1 STANDARD ERRORS ON DIFFERENCES
1 STANDARD ERRORS ON DIFFERENCES. How to compute the standard error of the difference between : – Two countries; – An OECD country and the OECD total.
Jan 12, 2016
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1
STANDARD ERRORS ON DIFFERENCES
• How to compute the standard error of the difference between :– Two countries;– An OECD country and the OECD total or the
OECD average– A partner country and the OECD total or the
OECD average– Two groups of students (e.g. boys versus girls,
natives versus non natives) within countries?
Standard Errors on Differences
Standard Errors on Differences
)ˆ,ˆcov(2
),cov(2
212
)ˆ(2
)ˆ(2
)ˆˆ(
2)(
2)(
2)(
2121
BABABA
School ID School mean Boys mean Girls mean
01 400 350 450
02 450 410 490
03 500 470 530
04 550 530 570
05 600 590 610
Mean 500 470 530
06 500 470 530
Mean if 01 replaced by 06 520 494 546
Mean if 05 replaced by 06 480 446 514
• The expected value of the covariance between the two estimates:– should be equal to 0 if the two samples are
independent, i.e.• Two countries• A partner country and the OECD Total or OECD
Average• Two explicit strata within a country
– should be different from 0 if the two samples are not independent
• Two groups within a country if the group variable was not used as explicit stratification variable
• An OECD country and the OECD Total or OECD Average
Standard Errors on Differences
• How important is this covariance?– Country correlation between school performance
for boys and school performance for girls, and country intraclass correlation
Standard Errors on Differences
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
0.2
0.4
0.6
0.8
1
1.2
Rho in Reading
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Standard Errors on Differences
Standard Errors on Differences
Standard Errors on Differences
Standard Errors on Differences
Standard Errors on Differences
Standard Errors on Differences
• These two macros can also be used to compute the SE on the difference for STD, Variance, percentiles (sas) , quartiles…
Differences in STD : reading
Study Nber NS(%) NNS(%) PNS(%) PS(%) VR
PIRLS01
COMBINED SCALE 36 28 56 17 1.09
INFO 36 22 64 14 1.08
LIT 36 22 58 19 1.08
PIRLS06
COMBINED SCALE 45 24 67 9 1.08
INFO 45 22 69 9 1.08
LIT 45 27 60 13 1.08
AVERAGE PIRLS 24.2% 62.3% 13.5% 0.0%
PISA00
COMBINED SCALE 42 62 33 5 1.16
RETRIEVE 42 64 33 2 1.17
INTERPRET 42 60 36 5 1.14
EVALUATE 42 60 38 2 1.16
PISA03
COMBINED SCALE 41 71 29 1.20
PISA06
COMBINED SCALE 56 75 23 2 1.20
PISA09
COMBINED SCALE 65 85 11 5 1.18
RETRIEVE 65 85 11 5 1.22
INTERPRET 65 69 26 5 1.15
EVALUATE 65 75 22 2 2 1.17
DIGITAL 19 58 37 5 1.08
AVERAGE PISA 69.3% 27.1% 3.4% 0.2%
AVERAGE 53.4% 39.5% 7.0% 0.1% 1.14
Study N P5 P10 MEAN P90 P95
PIRLS01 COMBINED SCALE 36 0.34 0.33 0.25 0.20 0.20
