1.1 Two types of hypothesis

At the core of hypothesis testing are two fundamental concepts: the null hypothesis and the alternative hypothesis. These form the backbone of the testing process and guide our interpretation of the results.

The null hypothesis is denoted as H₀. It serves as the default assumption, positing that there is no relationship between variables or that a population parameter equals a specified value. For instance, if we are testing whether a new training program improves employee productivity, the null hypothesis might state that the program has no effect on productivity.

On the other hand, the alternative hypothesis, represented as H₁ or H_a, is the statement that the decision-maker aims to demonstrate. It suggests that there is indeed an effect or a difference. In our training program example, the alternative hypothesis would state that the program does improve productivity.

To illustrate these concepts further, let us explore some examples that showcase the interplay between null and alternative hypotheses:

1. For centuries, the prevailing belief in astronomy was the geocentric model, which posited that the Earth was the centre of the universe. This theory, championed by ancient Greek philosophers like Aristotle and later refined by Ptolemy, served as the null hypothesis of its time. This belief persisted until the 16th century when Nicolaus Copernicus proposed a heliocentric model, suggesting that the Sun, not the Earth, was at the centre of the solar system. This revolutionary idea formed the alternative hypothesis.

• H₀: All planets orbit around the Earth.
• H₁: Not all planets orbit around the Earth.

Figure 2 Solar system

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Description: The image depicts a representation of our solar system. The central and most prominent feature is the Sun, depicted as a large, glowing, fiery ball in the middle of the image. Surrounding the Sun are the planets of the solar system, shown in their respective orbits as ellipses around the Sun.

Figure 2 Solar system

2. The gold standard, a monetary system where the value of a country’s currency is directly linked to gold, was widely adopted in the late 19th and early 20th centuries. This system represented a null hypothesis in economic theory. However, the Great Depression of the 1930s severely tested this hypothesis. As economic conditions worsened, many countries found the gold standard limited their ability to implement expansionary monetary policies to combat the depression. This led to the formulation of an alternative hypothesis.

• H₀: The value of paper money is equal to a fixed amount of gold.

• H₁:The value of paper money is not equal to a fixed amount of gold.

The United Kingdom abandoned the gold standard in 1931, followed by the United States in 1933. The economic recovery that followed in these countries provided evidence supporting the alternative hypothesis, leading to a fundamental shift in monetary policy.

3. For much of modern history, the value of money has been based on trust in central banks and governmental authorities. This forms our current null hypothesis in monetary theory. However, the advent of cryptocurrencies, particularly Bitcoin in 2009, has challenged this notion. Bitcoin operates on a decentralised network, independent of any central authority. This new form of currency presents an alternative hypothesis.

• H₀: The value of paper money is equal to people’s trust in central banks or monetary authorities.

• H₁:The value of paper money is not equal to people’s trust in central banks or monetary authorities.

While cryptocurrencies have gained significant traction, their role in the global financial system is still evolving. This ongoing "experiment" continues to test our hypotheses about the nature of money and value.