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Qualitative Statistics and Probability Fundamentals

## Thematic Analysis and Qualitative Statistics

Qualitative statistics: thematic analysis

1. Provide a link to the article you have selected. List the comments you have chosen, the key themes you identify and the number of times they occur from the comments

2. Describe the themes you identified and the key features that make the theme recognisable (words, metaphors, emotional language, etc.)

Probability and statistics fundamentals

3. Given the event E: “England will win the World Cup in 2022”, define the following events, both theoretically and giving a concrete example:

- an event F1 such that E and F1 are independent

- an event F2 such that E and F2 are dependent

4. Derive with mathematical steps the final formula of Bayes’ theorem. Describe in general terms in what cases the theorem is useful, and propose a concrete scenario where it can be used.

5. Describe the different scales of measurements. Provide two examples for each scale.

6. In a game, there are four medals (gold, silver, bronze and wood) on the table, but they are all wrapped with dark wrapping paper, such that it is impossible to distinguish them. You would like to find the gold medal.

The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but nowing where the gold medal was and avoiding to unwrap the gold medal if still on the table, to keep the game interesting to watch until the end.)

You have now three medals left to unwrap (one in your hand, two on the table).

At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Justify your solution by using Bayes’ theorem and calculating the conditional probabilities.

Hints: start calculating the probability of having Gold in our hands given that we know that the host unwraps Silver,