INFO 36 0.29 0.28 0.22 0.17 0.16LIT 36 0.34 0.34 0.27 0.23 0.23
PIRLS06 COMBINED SCALE 45 0.28 0.27 0.21 0.16 0.15
INFO 45 0.25 0.25 0.19 0.14 0.12LIT 45 0.28 0.28 0.21 0.17 0.16
AVERAGE PIRLS 0.30 0.29 0.22 0.18 0.17
PISA00 COMBINED SCALE 42 0.47 0.46 0.35 0.24 0.22
RETRIEVE 42 0.38 0.36 0.25 0.14 0.12INTERPRET 42 0.41 0.41 0.32 0.22 0.20
EVALUATE 42 0.58 0.57 0.46 0.35 0.33PISA03
COMBINED SCALE 41 0.52 0.50 0.36 0.25 0.23PISA06
COMBINED SCALE 56 0.56 0.54 0.42 0.30 0.27PISA09
COMBINED SCALE 65 0.56 0.56 0.45 0.33 0.31RETRIEVE 65 0.56 0.54 0.40 0.27 0.25
INTERPRET 65 0.51 0.50 0.42 0.31 0.29EVALUATE 65 0.59 0.59 0.48 0.37 0.35
DIGITAL 19 0.43 0.42 0.32 0.23 0.22
AVERAGE PISA 0.51 0.50 0.39 0.27 0.25
Differences in STD : reading
STUDY N NE NN PN PO
Primary IEA TIMSS95 P1 LG 24 25% 67% 8% 0%
TIMSS95 P1 UG 26 27% 65% 8% 0%
TIMSS03 P1 29 41% 48% 10% 0%
TIMSS07 P1 44 39% 55% 7% 0%
OECD - - - - - -
Total math primary 123 34% 58% 8% 0%
Secondary IEA TIMSS95 P2 LG 39 26% 67% 8% 0%
TIMSS95 P2 UG 41 29% 46% 24% 0%
TIMSS99 P2 38 34% 58% 5% 3%
TIMSS03 p2 51 39% 55% 6% 0%
TIMSS07 p2 57 49% 39% 12% 0%
OECD PISA00 42 40% 52% 7% 0%
PISA03 41 66% 27% 7% 0%
PISA06 57 60% 32% 9% 0%
PISA09 65 60% 34% 6% 0%
Total math secondary 431 46% 44% 9% 0%
Differences in STD: mathematics
STUDY N VR P5 P10 MEAN P90 P95 P95-P5
Primary IEA TIMSS95 P1 LG 24 1,10 0,00 -0,01 -0,08 -0,14 -0,16 -0,15
TIMSS95 P1 UG 26 1,10 0,06 0,04 -0,03 -0,08 -0,10 -0,15
TIMSS03 P1 29 1,10 0,07 0,05 -0,02 -0,09 -0,10 -0,17
TIMSS07 P1 44 1,12 0,09 0,06 -0,02 -0,09 -0,10 -0,19
OECD - - - - - - - - -
Mean math primary 123 1,11 0,05 0,03 -0,04 -0,10 -0,11 -0,17
Secondary IEA TIMSS95 P2 LG 39 1,10 0,00 -0,01 -0,07 -0,14 -0,16 -0,16
TIMSS95 P2 UG 41 1,12 0,01 -0,01 -0,08 -0,15 -0,15 -0,16
TIMSS99 P2 38 1,12 0,03 0,01 -0,05 -0,12 -0,13 -0,16
TIMSS03 p2 51 1,11 0,07 0,07 0,00 -0,07 -0,09 -0,16
TIMSS07 p2 57 1,14 0,13 0,12 0,03 -0,05 -0,07 -0,20
OECD PISA00 42 1,12 -0,01 -0,02 -0,09 -0,17 -0,19 -0,19
PISA03 41 1,17 0,01 -0,01 -0,11 -0,21 -0,24 -0,25
PISA06 57 1,13 -0,01 -0,03 -0,10 -0,19 -0,21 -0,20
PISA09 65 1,12 -0,01 -0,02 -0,10 -0,18 -0,20 -0,19
Mean math secondary 431 1,13 0,02 0,01 -0,06 -0,14 -0,16 -0,19
Differences in STD: mathematics
STUDY N NE NN PN PO
Primary IEA TIMSS95 P1 LG 24 25% 75% 0% 0%
TIMSS95 P1 UG 26 38% 58% 4% 0%
TIMSS03 P1 29 41% 48% 10% 0%
TIMSS07 P1 44 41% 45% 14% 0%
OECD - - - - - -
Total science primary 123 37% 54% 8% 0%
Secondary IEA TIMSS95 P2 LG 39 33% 59% 8% 0%
TIMSS95 P2 UG 41 32% 51% 17% 0%
TIMSS99 P2 38 42% 50% 8% 0%
TIMSS03 p2 51 39% 47% 14% 0%
TIMSS07 p2 57 54% 32% 14% 0%
OECD PISA00 42 43% 55% 2% 0%
PISA03 41 59% 39% 2% 0%
PISA06 57 68% 26% 5% 0%
PISA09 65 74% 22% 3% 2%
Total science secondary 431 52% 40% 8% 0%
Differences in STD: scienes
Standard Errors on Differences
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