第II部

第12章 二項検定

In [1]:
sapply(c("pipeR", "dplyr", "tidyr", "ggplot2", "readr", "readxl", "Cairo", "grid", "gridExtra"), 
       require, character.only = TRUE)

Loading required package: pipeR
Loading required package: dplyr
Warning message:
: package 'dplyr' was built under R version 3.3.1
Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Loading required package: tidyr
Loading required package: ggplot2
Loading required package: readr
Loading required package: readxl
Loading required package: Cairo
Loading required package: grid
Loading required package: gridExtra
Warning message:
: package 'gridExtra' was built under R version 3.3.1
Attaching package: 'gridExtra'

The following object is masked from 'package:dplyr':

    combine
pipeR
TRUE
dplyr
TRUE
tidyr
TRUE
ggplot2
TRUE
readr
TRUE
readxl
TRUE
Cairo
TRUE
grid
TRUE
gridExtra
TRUE
  • 日ハム : 楽天 = 17:3
  • 日ハムの方が強いか => 勝つ確率が0.5より大きいかどうか => 帰無仮説: 勝つ確率は0.5（片側検定）

勝つ確率が0.5の時に17勝する確率は

In [2]:
dbinom(17, 20, 0.5)
0.00108718872070313
In [3]:
options(repr.plot.width = 4, repr.plot.height = 4)
In [4]:
data.frame(x = c(0:20), y = dbinom(c(0:20), 20, 0.5)) %>>% 
    ggplot(aes(x = x, y = y)) + 
        geom_point()






























In [5]:



    


pbinom(c(0:20), 20, 0.5) %>>% round(digit = 4)






















    
	
  1. 0
    2. 
	
  2. 0
    3. 
	
  3. 2e-04
    4. 
	
  4. 0.0013
    5. 
	
  5. 0.0059
    6. 
	
  6. 0.0207
    7. 
	
  7. 0.0577
    8. 
	
  8. 0.1316
    9. 
	
  9. 0.2517
    10. 
	
  10. 0.4119
    11. 
	
  11. 0.5881
    12. 
	
  12. 0.7483
    13. 
	
  13. 0.8684
    14. 
	
  14. 0.9423
    15. 
	
  15. 0.9793
    16. 
	
  16. 0.9941
    17. 
	
  17. 0.9987
    18. 
	
  18. 0.9998
    19. 
	
  19. 1
    20. 
	
  20. 1
    21. 
	
  21. 1
    22. 



























棄却域は15勝以上













In [6]:



    


data.frame(win = c(0:20), prob = pbinom(c(0:20), 20, 0.5)) %>>% filter(prob >= 0.95)
























winprob


	
114.0000000 0.9793053

	
215.000000 0.994091

	
316.0000000 0.9987116

	
417.0000000 0.9997988

	
518.00000 0.99998

	
619.000000 0.999999

	
720 1





























$p$値は













In [7]:



    


pbinom(16, 20, 0.5, lower.tail = FALSE)





















0.00128841400146485
























12.3 じゃんけん


















10回中7回的中は1/3より高いか



















棄却域は7回以上













In [8]:



    


data.frame(x = c(0:10), prob = pbinom(c(0:10), 10, 1/3)) %>>% filter(prob >= 0.95)
























xprob


	
16.00000000.9803384

	
27.0000000.996596

	
38.00000000.9996444

	
49.00000000.9999831

	
510 1























In [9]:



    


pbinom(6, 10, 1/3, lower.tail = FALSE)





















0.0196616369455876


















In [10]:



    


devtools::session_info()





















Session info -------------------------------------------------------------------
Packages -----------------------------------------------------------------------
Session info -------------------------------------------------------------------
Packages -----------------------------------------------------------------------














 setting  value                       
 version  R version 3.3.0 (2016-05-03)
 system   x86_64, mingw32             
 ui       RTerm                       
 language (EN)                        
 collate  Japanese_Japan.932          
 tz       Asia/Tokyo                  
 date     2016-07-07                  

 package    * version    date       source                             
 assertthat   0.1        2013-12-06 CRAN (R 3.3.0)                     
 base64enc    0.1-3      2015-07-28 CRAN (R 3.3.0)                     
 Cairo      * 1.5-9      2015-09-26 CRAN (R 3.3.0)                     
 colorspace   1.2-6      2015-03-11 CRAN (R 3.3.0)                     
 DBI          0.4-1      2016-05-08 CRAN (R 3.3.0)                     
 devtools     1.11.1     2016-04-21 CRAN (R 3.3.0)                     
 digest       0.6.9      2016-01-08 CRAN (R 3.3.0)                     
 dplyr      * 0.5.0      2016-06-24 CRAN (R 3.3.1)                     
 evaluate     0.9        2016-04-29 CRAN (R 3.3.0)                     
 ggplot2    * 2.1.0      2016-03-01 CRAN (R 3.3.0)                     
 gridExtra  * 2.2.1      2016-02-29 CRAN (R 3.3.1)                     
 gtable       0.2.0      2016-02-26 CRAN (R 3.3.0)                     
 IRdisplay    0.3.0.9000 2016-06-20 Github (IRkernel/IRdisplay@69fd5d8)
 IRkernel     0.6        2016-06-20 Github (IRkernel/IRkernel@735d4ff) 
 jsonlite     0.9.22     2016-06-15 CRAN (R 3.3.0)                     
 labeling     0.3        2014-08-23 CRAN (R 3.3.0)                     
 lazyeval     0.2.0      2016-06-12 CRAN (R 3.3.0)                     
 magrittr     1.5        2014-11-22 CRAN (R 3.3.0)                     
 memoise      1.0.0      2016-01-29 CRAN (R 3.3.0)                     
 munsell      0.4.3      2016-02-13 CRAN (R 3.3.0)                     
 pbdZMQ       0.2-3      2016-05-20 CRAN (R 3.3.0)                     
 pipeR      * 0.6.1.3    2016-04-04 CRAN (R 3.3.0)                     
 plyr         1.8.4      2016-06-08 CRAN (R 3.3.0)                     
 R6           2.1.2      2016-01-26 CRAN (R 3.3.0)                     
 Rcpp         0.12.5     2016-05-14 CRAN (R 3.3.0)                     
 readr      * 0.2.2      2015-10-22 CRAN (R 3.3.0)                     
 readxl     * 0.1.1      2016-03-28 CRAN (R 3.3.0)                     
 repr         0.7        2016-05-13 CRAN (R 3.3.0)                     
 scales       0.4.0      2016-02-26 CRAN (R 3.3.0)                     
 stringi      1.1.1      2016-05-27 CRAN (R 3.3.0)                     
 stringr      1.0.0      2015-04-30 CRAN (R 3.3.0)                     
 tibble       1.0        2016-03-23 CRAN (R 3.3.0)                     
 tidyr      * 0.5.1      2016-06-14 CRAN (R 3.3.0)                     
 uuid         0.1-2      2015-07-28 CRAN (R 3.3.0)                     
 withr        1.0.1      2016-02-04 CRAN (R 3.3.0)