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How to Set Up a Hypothesis Test: Null versus Alternative

Which alternative hypothesis you choose in setting up your hypothesis test depends on what you’re interested in concluding, should you have enough evidence to refute the null hypothesis (the claim). The alternative hypothesis should be decided upon before collecting or looking at any data, so as not to influence the results.

the null hypothesis is rejected when it is true b.

CORRECTION: This misconception is based on the idea of falsification, philosopher Karl Popper's influential account of scientific justification, which suggests that all science can do is reject, or falsify, hypotheses — that science cannot find evidence that one idea over others. Falsification was a popular philosophical doctrine — especially with scientists — but it was soon recognized that falsification wasn't a very complete or accurate picture of how scientific knowledge is built. In science, ideas can never be completely proved or completely disproved. Instead, science accepts or rejects ideas based on supporting and refuting evidence, and may revise those conclusions if warranted by new evidence or perspectives.

the null hypothesis is not rejected when it is false c.

CORRECTION: This misconception may be reinforced by introductory science courses that treat hypotheses as "things we're not sure about yet" and that only explore established and accepted theories. In fact, hypotheses, theories, and laws are rather like apples, oranges, and kumquats: one cannot grow into another, no matter how much fertilizer and water are offered. Hypotheses, theories, and laws are all scientific explanations that differ in breadth — not in level of support. Hypotheses are explanations that are limited in scope, applying to fairly narrow range of phenomena. The term is sometimes used to refer to an idea about how observable phenomena are related — but the term is also used in other ways within science. Theories are deep explanations that apply to a broad range of phenomena and that may integrate many hypotheses and laws. To learn more about this, visit our page on .

CORRECTION: Scientists use all sorts of different reasoning modes at different times — and sometimes at the same time — when analyzing a problem. They also use their creativity to come up with new ideas, explanations, and tests. This isn't an either/or choice between induction and deduction. Scientific analysis often involves jumping back and forth among different modes of reasoning and creative brainstorming! What's important about scientific reasoning is not what all the different modes of reasoning are called, but the fact that the process relies on careful, logical consideration of how evidence supports or does not support an idea, of how different scientific ideas are related to one another, and of what sorts of things we can expect to observe if a particular idea is true. If you are interested in learning about the difference between induction and deduction, visit our .

the null hypothesis is probably wrong b.

CORRECTION: Perhaps because the last step of the Scientific Method is usually "draw a conclusion," it's easy to imagine that studies that don't reach a clear conclusion must not be scientific or important. In fact, scientific studies don't reach "firm" conclusions. Scientific articles usually end with a discussion of the limitations of the tests performed and the alternative hypotheses that might account for the phenomenon. That's the nature of scientific knowledge — it's inherently tentative and could be overturned if new evidence, new interpretations, or a better explanation come along. In science, studies that carefully analyze the strengths and weaknesses of the test performed and of the different alternative explanations are particularly valuable since they encourage others to more thoroughly scrutinize the ideas and evidence and to develop new ways to test the ideas. To learn more about publishing and scrutiny in science, visit our discussion of .

: In everyday language, the word usually refers to an educated guess — or an idea that we are quite uncertain about. Scientific hypotheses, however, are much more informed than any guess and are usually based on prior experience, scientific background knowledge, preliminary observations, and logic. In addition, hypotheses are often supported by many different lines of evidence — in which case, scientists are more confident in them than they would be in any mere "guess." To further complicate matters, science textbooks frequently misuse the term in a slightly different way. They may ask students to make a about the outcome of an experiment (e.g., table salt will dissolve in water more quickly than rock salt will). This is simply a prediction or a guess (even if a well-informed one) about the outcome of an experiment. Scientific hypotheses, on the other hand, have explanatory power — they are explanations for phenomena. The idea that table salt dissolves faster than rock salt is not very hypothesis-like because it is not very explanatory. A more scientific (i.e., more explanatory) hypothesis might be "The amount of surface area a substance has affects how quickly it can dissolve. More surface area means a faster rate of dissolution." This hypothesis has some explanatory power — it gives us an idea of a particular phenomenon occurs — and it is testable because it generates expectations about what we should observe in different situations. If the hypothesis is accurate, then we'd expect that, for example, sugar processed to a powder should dissolve more quickly than granular sugar. Students could examine rates of dissolution of many different substances in powdered, granular, and pellet form to further test the idea. The statement "Table salt will dissolve in water more quickly than rock salt" is not a hypothesis, but an expectation generated by a hypothesis. Textbooks and science labs can lead to confusions about the difference between a hypothesis and an expectation regarding the outcome of a scientific test. To learn more about scientific hypotheses, visit in our section on how science works.

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the result would be unexpected if the null hypothesis were true c.

CORRECTION: Perhaps because the Scientific Method presents a linear and rigid representation of the process of science, many people think that doing science involves closely following a series of steps, with no room for creativity and inspiration. In fact, many scientists recognize that creative thinking is one of the most important skills they have — whether that creativity is used to come up with an alternative hypothesis, to devise a new way of testing an idea, or to look at old data in a new light. Creativity is critical to science!

the null hypothesis is probably true d.

: In everyday language, suggests the state of being unsure of something. Scientists, however, usually use the word when referring to measurements. The uncertainty of a measurement (not to be confused with the inherent provisionality of all scientific ideas!) is the range of values within which the true value is likely to fall. In science, uncertainty is not a bad thing; it's simply a fact of life. Every measurement has some uncertainty. If you measure the length of a pen with a standard ruler, you won't be able to tell whether its length is 5.880 inches, 5.875 inches, or 5.870 inches. A ruler with more precision will help narrow that range, but cannot eliminate uncertainty entirely. For more on a related idea, see our discussion of below.

One can never prove the truth of a statistical (null) hypothesis.

: In everyday language, generally refers to something that a fortune teller makes about the future. In science, the term generally means "what we would expect to happen or what we would expect to observe if this idea were accurate." Sometimes, these scientific predictions have nothing at all to do with the future. For example, scientists have hypothesized that a huge asteroid struck the Earth 4.5 billion years ago, flinging off debris that formed the moon. If this idea were true, we would that the moon today would have a similar composition to that of the Earth's crust 4.5 billion years ago — a prediction which does seem to be accurate. This hypothesis deals with the deep history of our solar system and yet it involves predictions — in the scientific sense of the word. Ironically, scientific predictions often have to do with past events. In this website, we've tried to reduce confusion by using the words and instead of and . To learn more, visit in our section on the core of science.

failing to reject the null hypothesis when it is false.

: When we, in everyday language, say that we believe in something, we may mean many things — that we support a cause, that we have faith in an idea, or that we think something is accurate. The word is often associated with ideas about which we have strong convictions, regardless of the evidence for or against them. This can generate confusion when a scientist claims to "believe in" a scientific hypothesis or theory. In fact, the scientist probably means that he or she "" the idea — in other words, that he or she thinks the scientific idea is the most accurate available based on a critical evaluation of the evidence. Scientific ideas should always be accepted or rejected based on the evidence for or against them — not based on faith, dogma, or personal conviction.

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