* Encoding: UTF-8.
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*** T Test: Measures of Effect
Size and Nonoverlap, and Observed Power
*** Valentim R. Alferes (University of Coimbra, Portugal)
*** valferes@fpce.uc.pt
**
** This syntax does a T Test for
two independent groups and calculates
** measures of effect size,
measures of nonoverlap, and observed power.
**
** The output is divided into
four parts:
**
** PART I - SPSS T Test standard
output:
** - Descriptive statistics;
** - Levene's Test for Equality
of Variances
** - T-Test for Equality of Means
(Equal variances assumed
** and not assumed);
** - Confidence Interval of the
Difference.
**
** PART II - Measures of effect
size:
** - Cohen's d (D);
** - Hedges Correction (D_H);
** - r point biserial (R);
** - Squared r point biserial (R2);
** - Binomial Effect Size Display
(BESD_LO and BESD_UP).
**
** PART III - Measures of
nonoverlap (Cohen, 1988, pp. 21-23):
** - U1 (percent of nonoverlap
between the two distributions);
** - U2 (the highest percent in
Group 1 that exceds the same lowest
** percent in Group 2);
** - U3 (percentile standing =
percentile of the Group 2 distribution
** corresponding to the 50th percentile of
Group 1 distribution).
**
** PART IV - Observed power (for
algorithm, see Borenstein et al., 2001):
** - N1, N2, Harmonic N (N_HARM);
** - Alfa (ALFA) and observed
power (OPOWER).
**
** The user has two methods:
Analysing raw data or reproducing the SPSS
** T Test standard output from
summary statistics in published articles.
************************************************************************.
************************************************************************
** METHOD 2: Reproducing the SPSS
T Test standard output from
** summary statistics in
published articles.
* Enter, row by row, N, Mean, and
SD for Groups 1 and 2.
DATA LIST LIST /N(F8.0) M(F8.2)
SD(F8.2).
BEGIN DATA
17 7.46
1.98
15 5.34
2.14
END DATA.
COMPUTE IV=$CASENUM.
LOOP ID=1 TO N.
XSAVE OUTFILE='%temp%\XOUT1'.
END LOOP.
EXECUTE.
GET FILE='%temp%\XOUT1'.
COMPUTE DV=M.
COMPUTE K=SQR((SD**2*(N-1))/2).
IF (ID=1) DV=M+K.
IF (ID=2) DV=M-K.
EXECUTE.
* Enter confidence level for
confidence interval of difference
* (by default, confidence level =
.95).
T-TEST GROUPS=IV(1 2)/VARIABLES=DV/CRITERIA=CIN(.95).
T-Test
|
Group
Statistics |
|||||
|
|
IV |
N |
Mean |
Std.
Deviation |
Std. Error
Mean |
|
DV |
1 |
17 |
7.46 |
1.980 |
.480 |
|
2 |
15 |
5.34 |
2.140 |
.553 |
|
|
Independent
Samples Test |
||||||||||
|
|
Levene's
Test for Equality of Variances |
t-test for
Equality of Means |
||||||||
|
F |
Sig. |
t |
df |
Sig.
(2-tailed) |
Mean
Difference |
Std. Error
Difference |
95%
Confidence Interval of the Difference |
|||
|
Lower |
Upper |
|||||||||
|
DV |
Equal variances assumed |
.020 |
.889 |
2.910 |
30 |
.007 |
2.120 |
.728 |
.632 |
3.608 |
|
Equal variances not assumed |
|
|
2.896 |
28.773 |
.007 |
2.120 |
.732 |
.622 |
3.618 |
|
AGGREGATE/OUTFILE=*/BREAK=IV/N2=MEAN(N)/M2=MEAN(M)/DP2=MEAN(SD).
COMPUTE N1=LAG(N2,1).
COMPUTE M1=LAG(M2,1).
COMPUTE DP1=LAG(DP2,1).
EXECUTE.
SELECT IF(IV=2).
EXECUTE.
* Enter alfa for calculating
observed power (by default, ALFA = 0.05).
COMPUTE ALFA = 0.05.
COMPUTE SP2=(((N1-1)*(DP1**2))+((N2-1)*(DP2**2)))/(N1+N2-2).
COMPUTE T=(M1-M2)/SQR(SP2*((1/N1)+(1/N2))).
COMPUTE GL=N1+N2-2.
COMPUTE R=T/SQR((T**2)+GL).
COMPUTE R2=R**2.
COMPUTE D=T*SQR((1/N1)+(1/N2)).
COMPUTE D_H=D*(1-(3/(4*(N1+N2)-9))).
COMPUTE BESD_LO=.50-(R/2).
COMPUTE BESD_UP=.50+(R/2).
COMPUTE U3=CDF.NORMAL(D,0,1)*100.
COMPUTE U2=CDF.NORMAL((D/2),0,1)*100.
COMPUTE U2X=CDF.NORMAL((ABS(D)/2),0,1).
COMPUTE U1=(2*U2X-1)/U2X*100.
COMPUTE N_HARM=(2*N1*N2)/(N1+N2).
COMPUTE NCP=ABS((D*SQR(N_HARM))/SQR(2)).
COMPUTE T_ALPHA=IDF.T(1-ALFA/2,GL).
COMPUTE POWER1=1-NCDF.T(T_ALPHA,GL,NCP).
COMPUTE
POWER2=1-NCDF.T(T_ALPHA,GL,-NCP).
COMPUTE OPOWER=POWER1+POWER2.
FORMATS ALL(F8.4) N1 N2(F8.0) U1 U2 U3(F8.1).
SUMMARIZE/TABLES=D D_H R R2
BESD_LO BESD_UP/FORMAT=NOLIST TOTAL
/TITLE='PART II - Measures of Effect
Size'/CELLS=FIRST.
|
PART II -
Measures of Effect Size |
|||||
|
First |
|||||
|
D |
D_H |
R |
R2 |
BESD_LO |
BESD_UP |
|
1.0310 |
1.0050 |
.4692 |
.2202 |
.2654 |
.7346 |
|
PART III -
Measures of Nonoverlap |
||
|
First |
||
|
U1 |
U2 |
U3 |
|
56.5 |
69.7 |
84.9 |
|
PART IV -
Observed Power |
||||
|
First |
||||
|
N1 |
N2 |
N_HARM |
ALFA |
OPOWER |
|
17 |
15 |
15.9375 |
.0500 |
.8041 |
************************************************************************
** Borenstein, M., Rothstein, H.,
& Cohen, J. (2001). SamplePower 2.0
** [Computer Manual]. Chicago: SPSS Inc.
** Cohen, J. (1988). Statistical
power analysis for the behavioral
** sciences (2nd ed.). Hillsdale, NJ: Lawrence
Erbaum.
************************************************************************.