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If Then Because Hypothesis Statements Statistics

Null Hypothesis (H0)

In many cases the purpose of research is to answer a question or test a prediction, generally stated in the form of hypotheses (-is, singular form) -- testable propositions. Examples:

Does a training program in driver safety result in a decline in accident rate? People who take a driver safety course will have a lower accident rate than those who do not take the course.
Who is better in math, men or women? Men are better at math than women.
What is the relationship between age and cell phone use? Cell phone use is higher for younger adults than for older adults.
Is there a relationship between education and income? Income increases with years of education.
Can public education reduce the occurrence of AIDS?The number of AIDS cases is inversely related to the amount of public education about the disease.

The statistical procedure for testing a hypothesis requires some understanding of the null hypothesis. Think of the outcome (dependent variable). From a statistical (and sampling) perspective), the null hypothesis asserts that the samples being compared or contrasted are drawn from the same population with regard to the outcome variable. This means that

  • any observed differences in the dependent variable (outcome) must be due to sampling error (chance)
  • the independent (predictor) variable does NOT make a difference

The symbol H0 is the abbreviation for the null hypothesis, the small zero stands for null.

Oddly enough, we are in a sense betting against our research judgment. If we didn't think that some factor made a difference, we probably would not be doing the research in the first place. But statistically speaking, we temporarily adopt the critical stance that our independent variable does NOT matter.

Generally, when comparing or contrasting groups (samples), the null hypothesis is that the difference between means (averages) = 0. For categorical data shown on a contingency table, the null hypothesis is that any differences between the observed frequencies (counts in categories) and expected frequencies are due to chance.

Research Hypothesis (H1)

The research hypothesis (or hypotheses -- there may be more than one) is our working hypothesis -- our prediction, or what we expect to happen. It is also called the alternative hypothesis - because it is an alternative to the null hypothesis. Technically, the claim of the research hypothesis is that with respect to the outcome variable, our samples are from different populations (remember that population refers to the group from which the sample is drawn). If we predict that math tutoring results in better performance, than we are predicting that after the treatment (tutoring), the treated sample truly is different from the untreated one (and therefore, from a different population).

The research or alternative hypothesis is abbreviated asH1, and if there are more hypotheses,H2,H3,H4, etc.

Why the Null Hypothesis (H0)?

When we pose a research question, we want to know whether the outcome is due to the treatment (independent variable) or due to chance (in which case our treatment is probably not effective). For example, the claim that tutoring improves math performance generally does not predict exactly how much improvement. Each level of improvement has a different probability associated with it, and it would take a long time and a great deal of effort to specify the probability of each of the possible outcomes that would support our research hypothesis.

On the other hand, the null hypothesis is straightforward -- what is the probability that our treated and untreated samples are from the same population (that the treatment or predictor has no effect)? There is only one set of statistical probabilities -- calculation of chance effects. Instead of directly testing H1, we test H0. If we can reject H0, (and extraneous factors are under control), we can accept H1. To put it another way, the fate of the research hypothesis depends upon what happens to H0.

Here are some research or alternative hypotheses (testable statements)

  • Exercise leads to weight loss
  • Exposure to classical music increases IQ score
  • Extroverts are healthier than introverts
  • Sensitivity training reduces racial bias

The inferential statistics do not directly address the testable statement (research hypothesis). They address the null hypothesis. Statistically, we test "not." Here are the null hypotheses:

  • Exercise is unrelated to weight loss.
  • Exposure to classical music has no effect on IQ score.
  • Extrovert and introverts are equally healthy.
  • People exposed to sensitivity training are no more tolerant than those not exposed to sensitivity training.

NOTE: The null hypothesis is NOT the opposite of the research hypothesis. The null hypothesis states that any effects observed after treatment (or associated with a predictor variable) are due to chance alone. Statistically, the question that is being answered is "If these samples came from the same population with regard to the outcome, how likely is the obtained result?"

Self-test #1

Next section: Introduction to Inferential statistics (testing hypotheses)

What is a Hypothesis?

A hypothesis is a tentative, testable answer to a scientific question. Once a scientist has a scientific question she is interested in, the scientist reads up to find out what is already known on the topic. Then she uses that information to form a tentative answer to her scientific question. Sometimes people refer to the tentative answer as "an educated guess." Keep in mind, though, that the hypothesis also has to be testable since the next step is to do an experiment to determine whether or not the hypothesis is right!

