Archive for April 14th, 2007

If you recall, I was somewhat surprised to see statistically significant differences between the math of students in 2005 and the level of education of their parents. Curious, I went back to the Department of Ed site cruising for more data.

Before I get started, let me say that the moron in charge of analyzing data and making it available needs to die a slow, painful death. Not only is he under the impression that Excel is a tool for printing data so it looks like it came from a dot matrix printer, but there is seemingly no consistency among the reported data. So if you find more or less the same data for math and reading scores, the years will be different, or the math scores will include amount of homework while the reading scores will include amount of reading (but never vice versa). So while it’s pretty easy to find interesting data on the Dept of Ed site, it’s tedious to find data to compare and analyze.

I did, however, find NAEP math and reading scores over five years, aggregated by race, sex, and parental education. But back to that last analysis I mentioned.

I found no statistically significant difference between math and reading scores overall. Nor did per pupil spending have a statistically significant effect on either math or reading scores. I did, however, find a statistically significant relationship between parental level of education and student scores, even between adjacent groups:

ANOVA: Parental Ed and NAEP mean math score (No HS diploma, HS diploma)
Source of Variation SS df MS F P-value F crit
Between Groups 1304.6544 1 1304.6544 24.7627 2.7727E-06 3.9381
Within Groups 5163.2512 98 52.6862
Total 6467.9056 99        

ANOVA: Parental Ed and NAEP mean math score (HS diploma, Some college)
Source of Variation SS df MS F P-value F crit
Between Groups 4080.6544 1 4080.6544 77.0904 5.3483E-14 3.9381
Within Groups 5187.4712 98 52.9334
Total 9268.1256 99        

ANOVA: Parental Ed and NAEP mean math score (Some college, College grad)
Source of Variation SS df MS F P-value F crit
Between Groups 1429.5961 1 1429.5961 23.0638 5.6337E-06 3.9381
Within Groups 6074.4778 98 61.9845
Total 7504.0739 99        

These data were for only one year, and only for math scores. So the first thing I did was try to find the corresponding data for reading scores, but alas, because whoever analyzes the data and makes reports available is a moron, that didn’t happen. I did, however, find the math and reading score data for five selected years between 1984 and 2004, aggregated by sex, race, and parental education. First, the descriptive statistics:

Age 13, math
Less than high school Graduated high school Some education after high school Graduated college
Mean 255.6 265.4 278 284.6
SE 1.749286 1.50333 1.48324 2.227106
Median 255 264 277 285
Mode #N/A 263 277 280
Stdev 3.911521 3.361547 3.316625 4.97996
Sample Variance 15.3 11.3 11 24.8
Kurtosis 2.100474 2.315765 1.132231 -0.07772
Skewness 1.376861 1.595346 0.685253 0.719821
Range 10 8 9 12
Minimum 252 263 274 280
Maximum 262 271 283 292
Sum 1278 1327 1390 1423
Count 5 5 5 5
95% CL 4.856795 4.173912 4.118134 6.183437

Age 17, math
Less than high school Graduated high school Some education after high school Graduated college
Mean 284.8 295.2 306.4 316.4
SE 1.68523 1.019804 0.678233 0.678233
Median 285 295 306 317
Mode #N/A 295 305 317
Stdev 3.768289 2.280351 1.516575 1.516575
Sample Variance 14.2 5.2 2.3 2.3
Kurtosis 1.092045 2.818047 -3.08129 1.455577
Skewness -0.86339 1.492685 0.315356 -1.11808
Range 10 6 3 4
Minimum 279 293 305 314
Maximum 289 299 308 318
Sum 1424 1476 1532 1582
Count 5 5 5 5
95% CL 4.678948 2.83143 1.883077 1.883077

Age 13, reading
Less than high school Graduated high school Some education after high school Graduated from college
Mean 239.2 251.4 266.4 268.8
SE 0.734847 0.4 0.812404 0.583095
Median 240 251 266 269
Mode 240 251 266 270
Stdev 1.643168 0.894427 1.81659 1.30384
Sample Variance 2.7 0.8 3.3 1.7
Kurtosis -1.68724 5 1.07438 -1.48789
Skewness -0.51842 2.236068 0.2669 -0.54139
Range 4 2 5 3
Minimum 237 251 264 267
Maximum 241 253 269 270
Sum 1196 1257 1332 1344
Count 5 5 5 5
95% CL 2.040262 1.110578 2.255595 1.618932

Age 17, reading
Less than high school Graduated high school Some education after high school Graduated from college
Mean 266.2 277.6 293.6 300
SE 1.984943 1.860108 2.014944 0.894427
Median 268 276 295 300
Mode #N/A 274 295 302
Stdev 4.438468 4.159327 4.505552 2
Sample Variance 19.7 17.3 20.3 4
Kurtosis 1.565874 -2.46016 3.280109 -3
Skewness -1.39299 0.575349 -1.58644 0
Range 11 9 12 4
Minimum 259 274 286 298
Maximum 270 283 298 302
Sum 1331 1388 1468 1500
Count 5 5 5 5
95% CL 5.511086 5.164486 5.594382 2.483328

