** Normalization of raw scores ** Valentim R. Alferes (University of Coimbra, Portugal) ** valferes@fpce.uc.pt * This syntax job does normalization of raw scores and can be used * in a variety of measurement contexts (e.g., psychometrics). * Just a few words on terminology. * Normalization is a kind of nonlinear transformation (area * conversion) of scores, so that the new distribution may have a * normal or bell shape. We can do this by taking the cumulative * proportions of raw scores as probabilities, finding their * corresponding normal deviates, and converting them to normalized * scores with a desired mean and standard deviation. * Standardization is a simple linear transformation of raw scores, * so that the new distribution will have a mean of 1 and a sd of 0. * To find a standard score, just calculate z = (X â€“ mean)/sd. * You can do this in SPSS either by using the menus (DESCRIPTIVESâ€¦/Save * standardized values as variables) or by the simple syntax: * DESCRIPTIVES VARIABLES = VAR1 (ZVAR1). * Note that the standardization doesn't change the shape of the * original distribution. * You can also change the mean and the sd of standard scores * by calculating C = z*sd + mean. * This is also a linear transformation and the resulting scores (C) * are often known as converted scores. * Getting back to normalization, we have illustrated this syntax * with an example from the classic: * Guilford, J. P., & Fruchter, B. (1978). Fundamental statistics * in psychology and education (6th ed.). New York: McGraw-Hill. * In this example (Table 19.2, p. 479), we have 83 raw scores * grouped in 15 classes as well their upper limits and frequencies. * In Table 19.4 (p. 482), you can find all the raw scores for * which Guilford and Fruchter intend to have the normalized * or T Scores with a Mean of 50 and a SD of 10. * After running the syntax, you will have the output with normalized * scores rounded up to nearest integer (TSCORE1), to the nearest .5 * (TSCORE2) and to one decimal place (TSCORE3). Usually, we choose one * of the first two solutions, but it is up to you. DATA LIST FREE /UPPERLIM (F8.0). * Enter raw scores for which you desire normalized scores. * (Table 19.4, column 1, Guilford & Fruchter, 1978, p. 482). BEGIN DATA 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 END DATA. SAVE OUTFILE=OUTF1. DATA LIST LIST /SCORES(A20) UPPERLIM(F8.1) FREQ(F8.0). * Enter classes of observed scores, upper limits, and frequencies. * (Table 19.2, columns 1 to 3, Guilford & Fruchter, 1978, p. 479). BEGIN DATA 130-134 134,5 1 135-139 139,5 0 140-144 144,5 1 145-149 149,5 1 150-154 154,5 2 155-159 159,5 5 160-164 164,5 6 165-169 169,5 5 170-174 174,5 5 175-179 179,5 9 180-184 184,5 11 185-189 189,5 6 190-194 194,5 6 195-199 199,5 6 200-204 204,5 7 205-209 209,5 5 210-214 214,5 5 215-219 219,5 1 220-224 224,5 0 225-229 229,5 1 END DATA. * Enter mean for T Scores (50 in the Guilford & Fruchter example). COMPUTE MEAN = 50. * Enter standard deviation for T Scores (10 in the same example). COMPUTE SD= 10 . COMPUTE DUMMY=1. AGGREGATE/OUTFILE=OUTF2/BREAK=DUMMY/N=SUM(FREQ). MATCH FILES/FILE=*/TABLE=OUTF2/BY DUMMY. CREATE CUM_F=CSUM(FREQ). COMPUTE CUM_PRO=CUM_F/N. COMPUTE Z=IDF.NORMAL(CUM_PRO,0,1). COMPUTE T_SCORE=Z*SD+MEAN. FORMATS CUM_F (F8.0) CUM_PRO (F8.3) T_SCORE (F8.1). * This line produces Table 19.2 (Guilford & Fruchter, 1978, p. 479). LIST SCORES UPPERLIM FREQ CUM_F CUM_PRO T_SCORE. ADD FILES /FILE=*/FILE=OUTF1. REGRESSION/DEPENDENT T_SCORE/METHOD=ENTER UPPERLIM/SAVE PRED. COMPUTE TSCORE1=RND(PRE_1). COMPUTE TSCORE2=RND(2* PRE_1)/2. COMPUTE TSCORE3=RND(PRE_1*10)/10. SEL IF (SYSMIS(FREQ)). COMPUTE RAWSCORE=UPPERLIM. FORMATS RAWSCORE (F8.0) TSCORE1 (F8.0) TSCORE2 (F8.1) TSCORE3 (F8.1). * This line produces Table 19.4 (Guilford & Fruchter, 1978, p. 482). LIST RAWSCORE TSCORE1 TSCORE2 TSCORE3.