A hypothesis leads to one or more predictions that can be tested by experimenting.

Predictions often take the shape of "If ____then ____" statements, but do not have to. Predictions should include both an independent variable (the factor you change in an experiment) and a dependent variable (the factor you observe or measure in an experiment). A single hypothesis can lead to multiple predictions, but generally, one or two predictions is enough to tackle for a science fair project.

Examples of Hypotheses and Predictions

QuestionHypothesis Prediction
How does the size of a dog affect how much food it eats? Larger animals of the same species expend more energy than smaller animals of the same type. To get the energy their bodies need, the larger animals eat more food. If I let a 70-pound dog and a 30-pound dog eat as much food as they want, then the 70-pound dog will eat more than the 30-pound dog.
Does fertilizer make a plant grow bigger? Plants need many types of nutrients to grow. Fertilizer adds those nutrients to the soil, thus allowing plants to grow more. If I add fertilizer to the soil of some tomato seedlings, but not others, then the seedlings that got fertilizer will grow taller and have more leaves than the non-fertilized ones.
Does an electric motor turn faster if you increase the current? Electric motors work because they have electromagnets inside them, which push/pull on permanent magnets and make the motor spin. As more current flows through the motor's electromagnet, the strength of the magnetic field increases, thus turning the motor faster. If I increase the current supplied to an electric motor, then the RPMs (revolutions per minute) of the motor will increase.
Is a classroom noisier when the teacher leaves the room? Teachers have rules about when to talk in the classroom. If they leave the classroom, the students feel free to break the rules and talk more, making the room nosier. If I measure the noise level in a classroom when a teacher is in it and when she leaves the room, then I will see that the noise level is higher when my teacher is not in my classroom.

What if My Hypothesis is Wrong?

What happens if, at the end of your science project, you look at the data you have collected and you realize it does not support your hypothesis? First, do not panic! The point of a science project is not to prove your hypothesis right. The point is to understand more about how the natural world works. Or, as it is sometimes put, to find out the scientific truth. When scientists do an experiment, they very often have data that shows their starting hypothesis was wrong. Why? Well, the natural world is complex—it takes a lot of experimenting to figure out how it works—and the more explanations you test, the closer you get to figuring out the truth. For scientists, disproving a hypothesis still means they gained important information, and they can use that information to make their next hypothesis even better. In a science fair setting, judges can be just as impressed by projects that start out with a faulty hypothesis; what matters more is whether you understood your science fair project, had a well-controlled experiment, and have ideas about what you would do next to improve your project if you had more time. You can read more about a science fair judge's view on disproving your hypothesis here.

It is worth noting, scientists never talk about their hypothesis being "right" or "wrong." Instead, they say that their data "supports" or "does not support" their hypothesis. This goes back to the point that nature is complex—so complex that it takes more than a single experiment to figure it all out because a single experiment could give you misleading data. For example, let us say that you hypothesize that earthworms do not exist in places that have very cold winters because it is too cold for them to survive. You then predict that you will find earthworms in the dirt in Florida, which has warm winters, but not Alaska, which has cold winters. When you go and dig a 3-foot by 3-foot-wide and 1-foot-deep hole in the dirt in those two states, you discover Floridian earthworms, but not Alaskan ones. So, was your hypothesis right? Well, your data "supported" your hypothesis, but your experiment did not cover that much ground. Can you really be sure there are no earthworms in Alaska? No. Which is why scientists only support (or not) their hypothesis with data, rather than proving them. And for the curious, yes there are earthworms in Alaska.

Hypothesis Checklist

What Makes a Good Hypothesis?For a Good Hypothesis, You Should Answer "Yes" to Every Question
Is the hypothesis based on information from reference materials about the topic? Yes / No
Can at least one clear prediction be made from the hypothesis?Yes / No
Are predictions resulting from the hypothesis testable in an experiment?Yes / No
Does the prediction have both an independent variable (something you change) and a dependent variable (something you observe or measure)?Yes / No

Educator Tools for Teaching about Hypotheses

Using our Google Classroom Integration, educators can assign a quiz to test student understanding of hypotheses. Educators can also assign students an online submission form to fill out detailing the hypothesis of their science project.

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