Spatial Statistics and Hypothesis Testing

Play an AI-generated podcast conversation about this lesson

What is likely to occur when measuring something about the same object over time?

Measurements remain constant over time

Two observations far apart in time are similar in measurement

Measurements decrease over time

Two observations close to each other in time are similar in measurement (correct)

What is an example of exogenous spatial autocorrelation?

The growth of plants

The movement of tectonic plates

Rainfall (correct)

The spread of a disease

What is a consequence of spatial autocorrelation in both variables under investigation?

Increased degrees of freedom

Reduced sampling variance

Reduced number of degrees of freedom (correct)

Increased sample size

What is the result of positive spatial autocorrelation on standard inferential tests?

They underestimate the sampling variance Signup and view all the answers

What is the name of the ArcGIS tool that measures spatial autocorrelation?

Spatial Autocorrelation (Global Moran’s I) Signup and view all the answers

What is returned by the Spatial Autocorrelation (Global Moran’s I) tool?

Five values: Moran’s I Index, Expected Index, Variance, z-score, and p-value Signup and view all the answers

What is the primary purpose of assigning spatial weights to locations?

To determine the spatial autocorrelation statistics Signup and view all the answers

What type of spatial weight is used when wij = 1 for neighboring locations i and j?

Binary weight Signup and view all the answers

What determines the changing rate of weights over distance dij in the distance inverse weight?

Parameter α Signup and view all the answers

What is the main advantage of using spatial weights matrices?

They express our knowledge about spatial relationships and embed all observations in space together Signup and view all the answers

What is a common spatial question that spatial weights can help answer?

How many gas stations are within 5 miles of my stalled car? Signup and view all the answers

What is the purpose of defining the spatial relations among locations?

To calculate the spatial autocorrelation statistics Signup and view all the answers

What is the primary purpose of the Incremental Spatial Autocorrelation tool?

To evaluate the spatial pattern of a set of features Signup and view all the answers

What is the null hypothesis in the context of Moran's Index?

The spatial distribution of feature values is random Signup and view all the answers

What does a p-value indicate in the context of Moran's Index?

The statistical significance of the spatial pattern Signup and view all the answers

What does a positive z-score indicate in the context of Moran's Index?

The spatial distribution of feature values is clustered Signup and view all the answers

How can you access the Global Moran's I values in the Results window?

By right-clicking on the Messages entry and selecting View Global Moran's I Signup and view all the answers

What is the purpose of the derived output values generated by the Geoprocessing tool?

To provide input for models or scripts Signup and view all the answers

What is the formula for calculating the confidence interval in the context of Moran's I?

CI = Moran's I +/- z * sd Signup and view all the answers

What is the key concept of Complete Spatial Randomness (CSR) in spatial statistics?

Events are independent of each other and have an equal probability of occurring at any location Signup and view all the answers

What does high positive spatial autocorrelation indicate?

Similar values cluster together Signup and view all the answers

What is the purpose of hypothesis testing in spatial statistics?

To make inferences or draw conclusions about a population based on a sample of data Signup and view all the answers

What is the main purpose of spatial regression models?

To control for spatially auto-correlated error or dependent variable Signup and view all the answers

What is the term for the concept that the location of one event is independent of the location of another event?

2nd order effect Signup and view all the answers

What is the condition for a join to be counted?

wi j = xi = xj = 1 Signup and view all the answers

What is the focus of the local join count statistic?

Individual observations and their neighbors Signup and view all the answers

What is the purpose of the Global Moran's I tool?

To evaluate spatial autocorrelation based on feature locations and values Signup and view all the answers

What is the range of the normalized Moran's I Index value?

-1.0 to +1.0 Signup and view all the answers

What is the purpose of the z-score and p-value in the Global Moran's I tool?

To evaluate the significance of the Moran's I Index value Signup and view all the answers

What do the cross-products of deviation values in the Moran's I statistic indicate?

The similarity of neighboring feature values Signup and view all the answers