2 Forming Hypotheses Multiple Hypotheses and the Null

2. Forming Hypotheses Multiple Hypotheses and the Null Hypothesis • It is very important to have at least two hypotheses when performing investigations • Any potential tests of a hypothesis must measure its success compared to alternative hypotheses • The simplest alternative hypothesis is the “null hypothesis” • Suppose you have a hypothesis that A and B go together • Null hypothesis states that A and B have no connection – they are uncorrelated • Horoscopes predict your personality – Horoscopes have no predictive power for your personality • Aspirin diminishes headaches – Aspirin has no effect on headaches • Letters are arranged in boxes such that pairs of letters often appear near each other – Letters were arranged completely at random

Falsifiability • The most important aspect of a hypothesis is that it is falsifiable – Can be conclusively demonstrated to be false Which hypothesis is best: • When you release an object at rest, it will 1. Move either up or down 2. Fall down 3. Fall down with a speed proportional to the time it has fallen 4. Fall down with a speed proportional to the time it has fallen, with the same proportionality constant for all objects • The last hypothesis is the best, as it is most specific • It is the easiest to falsify • It is rare we get examples as clean as this

3. Discarding Hypotheses When Can We Immediately Reject Hypotheses? Not all hypotheses deserve to be experimentally tested • Some are so vague that we can’t test them – They make claims about intangible quantities that can’t be measured – Or invoke claims that • Some are so poorly motivated that they aren’t worth investigating • Some are so difficult to test that it just isn’t worth it • Some hypotheses can be rejected because they contradict well-tested previous data • Other hypotheses are self-contradictory

Rejecting Hypotheses Based on Old Data • We already have a wealth of data about the world around us • When a new hypothesis is proposed, we should first figure out how it disagrees with things we already know (or think we’ll know) • Often it will contradict a previously accepted theory – That’s okay – But it should explain why the previous theory worked up until now • Example, Einstein’s Special Theory of Relativity: – Rewrote all of Newton’s Laws • For example, the formula for momentum changed • But it was pointed out that for small velocities, the quantity v/c was small • So for low velocities, the formulas were almost identical • In other cases, it is found that the data underlying the existing theory is false

Rejecting Self-Contradictory or Illogial Hypotheses Some hypotheses make no logical sense • For example, some horoscopes claim they can help you pick winning lottery numbers based on your birth date • But there is only one winning lottery number • It therefore makes no sense to have customized lottery numbers Rejecting Poorly Motivated and Expensive Hypotheses Some hypotheses are so poorly motivated and difficult to test that we don’t test them • Once had a person claim they could cure AIDS with their touch – no evidence given • I could not find a doctor to help me participate in a test of this hypothesis