# Empirical Project 2 Collecting and analysing data from experiments

## Learning objectives

In this project you will:

• collect data from an experiment and enter it into Excel
• use summary measures, for example, mean and standard deviation, and line and column charts to describe and compare data
• define and explain what statistical significance means (and what it does not mean)
• calculate and interpret the p-value
• evaluate the usefulness of experiments for determining causality, and the limitations of these experiments.

### Key concepts

• Concepts needed for this project: mean, variance, correlation, and causation.
• Concepts introduced in this project: standard deviation, range, statistical significance, and p-value.

## Introduction

### CORE projects

This empirical project is related to material in:

• Unit 2 of Economy, Society, and Public Policy
• Unit 4 of The Economy.

Just as scientists use experiments to investigate how physical processes work under certain conditions, social scientists use experiments to investigate how people might behave in particular situations. Although we cannot perfectly predict how people will actually behave, the controlled environment of experiments allows us to isolate the effects of a given change and identify specific reasons for the observed behaviour. If we keep all conditions the same and only changed one thing, then we can be more certain that any differences we observe are due to that one change.

Economists use experiments to look at social interactions where one person’s decision affects the outcome for that individual and the outcomes for others. Some goods and services are called public goods because when one person bears the cost of providing the good, everyone can enjoy it. Irrigation projects and the production of new knowledge are examples of public goods. The problem with public goods provisioning is that completely self-interested people prefer to benefit from the good without paying anything for it—this is known as ‘free-riding’.

However, there are real-world examples of successful public goods provisioning, such as common irrigation projects in India and Nepal. What could explain such sustained contributions to a public good?

One explanation is that people contribute because they care about the wellbeing of others, or because they respect norms that ‘free riding is bad’. Or they might contribute for the shame they would feel (or worse) if they were publicly punished. If others in your community know that you haven’t contributed and could punish you (for example, by gossiping about you, withholding help in the future, or ostracizing you), then you may contribute either out of self-interest or because you want to be able to think of yourself as a good person. To see whether punishment could result in sustained contributions to a public good, researchers Herrmann, Thöni, and Gächter (2008) did a study where different groups of people, in various countries, participated in two public goods experiments.

The first experiment had ten rounds. In each round:

• Each person in the experiment (we call them subjects) is given $20. • The subjects are randomly sorted into small groups, typically of four people who don’t know each other. • They are asked to decide on a contribution from their$20 to a common pool of money.
• The pool of money is a public good. For every dollar contributed, each person in the group receives $0.40, including the contributor. • After each round, the participants are told how much other members of their group contributed. The second experiment was the same as the first, except with an additional punishment option. After observing the contributions of their group, individual players could pay to punish other players by making them pay a$3 fine. The punisher remained anonymous but had to pay \$1 per player punished. You can read the Herrmann et al. (2008) study, and the economic concepts behind their experiment in Section 2.7 of Economy, Society, and Public Policy.

In this project, we will first learn more about how experimental data can be collected by playing a public goods game to collect our own data. Then we will look at ways to describe and analyse the experimental data from the two experiments described above, in order to answer the following research questions:

• Were there any differences in behaviour (average contributions) between the experiments?
• Can we attribute the observed differences in behaviour to the change in conditions, rather than to chance or coincidence?