Before writing articles, some too hasty, originally thought as popular science, this noun told everyone can, the result should be this thing domestic popular Science article too little, many students take to do introductory reading, and also read, read reading, found, shrimp God your article inside many pits AH ...... The point is not clear, the key is still a lot of wrong place ...
Every time I meet this situation, I want to do this:
But pretending to be dead is not going to solve the problem ...
The so-called "teach then Not enough", many students have discussed with me about the space statistics of some of the content, so I was very inspired and educated, so I decided to put together some loopholes and holes to fill up.
Let's talk today about the Moran Index, an introductory concept of spatial statistics.
Another classmate asked, said the shrimp God you can say in ArcGIS How to use this tool ah ... When encountering this problem, the shrimp God first says:
But since the students have a request, then write.
Human nature has a habit of induction, such as seeing a bunch of things, will use a very simple word (words, sentences) to the whole expression of an impression, such as:
We'll say, "handsome." or "cool". or "Mighty".
and also:
For the parade of three elder brother ... Mitti The big leader also gave a word comment: Praise ...
So, for a single vote of data, we will first give a comprehensive comment. such as "This data is really a mess" ... Of course, this kind of comment is more "qualitative", for the scientific observation method, we have to give a quantitative assessment criteria, so there are various indices.
So the so-called Moran Index is a comprehensive evaluation of the extent to which spatial autocorrelation is measured-specifically the global Moran index.
On the spatial autocorrelation, I have written an article before, you are interested to go through the history article, here only for a brief review. In fact, spatial autocorrelation if the space two words to remove, is the classical statistics in the correlation analysis, coupled with space, has become a spatial and attribute interaction of the correlation analysis.
The self-related "self" means that you carry out the correlation observation statistic, which is derived from the same attribute of different objects, such as two students (different objects), and their mathematical results (uniform attributes) of the statistics, if they sit at the same table (spatial adjacency), and a good test B is good, A bad Test B also bad (high-end related), then basically can determine their spatial self-correlation is very strong-the test collusion cheating behavior. As shown in the following illustration:
So we can see that if the spatial relationship is ruled out, a cat and B cat, as well as the condition 2 a cat and X cat, are all related, especially the case that 2,a cat and x Cat are simply completely related.
But with the spatial relationship, the case of a cat and the X-Cat calculated in 2, may be completely irrelevant, the most important thing is to define their spatial relationship, this remote lakes, also can't hold modern communication tools Ah ... This exclusion is only defined by the spatial adjacency relationship in the conventional sense.
Therefore, the classical correlation analysis is the interdependence between the two data (attribute dimensions), then the spatial autocorrelation is the degree of interdependence within the spatial scope.
The overall Moran index is used to measure the degree of spatial autocorrelation. Within the ArcGIS toolset, this tool is simply called "Spatial autocorrelation" (spatial autocorrelation (Global Moran's)).
Using this tool, first take a look at the data, the United States, Russia and Minnesota, a statistical data on lung cancer, respectively, in 68, 78, 88, three years of male lung cancer records to be visualized, (the following data can be provided for download, see the article at the end):
As a whole, the volume of data is on the rise, and of course, the population is growing and the data of patients is correspondingly increasing, which is a reasonable thing.
So then, we can calculate the spatial autocorrelation, the spatial autocorrelation to explain what things. The explanation is whether the data of these patients is related to spatial distribution. In other words, whether the number of lung cancer patients in a county is related to the number of lung cancer patients in his neighboring counties. This decision needs to be judged both spatially and in terms of attributes.
The global Moran Index is a number between -1--1, as follows:
Of course, when reading, you also need to have p and Z scores to determine, p-value and Z-Score related content, also see the previous blog.
In ArcGIS, the tool is in the following location: Spatial Statistics tools--analyzing patterns--spatial autocorrelation (Moran ' s I)
After opening, the relevant parameters are described as follows:
Here's a conceptualization of spatial relationships. I chose Contiguity_edges_corners, the so-called Queen's case, where the common-side common points are considered adjacency elements. The choice of this parameter is very important, be sure to pay attention to the choice.
Then calculate the following, if you do not tick generate graphical results report, directly will pop up the calculation results:
It is easy to see that the P-value is greater than 0.05 of the 95% confidence level, and the Z-score does not have a threshold of 1.65, it is said that the data is biased to random ... The rest of the results are basically not read, the method of interpretation, please look at the previous write P-value and Z-score.
Of course, if you tick the Generate Graph results report, you will also generate an HTML page, as follows:
This report directly tells you that your Z-score has no threshold, so the data shows a significant random pattern ...
We calculate the 78 and 88 data in turn, and the results are as follows:
1978:
1988:
The resulting graphical reports are as follows:
1978 of the data has just crossed the threshold of 1.65, so the system tells us that this data is only less than 10% may be created randomly, and 1988, the Z-score is 2.14, this data only less than 5% is random, if according to Sir Fisher to reject the 0 hypothesis set threshold value, Only 1988 years of data rejected the 0 hypothesis, with significant clustering and spatial positive correlation possibilities. This possibility is greater than 95%.
Through the above analysis, finally we can write the analysis report, the data analysis staff like to find some self-righteous reasons, this is a very bad habit, shrimp God's personal advice is, if you write analysis report, it is best to directly carry out the phenomenon description:
Data Description: The results of global spatial autocorrelation calculation of the male lung cancer data in the United States of Russia.
In the 1968, there was a significant random distribution of data distribution, which could not be rejected by the 0 hypothesis without analytical value.
In 1978, the distribution of data was only less than 10%, and the likelihood of data aggregation was greater than the probability of random distribution, but it was not possible to reject the 0 hypothesis significantly.
In 1988, the distribution of data was less than 5%, and the likelihood of data aggregation was greater than that of random distributions, and the 0 hypothesis could be significantly rejected. The results show that in 1988, the spatial distribution of lung cancer data in the Russian-Huai-Minnesota was characterized by a certain aggregation, and the spatial positive correlation model was found.
Finally give the data download address:
Http://pan.baidu.com/s/1i4qPnt7
The data in each field in the package has a TXT document description, and the data itself is not projected, and there is no significant spatial reference, and the standard map can not be superimposed, only for everyone to learn to test the use.