From the descriptive statistics, it looks not only like these data are going to support my previous analysis for 2005, but also that the differences are more or less consistent across time for both math and reading. And testing for statistical significance:

Anova: Age 13 math
Source of Variation SS df MS F P-value F crit
Between Groups 2512.2 3 837.4 53.67949 1.42487E-08 3.238872
Within Groups 249.6 16 15.6
Total 2761.8 19        

Anova: Age 17 math
Source of Variation SS df MS F P-value F crit
Between Groups 2810.2 3 936.7333 156.1222 4.66274E-12 3.238872
Within Groups 96 16 6
Total 2906.2 19        

Anova: Age 13 reading
Source of Variation SS df MS F P-value F crit
Between Groups 2872.95 3 957.65 450.6588 1.16308E-15 3.238872
Within Groups 34 16 2.125
Total 2906.95 19        

Anova: Age 17 reading
Source of Variation SS df MS F P-value F crit
Between Groups 3527.35 3 1175.783 76.72322 1.03206E-09 3.238872
Within Groups 245.2 16 15.325
Total 3772.55 19        

So over these five years, we see statistically significant differences for both age groups between reading and math scores and the level of parental education. Let’s turn to race. First, the descriptive statistics:

13 year-olds, math
White
Black
Hispanic
Mean 280.4 252.6 257.8
SE 2.501999 2.420744 1.984943
Median 281 251 256
Mode #N/A 249 #N/A
Stdev 5.59464 5.412947 4.438468
Sample Variance 31.3 29.3 19.7
Kurtosis -1.06595 3.866906 1.565874
Skewness 0.260404 1.925607 1.39299
Range 14 13 11
Minimum 274 249 254
Maximum 288 262 265
Sum 1402 1263 1289
Count 5 5 5
95% CL 6.946663 6.721062 5.511086

17 year-olds, math
White
Black
Hispanic
Mean 311.4 284.4 288
SE 1.28841 1.661325 1.949359
Median 312 285 289
Mode #N/A #N/A #N/A
Stdev 2.880972 3.714835 4.358899
Sample Variance 8.3 13.8 19
Kurtosis -1.80433 0.589162 -2.50139
Skewness -0.03764 -0.47596 -0.18112
Range 7 10 10
Minimum 308 279 283
Maximum 315 289 293
Sum 1557 1422 1440
Count 5 5 5
95% CL 3.577199 4.612577 5.412288

13 year-olds, reading
White
Black
Hispanic
Mean 264.6 238.6 239.8
SE 0.927362 1.777639 1.56205
Median 265 238 240
Mode #N/A #N/A #N/A
Stdev 2.073644 3.974921 3.49285
Sample Variance 4.3 15.8 12.2
Kurtosis -1.96322 -1.10479 -0.64364
Skewness -0.23551 0.372589 -0.30977
Range 5 10 9
Minimum 262 234 235
Maximum 267 244 244
Sum 1323 1193 1199
Count 5 5 5
95% CL 2.574769 4.935517 4.336946

17 year-olds, reading
White
Black
Hispanic
Mean 295.2 265 268.2
SE 0.663325 0.632456 2.222611
Median 295 264 268
Mode 295 264 #N/A
Stdev 1.48324 1.414214 4.969909
Sample Variance 2.2 2 24.7
Kurtosis 0.867769 -1.75 -1.35767
Skewness -0.55162 0.883883 0.413012
Range 4 3 12
Minimum 293 264 263
Maximum 297 267 275
Sum 1476 1325 1341
Count 5 5 5
95% CL 1.841685 1.755978 6.170958

Although math and reading scores for all three groups increased over the twenty year span, it appears from eyeballing the descriptive statistics that there are math and reading score differences among the three groups. And indeed:

Anova: 13 year-olds, math
Source of Variation SS df MS F P-value F crit
Between Groups 2184.4 2 1092.2 40.804483 4.438E-06 3.8852938
Within Groups 321.2 12 26.766667
Total 2505.6 14        

Anova: 17 year-olds, math
Source of Variation SS df MS F P-value F crit
Between Groups 2149.2 2 1074.6 78.437956 1.287E-07 3.8852938
Within Groups 164.4 12 13.7
Total 2313.6 14        

Anova: 13 year-olds, reading
Source of Variation SS df MS F P-value F crit
Between Groups 2154.1333 2 1077.0667 100.03715 3.282E-08 3.8852938
Within Groups 129.2 12 10.766667
Total 2283.3333 14        

Anova: 17 year-olds, reading
Source of Variation SS df MS F P-value F crit
Between Groups 2752.1333 2 1376.0667 142.84429 4.291E-09 3.8852938
Within Groups 115.6 12 9.6333333
Total 2867.7333 14        

So over the twenty year span, the difference in both math and reading scores for the three racial groups are statistically significant. Finally, let’s turn to sex:

