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					               The Big Idea
 • More studies are better
     than less studies.
Let me ask a
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
  I am glad you asked that
     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…


                                                        I heard something about
                                                        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
       copy you received earlier.




                                                     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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