c:ma:2016:schedule:week09_answer
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c:ma:2016:schedule:week09_answer [2016/11/09 07:54] – created hkimscil | c:ma:2016:schedule:week09_answer [2016/11/09 09:52] (current) – [E.g. 6] hkimscil | ||
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====== E.g. 1====== | ====== E.g. 1====== | ||
MASS data의 Cars93 data에서 Origin에 따른 city Mileage와 highway Mileage, Engine size를 비교하라. | MASS data의 Cars93 data에서 Origin에 따른 city Mileage와 highway Mileage, Engine size를 비교하라. | ||
- | - 가설 만들기 | + | - 가설 만들기: |
+ | * $\text{MPG.city: | ||
+ | * $\text{MPG.highway: | ||
+ | * $\text{EnginSize: | ||
- 영가설 만들기 | - 영가설 만들기 | ||
+ | * $\text{MPG.city: | ||
+ | * $\text{MPG.highway: | ||
+ | * $\text{EnginSize: | ||
- 각 그룹의 평균과 표준편차 | - 각 그룹의 평균과 표준편차 | ||
- 가설 테스트 | - 가설 테스트 | ||
- 테스트 결과 | - 테스트 결과 | ||
+ | |||
+ | < | ||
+ | > CarData | ||
+ | Origin MPG.city MPG.highway EngineSize | ||
+ | 1 non-USA | ||
+ | 2 non-USA | ||
+ | 3 non-USA | ||
+ | 4 non-USA | ||
+ | 5 non-USA | ||
+ | 6 USA | ||
+ | 7 USA | ||
+ | 8 USA | ||
+ | 9 USA | ||
+ | 10 | ||
+ | 11 | ||
+ | 12 | ||
+ | 13 | ||
+ | 14 | ||
+ | 15 | ||
+ | 16 | ||
+ | 17 | ||
+ | 18 | ||
+ | 19 | ||
+ | 20 | ||
+ | 21 | ||
+ | 22 | ||
+ | 23 | ||
+ | 24 | ||
+ | 25 | ||
+ | 26 | ||
+ | 27 | ||
+ | 28 | ||
+ | 29 | ||
+ | 30 | ||
+ | 31 | ||
+ | 32 | ||
+ | 33 | ||
+ | 34 | ||
+ | 35 | ||
+ | 36 | ||
+ | 37 | ||
+ | 38 | ||
+ | 39 non-USA | ||
+ | 40 non-USA | ||
+ | 41 non-USA | ||
+ | 42 non-USA | ||
+ | 43 non-USA | ||
+ | 44 non-USA | ||
+ | 45 non-USA | ||
+ | 46 non-USA | ||
+ | 47 non-USA | ||
+ | 48 non-USA | ||
+ | 49 non-USA | ||
+ | 50 non-USA | ||
+ | 51 | ||
+ | 52 | ||
+ | 53 non-USA | ||
+ | 54 non-USA | ||
+ | 55 non-USA | ||
+ | 56 non-USA | ||
+ | 57 non-USA | ||
+ | 58 non-USA | ||
+ | 59 non-USA | ||
+ | 60 | ||
+ | 61 | ||
+ | 62 non-USA | ||
+ | 63 non-USA | ||
+ | 64 non-USA | ||
+ | 65 non-USA | ||
+ | 66 non-USA | ||
+ | 67 non-USA | ||
+ | 68 | ||
+ | 69 | ||
+ | 70 | ||
+ | 71 | ||
+ | 72 | ||
+ | 73 | ||
+ | 74 | ||
+ | 75 | ||
+ | 76 | ||
+ | 77 | ||
+ | 78 non-USA | ||
+ | 79 | ||
+ | 80 non-USA | ||
+ | 81 non-USA | ||
+ | 82 non-USA | ||
+ | 83 non-USA | ||
+ | 84 non-USA | ||
+ | 85 non-USA | ||
+ | 86 non-USA | ||
+ | 87 non-USA | ||
+ | 88 non-USA | ||
+ | 89 non-USA | ||
+ | 90 non-USA | ||
+ | 91 non-USA | ||
+ | 92 non-USA | ||
+ | 93 non-USA | ||
+ | > | ||
+ | > sapply(CarData, | ||
+ | $Origin | ||
+ | USA non-USA | ||
+ | | ||
+ | |||
+ | $MPG.city | ||
+ | Min. 1st Qu. Median | ||
+ | 15.00 | ||
+ | |||
+ | $MPG.highway | ||
+ | Min. 1st Qu. Median | ||
+ | 20.00 | ||
+ | |||
+ | $EngineSize | ||
+ | Min. 1st Qu. Median | ||
+ | 1.000 | ||
+ | > | ||
+ | </ | ||
+ | < | ||
+ | > tapply(CarData$MPG.city, | ||
+ | $USA | ||
+ | Min. 1st Qu. Median | ||
+ | 15.00 | ||
+ | |||
+ | $`non-USA` | ||
+ | Min. 1st Qu. Median | ||
+ | 17.00 | ||
+ | |||
+ | > tapply(MPG.city, | ||
+ | | ||
+ | 3.994455 6.672876 | ||
+ | |||
+ | > plot(MPG.city~Origin) | ||
+ | </ | ||
+ | |||
+ | {{t-test_mpg.city.png}} | ||
+ | |||
+ | < | ||
+ | |||
+ | Welch Two Sample t-test | ||
+ | |||
+ | data: MPG.city by Origin | ||
+ | t = -2.5296, df = 71.024, p-value = 0.01364 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean in group USA mean in group non-USA | ||