13 year-olds, math
Male
Female
Mean 275.4 272.8
SE 2.336664 1.881489
Median 276 273
Mode #N/A #N/A
Stdev 5.22494 4.207137
Sample Variance 27.3 17.7
Kurtosis -0.33853 0.267165
Skewness 0.586087 0.601614
Range 13 11
Minimum 270 268
Maximum 283 279
Sum 1377 1364
Count 5 5
95% CL 6.48762 5.22385

17 year-olds, math
Male
Female
Mean 307.6 303.6
SE 0.927362 1.32665
Median 308 304
Mode #N/A #N/A
Stdev 2.073644 2.966479
Sample Variance 4.3 8.8
Kurtosis -1.96322 1.448864
Skewness -0.23551 -0.88489
Range 5 8
Minimum 305 299
Maximum 310 307
Sum 1538 1518
Count 5 5
95% CL 2.574769 3.683371

13 year-olds, reading
Male
Female
Mean 252.6 264
SE 0.678233 0.707107
Median 253 264
Mode 251 #N/A
Stdev 1.516575 1.581139
Sample Variance 2.3 2.5
Kurtosis -3.08129 -1.2
Skewness -0.31536 6.94E-17
Range 3 4
Minimum 251 262
Maximum 254 266
Sum 1263 1320
Count 5 5
95% CL 1.883077 1.963243

17 year-olds, reading
Male
Female
Mean 281.8 294.4
SE 1.113553 0.678233
Median 282 295
Mode 284 295
Stdev 2.48998 1.516575
Sample Variance 6.2 2.3
Kurtosis 0.317378 1.455577
Skewness -0.91982 -1.11808
Range 6 4
Minimum 278 292
Maximum 284 296
Sum 1409 1472
Count 5 5
95% CL 3.091718 1.883077

Note that at both age groups, the descriptive statistics would seem to indicate a difference in reading scores between male and female students. Yet while there is a very small difference in math scores at age 13 between male and female students, the gap seems to widen by age 17. But are these statitically significant differences, or are they due to random variation? This time, because we may be seeing two different things going on, I’ll first do the reading and discuss it, then the math.

Anova: 13 year-olds, reading
Source of Variation SS df MS F P-value F crit
Between Groups 324.9 1 324.9 135.375 2.712E-06 5.317655
Within Groups 19.2 8 2.4
Total 344.1 9        

Anova: 17 year-olds, reading
Source of Variation SS df MS F P-value F crit
Between Groups 396.9 1 396.9 93.388235 1.095E-05 5.317655
Within Groups 34 8 4.25
Total 430.9 9        

So the reading scores for the two sexes at both age groups are statistically significant. How about the math scores?

Anova: 13 year-olds, math
Source of Variation SS df MS F P-value F crit
Between Groups 16.9 1 16.9 0.7511111 0.4113632 5.3176551
Within Groups 180 8 22.5
Total 196.9 9        

Anova: 17 year-olds, math
Source of Variation SS df MS F P-value F crit
Between Groups 40 1 40 6.1068702 0.0386376 5.3176551
Within Groups 52.4 8 6.55
Total 92.4 9        

From these data–only five years–it appears that at age 13, the math score difference between male and female students is not statistically significant. However, by age 17, the math score difference between the sexes is statistically significant (6.1068702 > 5.3176551, or 0.0386376 < 0.05).

I realize that these data only confirm what we’ve always heard, that there are statistically significant differences for math and reading scores between the racial groups, that there are statistically significant differences between the reading scores for male and female students, and that while at younger ages, there is no statistically significant difference between the math scores of boys and girls, it does emerge. However (are you listening, Department of Education people?) these demographic data are national, and an analysis of at least data aggregated by state would be more reliable, if such data were available for the same years and same demographic categories for both math and reading scores. Also, these are cross-sectional data. If one wants to look at trends or patterns over time, such as the emergence of a difference in math scores between the sexes, one really needs longitudinal data.

Posted by rightwingprof on April 14, 2007 at 5:25 pm under Education.
1 Comment.

After reading this teaser about last week’s Lost episode, I had high hopes. All I can figure is that whoever wrote this breathless post was either a pre-teen or on some bad drugs.

Yeah, Claire came down with some strange illness, but we find out what it is at the end of the episode. That’s also when we find out that Juliet is a cast-iron cold lying bitch who has infiltrated the camp for the Others.

Like that’s a surprise.

There was far less “revealed information” than the article suggested. We find out that the house (the one blown up a couple of episodes back) really was the communications station. Yawn. We find out how Juliet got to the island. Yawn. We find out that there’s some kind of island effect that causes the immune systems of pregnant women to attack their babies. Okay, that could be interesting. We find out that Juliet’s sister is alive and gave birth to a son. Yawn. We possibly learn the reason for Juliet’s antagonism toward Ben.

Except that this episode called into question how literally we can interpret the flashbacks. Now that is perhaps the most interesting thing that happened this episode–though it’s also potentially annoying. Did Juliet actually want Jack to let Ben die on the table? Are the flashbacks about how she got there reliable? If so, why is she still cooperating with Ben and the Others?

I’m starting to get the feeling that the writers are flying by the seats of their pants. That’s not good.

Posted by rightwingprof on April 14, 2007 at 10:18 am under Lost.
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