The reduction, if any, is a function of the number of input features and the neighborhood structure employed. When this parameter is checked, the False Discovery Rate (FDR) procedure will potentially reduce the critical p-value thresholds shown in the table above in order to account for multiple testing and spatial dependency. The local spatial pattern analysis tools including Hot Spot Analysis and Cluster and Outlier Analysis Anselin Local Moran's I provide an optional Boolean parameter Apply False Discovery Rate (FDR) Correction. For the Hot Spot Analysis tool, for example, unusual means either a statistically significant hot spot or a statistically significant cold spot. When the absolute value of the z-score is large and the probabilities are small (in the tails of the normal distribution), however, you are seeing something unusual and generally very interesting. In this case, it is possible to reject the null hypothesis and proceed with figuring out what might be causing the statistically significant spatial structure in your data.Ī key idea here is that the values in the middle of the normal distribution (z-scores like 0.19 or -1.2, for example), represent the expected outcome. If the z-score falls outside that range (for example, -2.5 or +5.4 standard deviations), the observed spatial pattern is probably too unusual to be the result of random chance, and the p-value will be small to reflect this. If your z-score is between -1.96 and +1.96, your uncorrected p-value will be larger than 0.05, and you cannot reject your null hypothesis because the pattern exhibited could very likely be the result of random spatial processes. The uncorrected p-value associated with a 95 percent confidence level is 0.05. The critical z-score values when using a 95 percent confidence level are -1.96 and +1.96 standard deviations. The table below shows the uncorrected critical p-values and z-scores for different confidence levels.Ĭonsider an example. A confidence level of 99 percent would be the most conservative in this case, indicating that you are unwilling to reject the null hypothesis unless the probability that the pattern was created by random chance is really small (less than a 1 percent probability). Typical confidence levels are 90, 95, or 99 percent. Consequently, before you run the spatial statistic, you select a confidence level. To reject the null hypothesis, you must make a subjective judgment regarding the degree of risk you are willing to accept for being wrong (for falsely rejecting the null hypothesis). When you run a feature pattern analysis tool and it yields small p-values and either a very high or a very low z-score, this indicates it is unlikely that the observed spatial pattern reflects the theoretical random pattern represented by your null hypothesis (CSR). Very high or very low (negative) z-scores, associated with very small p-values, are found in the tails of the normal distribution. Both z-scores and p-values are associated with the standard normal distribution as shown below. If, for example, a tool returns a z-score of +2.5, you would say that the result is 2.5 standard deviations. You might ask: How small is small enough? Good question. When the p-value is very small, it means it is very unlikely (small probability) that the observed spatial pattern is the result of random processes, so you can reject the null hypothesis. For the pattern analysis tools, it is the probability that the observed spatial pattern was created by some random process. Whenever you see spatial structure such as clustering in the landscape (or in your spatial data), you are seeing evidence of some underlying spatial processes at work, and as a geographer or GIS analyst, this is often what you are most interested in. Often, you will run one of the pattern analysis tools, hoping that the z-score and p-value will indicate that you can reject the null hypothesis, because it would indicate that rather than a random pattern, your features (or the values associated with your features) exhibit statistically significant clustering or dispersion. The z-scores and p-values returned by the pattern analysis tools tell you whether you can reject that null hypothesis or not. The null hypothesis for the pattern analysis tools ( Analyzing Patterns toolset and Mapping Clusters toolset) is Complete Spatial Randomness (CSR), either of the features themselves or of the values associated with those features. Most statistical tests begin by identifying a null hypothesis.
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