: The two populations are equal
: The two populations are not equal
![Rendered by QuickLaTeX.com R_1,R_2](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-caa9c3e671a05deb5d9015843669204f_l3.png)
![](https://research.miidas.jp/wp-content/uploads/2019/01/Screen-Shot-2019-01-21-at-10.18.10.png)
![Rendered by QuickLaTeX.com R_1 = 32.5, R_2 = 32.5](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-efff93ad71a91189d9c362bd49ac7321_l3.png)
独立じゃないときは?(i.e. matched or paired)
たとえば The sign test これは最もシンプルなノンパラテストで中央値の差を検定します。ちなみに、独立じゃない時、と言いましたがこれはたとえば同じグループで実験した際に得られるデータとかになります。なので : The median difference is zero
: The median difference is not zero α=?
![](https://research.miidas.jp/wp-content/uploads/2019/01/Screen-Shot-2019-01-21-at-10.22.02.png)
どうやって?
![Rendered by QuickLaTeX.com \pm](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-7e6df2d33e1750d02a2b0cb14612da8f_l3.png)
![Rendered by QuickLaTeX.com (p=0.5)](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-ca8d599b5167889e83dfbc68f34d532d_l3.png)
![Rendered by QuickLaTeX.com \alpha](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-8f0b6b1a01f8fcc2f95be0364c090397_l3.png)
だけで判断するのはええのか?
![](https://research.miidas.jp/wp-content/uploads/2019/01/Screen-Shot-2019-01-21-at-11.01.58.png)
![Rendered by QuickLaTeX.com W_+,W_-](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-6e848b1ae4d1486d6a2d663192eaa39d_l3.png)
![Rendered by QuickLaTeX.com W_+,W_-](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-6e848b1ae4d1486d6a2d663192eaa39d_l3.png)
![Rendered by QuickLaTeX.com W=W_- \geq 4](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-fe8cb7067178095ac73cce15b859b6a6_l3.png)
![Rendered by QuickLaTeX.com H_0](https://research.miidas.jp/wp-content/ql-cache/quicklatex.com-a4fc152da9c0802275c766010d183a54_l3.png)
- https://machinelearningmastery.com/nonparametric-statistical-significance-tests-in-python/
- https://www.youtube.com/watch?v=TqCg2tb4wJ0
- http://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_nonparametric/BS704_Nonparametric4.html
- http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Nonparametric/BS704_Nonparametric5.html