12/3 P> 5% or < 5%

P值指的是比較的兩者的差別是由機遇所致的可能性大小。
P值越小，越有理由認為對比事物間存在差異。
例如，P<0.05,就是說結果顯示的差別是由機遇所致的可能性不足5%，或者說，別人在同樣的條件下重複同樣的研究，得出相反結論的可能性不足5%。
P>0.05稱“不顯著”；P<=0.05稱“顯著”，P<=0.01稱“非常顯著”。
由於常用“顯著”來表示P值大小，所以P值最常見的誤用是把統計學上的顯著與臨床或實際中的顯著差異相混淆，即混淆“差異具有顯著性”和“具有顯著差異”二者的意思。其實，前者指的是p<=0.05，即說明有充分的理由認為比較的二者來自同一總體的可能性不足5%，因而認為二者確實有差異，下這個結論出錯的可能性<=5%。而後者的意思是二者的差別確實很大。舉例來說，4和40的差別很大，因而可以說是“有顯著差異”，而4和4.2差別不大，但如果計算得到的P值<=0.05，則認為二者“差別有顯著性”，但是不能說“有顯著差異”。

由於“有顯著差異”和“差異具有顯著性”容易混淆，因而現在有些期刊提倡用“差異有統計意義”來代替“差異有顯著性”，用“差異無統計意義”、“差異有高度統計意義”來代替“差異不顯著”和“差異有高度顯著性”。
如果P>5%，是否我們就可以下結論說比較的二者沒有差別呢？
不能。P>5%只能說明沒有充分的證據說明二者確有差別，但是也不能說二者沒有差別或差別很小。在這兩個極端之間還有一個過渡區間，即無論下有差別還是沒有差別或差別很小的證據都不足。要推斷二者沒有差別或差別很小，需要採用等效檢驗的統計推斷方法。
虛無假設（null　hypothesis)通常是表示沒有差異的假設，也叫原假設。
discussing the p-value related to the correlation coefficient. Of course, the p-value represents the probability of incorrectly rejecting the null hypothesis. If the p-value is less than some significance level, alpha, (typically practitioners use an alpha of 0.05) then we say that the result is statistically significant (at the 5% level) - i.e. the probability of incorrectly rejecting the null hypothesis is less than 5%.
"For the test I think you're alluding to, it would indicate that we would reject the null hypothesis that rho (the true correlation coeff) is equal to zero, hence there may be some evidence to suggest that a linear relation is present. Don't ignore a scatter diagram though, of course!"
...If the p-value for a correlation coefficient test is less than 0.05, it indicates that the correlation coefficient IS significantly different from zero (either positive or negative) at the alpha = 0.05 level. This means that there is some significant amount of linear relationship between your two variables of interest.
Imagine that there is a universe of points from the process you are studying. You take a sample of those to see if you can prove or disprove correlation. The truth that you are assuming is that there is no or null correlation.

"Now you develop some test or way to mathematically relate the sample to some statistic, in this case rho. You then compare it to some reference distribution. The probability (p) that you selected the sample in such a way that you got a sample that shows there is some correlation, i.e. that rho is not zero, when in fact it is zero, the truth you assumed; is the p value. In other words it is the probability that your sample indicates that the state of nature in the universe is different than the truth you assumed when your assumption was the correct one. In this case it is the probability that the rho or correlation is zero when your sample indicates that it is not zero.

"Usually if we have a one in twenty (0.05) chance of making the wrong decision, we are satisfied that there is a difference , i.e. statistical significence, and we reject the null hypothesis that there is no difference. You can set this level based on your need to be right. In drug testing work for instance, a p= 0.01 is often used since the consequences of being wrong are much more severe than being wrong about a knob for a radio."
referenced :http://www.isixsigma.com/library/content/c011119a.asp

做出是否拒絕虛無假設的決定，有四種拒絕虛無假設的方法
　（１）如果最終統計量落入拒絕域之內，則拒絕虛無假設
　（２）如果最終統計量大於臨界值，則拒絕虛無假設
　（３）如果ｐ－ｖａｌｕｅ值小於顯著水準，則拒絕虛無假設
　（４）如果虛無假設的值落在信賴區間之外，則拒絕虛無假設

如果減小了顯著水準α，那麼在檢驗一個實際上是真實的假設時，我們就減小了拒絕該假設的可能性；但是在另一方面，減小顯著水準卻可能增加了接受不真實的假設的可能性