Basics of statistical analysis

Statistical analysis

This term refers to a wide range of techniques to. . . 1. (Describe) 2. Explore 3. Understand 4. Prove 5. Predict . . . based on sample datasets collected from populations, using some sampling strategy.

Why?

1. We want to summarize some data in a shorter form  2. We are trying to understand some process and possible predict based on this understanding  • So we need model it, i.e. make a conceptual or mathematical representation, from which we infer the process. • But how do we know if the model is “correct”? * Are we imagining relations where there are none? * Are there true relations we haven’t found? • Statistical analysis gives us a way to quantify the confidence we can have in our inferences.

Populations and samples

• Population: a set of elements (individuals)  * Finite vs. “infinite” • Sample: a subset of elements taken from a population * Representative vs. biased • We make inferences about a population from a sample taken from it. • In some situations we can examine the entire population; then there is no inference from a sample. Example: all pixels in an image.

Types of Variables

1. Nominal  2. Ordinal 3. Interval 4. Ratio

Data analysis strategy

1. Posing the research questions  2. Examining data items and their support  3. Exploratory non-spatial data analysis 4. Non-spatial modelling  5. Exploratory spatial data analysis 6. Spatial modelling 7. Prediction 8. Answering the research questions