+ | | ||
+ | |||
+ | > | ||
+ | > t.test(MPG.city~Origin, | ||
+ | |||
+ | Two Sample t-test | ||
+ | |||
+ | data: MPG.city by Origin | ||
+ | t = -2.5688, df = 91, p-value = 0.01183 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean in group USA mean in group non-USA | ||
+ | | ||
+ | |||
+ | > | ||
+ | </ | ||
+ | < | ||
+ | $USA | ||
+ | Min. 1st Qu. Median | ||
+ | 20.00 | ||
+ | |||
+ | $`non-USA` | ||
+ | Min. 1st Qu. Median | ||
+ | 21.00 | ||
+ | |||
+ | > | ||
+ | |||
+ | > tapply(MPG.highway, | ||
+ | | ||
+ | 4.151337 6.247990 | ||
+ | > plot(MPG.highway~Origin) | ||
+ | </ | ||
+ | |||
+ | {{t-test_mpghighway.png}} | ||
+ | |||
+ | < | ||
+ | |||
+ | Welch Two Sample t-test | ||
+ | |||
+ | data: MPG.highway by Origin | ||
+ | t = -1.7545, df = 75.802, p-value = 0.08339 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean in group USA mean in group non-USA | ||
+ | | ||
+ | |||
+ | </ | ||
+ | < | ||
+ | $USA | ||
+ | Min. 1st Qu. Median | ||
+ | 1.300 | ||
+ | |||
+ | $`non-USA` | ||
+ | Min. 1st Qu. Median | ||
+ | 1.000 | ||
+ | |||
+ | > tapply(EngineSize, | ||
+ | USA | ||
+ | 1.1353757 0.7171563 | ||
+ | > plot(EngineSize~Origin) | ||
+ | > | ||
+ | </ | ||
+ | {{t-test_enginesize.png}} | ||
+ | < | ||
+ | |||
+ | Welch Two Sample t-test | ||
+ | |||
+ | data: EngineSize by Origin | ||
+ | t = 4.2135, df = 80.033, p-value = 6.55e-05 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean in group USA mean in group non-USA | ||
+ | | ||
+ | |||
+ | > | ||
+ | </ | ||
+ | |||
====== E.g. 2 ====== | ====== E.g. 2 ====== | ||
- Seatbelts 데이터를 불러온 후 | - Seatbelts 데이터를 불러온 후 | ||
Line 14: | Line 249: | ||
- null hypothesis | - null hypothesis | ||
- test result | - test result | ||
+ | |||
+ | < | ||
+ | > attach(sb) | ||
+ | The following objects are masked from sb (pos = 3): | ||
+ | |||
+ | drivers, DriversKilled, | ||
+ | PetrolPrice, | ||
+ | |||
+ | The following object is masked from package: | ||
+ | |||
+ | drivers | ||
+ | > | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | $`0` | ||
+ | Min. 1st Qu. Median | ||
+ | | ||
+ | |||
+ | $`1` | ||
+ | Min. 1st Qu. Median | ||
+ | | ||
+ | > | ||
+ | |||
+ | > tapply(DriversKilled, | ||
+ | | ||
+ | 24.26088 22.22860 | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | |||
+ | Welch Two Sample t-test | ||
+ | |||
+ | data: DriversKilled by law | ||
+ | t = 5.1253, df = 29.609, p-value = 1.693e-05 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean in group 0 mean in group 1 | ||
+ | | ||
+ | </ | ||
====== E.g. 3 ====== | ====== E.g. 3 ====== | ||
Line 21: | Line 298: | ||
- 테스트를 한 후 | - 테스트를 한 후 | ||
- 결과를 보고하시오. | - 결과를 보고하시오. | ||
+ | |||
+ | < | ||
+ | |||
+ | . . . . | ||
+ | |||
+ | > md = subset(anorexia, | ||
+ | > md | ||
+ | Treat Prewt Postwt | ||
+ | 56 FT 83.8 95.2 | ||
+ | 57 FT 83.3 94.3 | ||
+ | 58 FT 86.0 91.5 | ||
+ | 59 FT 82.5 91.9 | ||
+ | 60 FT 86.7 100.3 | ||
+ | 61 FT 79.6 76.7 | ||
+ | 62 FT 76.9 76.8 | ||
+ | 63 FT 94.2 101.6 | ||
+ | 64 FT 73.4 94.9 | ||
+ | 65 FT 80.5 75.2 | ||
+ | 66 FT 81.6 77.8 | ||
+ | 67 FT 82.1 95.5 | ||
+ | 68 FT 77.6 90.7 | ||
+ | 69 FT 83.5 92.5 | ||
+ | 70 FT 89.9 93.8 | ||
+ | 71 FT 86.0 91.7 | ||
+ | 72 FT 87.3 98.0 | ||
+ | |||
+ | > t.test(md$Prewt, | ||
