Vernacular spatial Statistics Four: P-values and Z-VALUES (top): 0 hypothesis

Originally wanted to talk about the software operation, and later found that there are several important indicators did not say, simply after all said in the Operation bar, otherwise the results will be found a large number of "unknown".

The first is the mysterious two values in the space statistics: P Values and Z values.

To say these two values before, or to review the concept of statistics, after all, the theoretical basis of spatial statistics is based on classical statistics.

First of all, in statistics, there is a concept called "0 hypothesis" that is very powerful and must be said.

0 Assumptions ( null hypothesis), and sometimes called the original hypothesis, The official explanation is: a pre-established hypothesis when conducting statistical tests. that is, before you test your results, let's assume a numerical interval for these results, which is usually in accordance with a certain probability distribution, and if your true result deviates from the interval you set, it indicates that a small probability event has occurred. So your original hypothesis is not set up.

As shown in the following:

if the results of your calculations fall on - 2 to the 2 , it means that your hypothesis is acceptable, but not within this range, indicating the small probability event of the message. Since there are small probability events, there are two possible:1, your hypothesis is wrong;2, an outlier has occurred.

What is the use of this magical 0 hypothesis? Look at the following example:

we're going to toss a coin, (I found statistics, especially classical statistics, like tossing a coin), and before we lose it, we've set the odds on both sides .50%around, (actually closer48%--52%this interval) so if we throw out the result, there's a positive probability up to80%, and the opposite appears.20%, that is, beyond the scope of my pre-set, there is a small probability phenomenon, then this small probability phenomenon is worth studying, shrimp God personally think, if this happens, the most likely is that the coin was made of hands and feet.

Of course, there is also the possibility of a coin standing up to such a small probability of things ... This has to be sorted into outliers.

(Another way of thinking about tossing coins is to read this article: Two ways of thinking about coin toss:

http://mp.weixin.qq.com/s?__biz=MzA4ODk4NzgyNA==&mid=200720156&idx=1&sn= 564f0b6fe95276180c625373a7cea70f#rd

In the classic statistics, 0 assumes that you calculate the data is in line with a certain probability, then in the spatial statistics, what is the 0 hypothesis?

Look at the following example:

     if said, a City in 7 200 200 The case should be evenly distributed in a Every region of the city, but in fact it is impossible, We will find that in some areas the crime rate is much higher than in other regions.

so the above proposition, at the very beginning, we explained, $ case, the average distribution in all parts of the city, is the so-called "0 hypothesis", in the spatial statistics, 0 hypothesis refers to the space position in a certain area of the full random (uniform) distribution (in the natural phenomenon, the uniform distribution is a minimum probability will appear, basically can be ignored , so the general talk is completely random).

According to this hypothesis, we can make a statistical analysis of the location of the crime in the whole city, if the calculated result is in line with our hypothesis, then it can only be said that this $ The occurrence of the case, the location is random, no aggregation or discrete laws.

In the analysis of spatial data, it is important to know whether the data distribution is regular.

To get a copy of the data, the first time, to understand is that the data is not a regular, because the regular data for better analysis. And if you get this data is a random distribution of data, then generally speaking, there is no analysis of the possibility of research. because pure random (completely random) is unpredictable and unable to find patterns , like prime numbers (the position of prime numbers on the axis is completely random, can not find any rules and patterns).

So-called pure random, there are three possibilities, one is that your hypothesis is purely random, the second is that the data you want to calculate is purely random, and the third is that the data you want to calculate with its peripheral data is purely random.

So how do you judge a random hypothesis? In other words, your result is to accept the 0 hypothesis or reject the 0 hypothesis, which can help us to judge by the results of PandZ two values.

(not to be continued)

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Vernacular spatial Statistics Four: P-values and Z-VALUES (top): 0 hypothesis