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Statistics - Statistical Inference


Statistical Inference

Using data analysis and statistics to make conclusions about a population is called statistical inference.

The main types of statistical inference are:

  • Estimation
  • Hypothesis testing

Estimation

Statistics from a sample are used to estimate population parameters.

The most likely value is called a point estimate.

There is always uncertainty when estimating.

The uncertainty is often expressed as confidence intervals defined by a likely lowest and highest value for the parameter.

An example could be a confidence interval for the number of bicycles a Dutch person owns:

"The average number of bikes a Dutch person owns is between 3.5 and 6."


Hypothesis Testing

Hypothesis testing is a method to check if a claim about a population is true. More precisely, it checks how likely it is that a hypothesis is true is based on the sample data.

There are different types of hypothesis testing.

The steps of the test depends on:

  • Type of data (categorical or numerical)
  • If you are looking a at:
    • A single group
    • Comparing one group to another
    • Comparing the same group before and after a change

Some examples of claims or questions that can be checked with hypothesis testing:

  • 90% of Australians are left handed
  • Is the average weight of dogs more than 40kg?
  • Do doctors make more money than lawyers?

Probability Distributions

Statistical inference methods rely on probability calculation and probability distributions.

You will learn about the most important probability distributions in the next pages.