+ | |||
+ | Paired t-test | ||
+ | |||
+ | data: md$Prewt and md$Postwt | ||
+ | t = -4.1849, df = 16, p-value = 0.0007003 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean of the differences | ||
+ | -7.264706 | ||
+ | </ | ||
+ | |||
+ | |||
====== E.g. 4 ====== | ====== E.g. 4 ====== | ||
<WRAP box> | <WRAP box> | ||
Line 27: | Line 345: | ||
</ | </ | ||
두 그룹의 평균의 차이를 비교하시오. | 두 그룹의 평균의 차이를 비교하시오. | ||
+ | |||
+ | < | ||
+ | [1] 175 168 168 190 156 181 182 175 174 179 | ||
+ | > b | ||
+ | [1] 185 169 173 173 188 186 175 174 179 180 | ||
+ | > ab <- data.frame(a, | ||
+ | > ab | ||
+ | | ||
+ | 1 175 185 | ||
+ | 2 168 169 | ||
+ | 3 168 173 | ||
+ | 4 190 173 | ||
+ | 5 156 188 | ||
+ | 6 181 186 | ||
+ | 7 182 175 | ||
+ | 8 175 174 | ||
+ | 9 174 179 | ||
+ | 10 179 180 | ||
+ | > | ||
+ | |||
+ | > summary(ab) | ||
+ | | ||
+ | | ||
+ | 1st Qu.: | ||
+ | | ||
+ | | ||
+ | 3rd Qu.: | ||
+ | | ||
+ | |||
+ | > abs <- stack(ab) | ||
+ | > tapply(abs$values, | ||
+ | $a | ||
+ | Min. 1st Qu. Median | ||
+ | 156.0 | ||
+ | |||
+ | $b | ||
+ | Min. 1st Qu. Median | ||
+ | 169.0 | ||
+ | |||
+ | > tapply(abs$values, | ||
+ | | ||
+ | 9.342852 6.442912 | ||
+ | > | ||
+ | |||
+ | > t.test(ab$a, | ||
+ | |||
+ | Welch Two Sample t-test | ||
+ | |||
+ | data: ab$a and ab$b | ||
+ | t = -0.94737, df = 15.981, p-value = 0.3576 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean of x mean of y | ||
+ | 174.8 | ||
+ | |||
+ | </ | ||
====== E.g. 5 ====== | ====== E.g. 5 ====== | ||
Line 33: | Line 409: | ||
아이스크림의 박테리아가 0.3 MPN/g 보다 커서 유통되기에 위험하다고 할 수 있을까? | 아이스크림의 박테리아가 0.3 MPN/g 보다 커서 유통되기에 위험하다고 할 수 있을까? | ||
+ | < | ||
+ | > ir | ||
+ | [1] 0.593 0.142 0.329 0.691 0.231 0.793 0.519 0.392 0.418 | ||
+ | |||
+ | > t.test(ir, mu=.3) | ||
+ | |||
+ | One Sample t-test | ||
+ | |||
+ | data: ir | ||
+ | t = 2.2051, df = 8, p-value = 0.05853 | ||
+ | alternative hypothesis: true mean is not equal to 0.3 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean of x | ||
+ | 0.4564444 | ||
+ | |||
+ | > | ||
+ | |||
+ | > t.test(ir, alternative=" | ||
+ | |||
+ | One Sample t-test | ||
+ | |||
+ | data: ir | ||
+ | t = 2.2051, df = 8, p-value = 0.02927 | ||
+ | alternative hypothesis: true mean is greater than 0.3 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean of x | ||
+ | 0.4564444 | ||
+ | |||
+ | > | ||
+ | </ | ||
====== E.g. 6 ====== | ====== E.g. 6 ====== | ||
Line 40: | Line 450: | ||
흡연이 기억에 영향을 준다고 할 수 있을까? | 흡연이 기억에 영향을 준다고 할 수 있을까? | ||
+ | < | ||
+ | > smoke <- c(18, | ||
+ | > nosmoke <- c(16, | ||
+ | |||
+ | > sn <- data.frame(smoke, | ||
+ | > ss <- stack(sn) | ||
+ | > plot(ss$values~ss$ind) | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | |||
+ | Welch Two Sample t-test | ||
+ | |||
+ | data: ss$values by ss$ind | ||
+ | t = -2.2573, df = 16.376, p-value = 0.03798 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean in group nosmoke | ||
+ | | ||
+ | |||
+ | > | ||
+ | |||
+ | > | ||
+ | </ | ||
====== E.g. 7 ====== | ====== E.g. 7 ====== | ||
- MASS package를 불러온 후, survey 데이터를 활용하여 담배와 운동량 간의 관계에 대한 가설테스트를 하시오. | - MASS package를 불러온 후, survey 데이터를 활용하여 담배와 운동량 간의 관계에 대한 가설테스트를 하시오. |
c/ma/2016/schedule/week09_answer.1478647482.txt.gz · Last modified: 2016/11/09 07:54 by hkimscil