Android with root Git for version control Lircd with Raspberry Pi for IR receiver and sender Tips for Windows Depolying your own password management tool -- KeeWeb Depoly your flask app into Heroku Fix shit IE code manually ISBN to Book Category by Scraping DangDang A Generic Makefile for C/C++ Program Configure Raspberry pi Remove watermark with PyPDF2 tips for docker Anaconda+TensorFlow+CUDA Snippets Configure Remote Mathematica Kernel Build your own ngrok server Access Array SSL VPN 使用Rstudio制作html5幻灯片 tips for Mac OS X system Tips for ipython notebook 配置Ubuntu server + Openbox (Obuntu) tips for Vimperator tips for Vim 安装CUDA My First Jekyll Blog rsync常见选项 在Linux中读取Ipod touch的文件 tip for texmacs 在VPS上建站的一些tip Gnuplot绘图札记 Samba系统和autofs自动挂载 Linux中alsamixer声卡无法录音 搭建自己的RSS订阅器——Tiny Tiny RSS Grub2引导安装Ubuntu awk tips 将Ubuntu系统装入U盘 The Great Rtorrent 编译GCC 再这样剁手!!!该死的libgd 使用ulimit进行资源限制 使用SSH代理上IPV6 使用RCurl抓取网页数据 修复Ubuntu Grub记 openbox中的文件关联 在Ubuntu 12.04下编译qtiplot 处理BCM4312网卡驱动纪实 配置我的Ubuntu Server记 Cygwin杂记 Linux 使普通用户具有以超级权限执行脚本 让firefox自定义地处理文件类型 WordPress优秀主题及插件 在phpcloud上搭建wordpress UBUNTU下用pptpd做VPN server ubuntu升级内核过后的一些问题 安装telnet服务 kubuntu札记 64位kubuntu札记 统计软件R Virtualbox stardict星际译王 Ubuntu重装windows系统后的grub引导修复 SSH服务及花生壳域名解析 采用cbp2make工具由code::blocks工程创建makefile文件 UBUNTU 札记

Null Hypothesis and Alternative Hypothesis

2015年11月12日

The following text come from this link.

The null hypothesis reflects that there will be no observed effect for our experiment. In a mathematical formulation of the null hypothesis there will typically be an equal sign. This hypothesis is denoted by $H_0$.

The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either $H_a$ or by $H_1$.

The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis.

The null hypothesis is what we are attempting to overturn by our hypothesis test. We hope to obtain a small enough p-value that we are justified in rejecting the null hypothesis.

If the null hypothesis is rejected( we got small enough p-value), then we are correct to say that we accept the alternative hypothesis.

However, if the null hypothesis is not rejected, then we do not say that we accept the null hypothesis.

In many ways the philosophy behind a test of significance is similar to that of a trial. If there is not enough evidence, then the defendant is declared “not guilty.” Again this is not the same as saying that the defendant is innocent. It only says that the prosecution was not able to provide enough evidence to convince a jury that the defendant was guilty. In a similar way, if we fail to reject the null hypothesis it does not mean that the null hypothesis is true. It only means that we were not able to provide enough evidence to support the alternative hypothesis.

P-values are related to the test statistic and give us a measurement of evidence against the null hypothesis.

Test statistics vary greatly depending upon what parameters our hypothesis test concerns. Some common test statistics include:

  • z - statistic for hypothesis tests concerning the population mean, when we know the population standard deviation.
  • t - statistic for hypothesis tests concerning the population mean, when we do not know the population standard deviation.
  • t - statistic for hypothesis tests concerning the difference of two independent population mean, when we do not know the standard deviation of either of the two populations.
  • z - statistic for hypothesis tests concerning a population proportion.
  • Chi-square - statistic for hypothesis tests concerning the difference between an expected and actual count for categorical data.

A p-value is a probability. If our p-value is small, then this could mean one of two things:

  • The null hypothesis is true, but we were just very lucky in obtaining our observed sample. Our sample is the way it is due to the fact that the null hypothesis is false.
  • In general, the smaller the p-value, the more evidence that we have against our null hypothesis.

In general, the smaller the p-value, the more evidence that we have against our null hypothesis.