Re: regression to the mean

[Paul R Swank]

But if you group the subjects on the basis of their pretest scores, the lowest group gains 23.1 points while the highest group only gains 19.2. Looking at the graph, I note that the person who scored 34 on the pretest did not increase as much as I might expect while the person who scored 10 increased more than I might expect. The best fit line is obviously flatter than the best fit l;ione for the pre and post tests.

At 09:29 AM 1/17/01 -0500, you wrote:
>
>here is an example to ponder ...
>let's say that you are an instructor in a course and have decided to
>administer a 100 point final exam ... the very first day of class ... and
>then some alternate form of that 100 item test the very last day of class
>... in general, to see what people "gain"
>
>now, scores are pretty low on the first day ... and since kids learn alot
>... the scores went up alot by the end of the course .... have a look at
>these data
>=========
>
>
> - *
> post - * *
> - *
> - 2 *
> 80+ * 2 *
> - 2 * * *
> - * * *
> - * *
> - * *
> 60+
> - * *
> - * * *
> -
> - *
> 40+ *
> -
> -
> ----+---------+---------+---------+---------+---------+--pre
> 10.0 15.0 20.0 25.0 30.0 35.0
>
>positive r between pre and post ... makes sense
>
>MTB > desc c16 c17
>
>Descriptive Statistics: pre, post
>
>
>Variable N Mean Median TrMean StDev SE Mean
>pre 30 25.200 25.500 25.615 5.006 0.914
>post 30 71.53 76.50 72.23 14.30 2.61
>
>Variable Minimum Maximum Q1 Q3
>pre 11.000 34.000 22.000 29.000
>post 39.00 95.00 61.50 81.50
>
>MTB > corr c16 c17
>
>Correlations: pre, post
>
>
>Pearson correlation of pre and post = 0.604
>P-Value = 0.000
>
>now, what if you look at the gain ... from pre to post ... then plot the
>pre scores against the gain
>
>MTB > plot c30 c16
>
>Plot
>
>
> gain -
> - *
> - *
> 60+ *
> - 2 * 2 * * *
> - * * *
> - * * * *
> - * * *
> 40+ * * * *
> -
> - * *
> - *
> - *
> 20+
> -
> - *
> -
> ----+---------+---------+---------+---------+---------+--pre
> 10.0 15.0 20.0 25.0 30.0 35.0
>
>MTB > corr c16 c30
>
>Correlations: pre, gain
>
>
>Pearson correlation of pre and gain = 0.303
>P-Value = 0.104
>
>the correlation between pre and gain is POSITIVE .3 ... not high of course
>but, it is POSITIVE
>this means that the ones who scored highest on the pre GAINED THE MOST
>the ones who scored lowest on the pre ... GAINED THE LEAST
>
>
>
>MTB > sort c16(c30), c31(c32);
>SUBC> desc c16.
>MTB > prin c31 c32
>
>if i sort the pre from high to low and then list the gain ... we can see
>easily that the high pres gain more in fact, the top 6 gain about 51 points
>on average ... while the low 6 gain only about 35 points on average
>
> Row sortpre samegain
>
> 1 34 53
> 2 31 54
> 3 31 46
> 4 30 53
> 5 30 47
> 6 30 55
> 7 29 41
> 8 29 61
> 9 28 67
> 10 28 49
> 11 28 29
> 12 28 62
> 13 27 12
> 14 27 41
> 15 26 54
> 16 25 54
> 17 25 54
> 18 24 57
> 19 24 46
> 20 24 44
> 21 24 41
> 22 22 54
> 23 22 50
> 24 22 55
> 25 22 31
> 26 21 42
> 27 20 32
> 28 20 24
> 29 14 39
> 30 11 43
>
>if you are thinking about regression to the mean in the typical way ... how
>come this "regression reversal" seems to have occured?
>
>
>
>
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------------------------------------
Paul R. Swank, PhD.
Professor & Advanced Quantitative Methodologist
UT-Houston School of Nursing
Center for Nursing Research
Phone (713)500-2031
Fax (713) 500-2033

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