     -1 Mean +1          +2
SD     SD      SD          SD

Below                                   Above
meta.ppt
Generally, the ‘average range’ is
considered between -1 and +1 standard
deviations (SD).

50%                     50%

34% 34%
Average Range

14%                     14%
2%                                  2%

-2        -1 Mean +1              +2
SD        SD      SD              SD

meta.ppt
Here I am back at Diamondhead. Now
that you can see characteristics of the
bell-shaped curve, please take out the

How about now. Let’s mix a break with
Thanks for the handout, Dave.                          a job. Tell your neighbor what
How soon can we break?                              percentile ranks begin and end the
meta.ppt    ‘average range.’ Discovery learning.
The Curve

meta.ppt
Note: Other Bell-shaped Curves

meta.ppt
Back to Meta-Analysis
Recall the description of meta-analysis.
•   In meta-analysis, a researcher examines many studies
on a particular strategy and derives a numerical
A              indicator of the relative effectiveness of the strategy,
averaged across all studies. This indicator is called an
effect size (ES).
Such an analysis of research not only provides a
numerical indicator of the relative effect of a
particular intervention, but the effect size (ES) also
allows comparison with other approaches used in
special education or related services.

B or C       •   Suppose we had an intervention like giving
vitamins (A) that was being compared to either
another intervention (B) like giving candy, or no
treatment (C).
•   Suppose that the groups who received vitamins
(A) and the groups who received (B) “candy” or
(C) “nothing” performed equally at the start on
a math test.

meta.ppt
Further, suppose that we monitored the progress of both groups
over time, and the treatments were provided with fidelity.
A
Math Scores

The two
collections
B or C                     of groups
Math Scores

are equal.

+1           +2             +3
Now
Month        Month          Month

Time
meta.ppt
Further, suppose that we monitored the progress of both groups
over time, and the treatments were provided with fidelity.
A

Math Scores
After one
month, we
B or C       see this
Math Scores

pattern.

+1          +2           +3
Now
Month       Month        Month

Time
meta.ppt
Further, suppose that we monitored the progress of both groups
over time, and the treatments were provided with fidelity.
A

Math Scores
After two
months, we
B or C          see this

Math Scores
pattern.

+1                         +2              +3
Now
Month                      Month           Month

Time
meta.ppt
Further, suppose that we monitored the progress of both groups
over time, and the treatments were provided with fidelity.
A

Math Scores
After three
months, we                                      B or C
see this

Math Scores
pattern.

+1                 +2                             +3
Now
Month              Month                          Month

Time
meta.ppt
If this was the result, which method would you choose to use in
your classroom, A, B, or C?
A

Math Scores
B or C

Math Scores

+1            +2                            +3
Now           Mont          Mont                          Mont
h             h                             h
Time
meta.ppt
By drawing a line along the mean (0 SD) we can see that method
A’s mean is actually 1 SD higher than the B and C.
A

Math Scores
B or C

Math Scores

+1             +2                             +3
Now
Month          Month                          Month

Time
meta.ppt
By drawing a line along the mean (0 SD) we can see that method
A’s mean is actually 1 SD higher than the B and C.
A

Math Scores
B or C

Math Scores

+1            +2                            +3
Now           Mont          Mont                          Mont
h             h                             h
Time
meta.ppt
Effect size (ES) is based on aggregated data
A

Math Scores
When several studies create the                                B or C

Math Scores
pattern we see here, we are
more confident that the results
are trustworthy (valid).

+1                +2                             +3
Now
Month             Month                          Month

Time
meta.ppt
Effect size (ES) is based on aggregated data
A

Math Scores
Since the performance of group                                    B or C

Math Scores
A is +1 SD beyond group B or C,
we say that method A (giving
vitamins) has an effect size of +1.

+1                  +2                             +3
Now
Month               Month                          Month

Time
meta.ppt
Is it always an even
number like 1, 2, 3?

The answer is ‘no.’ Effect sizes can be fractions
(e.g., ES = +.5 (half an SD) or ES = +.35). It could
also be negative (ES = -.6). Generally ESs that
are worth paying attention to as a teacher are
+.40 or higher. The highest EF that I know is
1.62 for using mnemonics as an instructional
tool. Any questions from the class?

meta.ppt
Summary
• Meta-analysis aggregates data from several
studies that deal with a particular treatment.
• The number that describes how well the
treatment works is called effect size (ES).
• ESs can be positive (+) or negative (-).
• Generally the bigger the ES for the treatment,
the more you can take it to the bank.
•   Distribute Forness’ article on meta-analysis
•   Display some sources of information that are based on meta-analysis.

meta.ppt

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