Statistical Analysis for Education and Psychology Researchers

has the effect of moving both high and low percentage scores towards the middle of a
distribution.
The original distribution for the variable CORRD—percentage correct score of
syntactic awareness (difficult reading passage) in Figure 5.9 had a positive skew. The
variable CORRE—percentage correct score of syntactic awareness (easy reading
passage) shown in Figure 5.10 had a negative skew. Both of these variables were
transformed using the modified arcsine transformation using the following SAS code:

data a;

infile 'a:amanda.dat' lrec1= 72;

input id 1–3 corre 57–58 vocab 67–69 corrd 70–72

label corrd='% CORRECT SYNTACTIC SCORE (difficult)'

vocab='VOCABULARY SCORE (RAW SCORE)'

corre='% CORRECT SYNTACTIC SCORE (easy)'

newd='ARCSINE % CORRECT (difficult)'

newe='ARCSINE % CORRECT (easy)';

data a; set a;

newd=round(2 *(arsin (sqrt (corrd/100))), .001);

newe=round (2*(arsin (sqrt (corre/100))), .001);

Shown in Figures 5.13 and 5.14 are histograms and normal probability plots for the two
transformed variables NEWD arcsine transformed percentage correct difficult reading
passage (original +ve skew), and NEWE arcsine transformed percentage correct easy
reading passage (original −ve skew).

Statistical analysis for education and psychology researchers 154