## Topic outline

• Data Application: Analysis
• • #### Topic 1: Estimation

We start by exploring the difference between descriptive statistics and inferential statistics, and consider how you can use your sample data to make statements about the population(s) you are studying.

If your research questions include trying to find out the true value of some population parameter, then they are 'problems of estimation'. For example:

• "What is the average daily rainfall across all of London in June?"
• "How much does the sea surface temperature vary throughout the year in the North Sea?"
• "What is the probability of rolling 3 sixes in a row with a weighted dice?

To answer all of these questions, you can use measured data to calculate appropriate statistics, like the sample mean daily rainfall, the sample variance of the sea surface temperature, or the proportion of sixes rolled during an experiment. But those statistics are only for your data - which are limited in scope. To turn these calculations into estimates of the true values, you need to use some statistical tools.

The presentation and video here introduce some of those tools and explain the concepts behind them.

• #### Topic 2: Comparison

Often, you will have research questions that involve comparing different populations, or comparing a population against a known or predicted value.

This topic introduces hypothesis tests as a useful tool for investigating whether results gained from comparing your sample datasets could be due to chance. We run through the core concepts of hypothesis testing, and then discuss how you can interpret the outputs from the tests.

As this topic references ideas of estimation, we recommend checking you are comfortable with the concepts of a sample, population, and measures of precision discussed in the first topic, before diving in to this one.

• #### Topic 3: Modelling

Statistical modelling is a powerful way of exploring the possible relationships between different variables in your data. In a lot of areas of science, particularly in climate science, complex models are created to allow us to make statements and predictions about the real world based on previously collected data.

This topic provides a very brief introduction to statistical modelling. We explore the core idea of using a sample dataset to model a population, and run through the process of creating a very simple model

We also show how the modelling process involves the other topics discussed in this module:

• Estimation: to allow you to make statements using the model, and give a measure of precision about those statements;
• Hypothesis testing: to allow you to check whether the relationships you see in your sample data could just be due to chance.

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