#f-test

Yep, we’re getting right back into it. I’m still working out things from yesterday, so we can just talk more statistics. This will be an interesting one and hopefully it will be pretty straightforward. The f-test, which in this case is really the f-test to compare two variances. You may have guessed, but the t-test uses the t-distribution (sort of like the normal), well the f-test uses the…

一、無母數統計法：不使用常態分配理論為基礎的檢定方法 。     說明：一般常用的 t-test，F-test，或ANOVA都是針對常態母體，或是大樣本所推導出的方法，主要用的統計量是平均數及標準差。

二、何時需要用及無母數法

類別資料或等級資料

小樣本且資料不符合常態分配

資料來自不同族群

    ps.一般資料分為：(第一章)

類目資料 nominal or categorical data

等級資料 ordinal or rank data

計量資料 measurement or interval data

比例資料 ratio data

三、類目資料的分析法通常使用卡方檢定，無法使用 t-檢定或變異數分析。

四、基本假設             

(1)隨機抽樣(randomised)；

(2)獨立性(independent)；

(3)至少為順序變項的資料(ordinal)。

五、測試某樣品是否來自某特定族群，如檢定資料之常態性。

類目資料使用 Chi-square test,

例：黃花：白花=3:1

計量資料使用 Kolmogorov-Smirnov test，檢定血糖濃度資料遵循常態分佈

其他常態性檢定法： Shapiro-Wilk, Cramer-von Mises, Anderson-Darling

ps. Kolmogorov-Smirnov 統計測試法（簡稱KS-test）被廣泛地應用來分析分佈型之數據組，KS-test不需對樣本數據組之分佈做任何假設，它對樣本數據組之CDF曲線的形狀及位置敏感，只在乎數據組間的相對分佈，而與X-軸的座標尺規無關。

http://archived.chns.org/s.php@page=11&id=34&id2=1222.html

五、(獨立)多樣本中位數差異檢定 Kruskal-Wallis test由William Kruskal與W. Allen Wallis兩位統計學家將無母數方法中，雙樣本中位數檢定推廣至多組樣本後所提出。

方法    (獨立)多樣本中位數差異檢定  Kruskal-Wallis test 使用時機

當資料中樣本數較小時(通常以樣本筆數<30為區分標準)。

當資料中包含多組樣本(三組以上之樣本)，且欲了解多組樣本間母體中位數是否有差異。

備註

當資料中樣本數較大時(樣本筆數≧30)、包含多組樣本(三組以上之樣本)，且欲了解多組樣本間母體平均數是否有差異，可使用(獨立)多樣本平均數差異檢定(或稱變異數分析)  ANalysis Of VAriance(ANOVA)進行分析。

In simple regression, the overall F-test evaluated whether your predictor did a better job of explaining the outcome than the grand mean. You could also say it tested whether R-squared was different from zero.  

The overall F-test in multiple regression means something slightly different than it did in simple linear regression. Now this F-test asks the question: Does this combination of variables do better at predicting the outcome than the grand mean did - PER PARAMETER.

To see why, check out the formula for the F-test (don't be scared!!) In this example, my variance explained (R squared) was 38%. I had 15 rows (15 people, n) and my multiple regression included 2 predictors (k).

Because the number of predictors is included in the denominator, it means that the F test takes into account how many predictors you have. 

(Here's the output with that F-test from SPSS so you can see I'm not lying)

ALSO because it takes into account how many predictors you have, you can think of the F-test as a test of overall model fit. You're assessing whether you are explaining a large enough proportion of the variance given how many predictors you just included. 

So! When you interpret a significant F-test, you can say something like: "This combination of predictors fits the data well"  If the F-test is not significant in a multiple regression, it means you should re-evaluate what you've included in your model.