Null hypothesis

In statistics, a null hypothesis is a hypothesis that is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. It is a hypothesis that you are interested in showing to be false! Often it is a statement about a parameter that is a property of a population, the whole population being unobservable, and the test being based on a random sample from the population. Such a parameter is often a mean or a standard deviation.

Not unusually, such a hypothesis states that the parameters, or mathematical characteristics, of two or more populations are identical. For example, if we want to compare the test scores of two random samples of men and women, the null hypothesis would be that the mean score in the male population from which the first sample was drawn was the same as the mean score in the female population from which the second sample was drawn:

H 0 :μ 1 = μ 2

where:

H₀ = the null hypothesis

μ₁ = the mean of population 1, and

μ₂ = the mean of population 2.

Alternatively, the null hypothesis can postulate that the two samples are drawn from the same population:

H 0 :μ 1 - μ 2 = 0

Formulation of the null hypothesis is a vital step in statistical significance testing. Having formulated such a hypothesis, we can then proceed to establish the probability of observing the data we have actually obtained, or data more different from the prediction of the null hypothesis, if the null hypothesis is true. That probability is what is commonly called the "significance level" of the results.

In formulating a particular null hypothesis, we are always also formulating an alternative hypothesis, which we will accept if the observed data values are sufficiently improbable under the null hypothesis. The precise formulation of the null hypothesis has implications for the alternative. For example, if the null hypothesis is that sample A is drawn from a population with the same mean as sample B, the alternative hypothesis is that they come from populations with different means (and we shall proceed to a two-tailed test of significance). But if the null hypothesis is that sample A is drawn from a population whose mean is no lower than the mean of the population from which sample B is drawn, the alternative hypothesis is that sample A comes from a population with a larger mean than the population from which sample B is drawn, and we will proceed to a one-tailed test.

A null hypothesis is only useful if it is possible to calculate the probability of observing a data set with particular parameters from it. In general it is much harder to be precise about how probable the data would be if the alternative hypothesis is true.

If experimental observations contradict the prediction of the null hypothesis, it means that either the null hypothesis is false, or we have observed an event with very low probability. This gives us high confidence in the falsehood of the null hypothesis, which can be improved by increasing the number of trials. However, accepting the alternative hypothesis only commits us to a difference in observed parameters; it does not prove that the theory or principles that predicted such a difference is true, since it is always possible that the difference could be due to additional factors not recognised by the theory.

For example, rejection of a null hypothesis (that, say, rates of symptom relief in a sample of patients who received a placebo and a sample who received a medicinal drug will be equal) allows us to make a non-null statement (that the rates differed); it does not prove that the drug relieved the symptoms, though it gives us more confidence in that hypothesis.

The formulation, testing, and rejection of null hypotheses is methodologically consistent with the falsificationist model of scientific discovery formulated by Karl Popper and widely believed to apply to most kinds of empirical research. However, concerns regarding the high power of statistical tests to detect differences in large samples have led to suggestions for re-defining the null hypothesis, for example as a hypothesis that an effect falls within a range considered negligible.

In 2002, a group of psychologists launched a new journal dedicated to experimental studies in psychology which support the null hypothesis. The Journal of Articles in Support of the Null Hypothesis (JASNH) was founded to address a scientific publishing bias against such articles. [1] According to the editors,

"other journals and reviewers have exhibited a bias against articles that did not reject the null hypothesis. We plan to change that by offering an outlet for experiments that do not reach the traditional significance levels (p < 0.05). Thus, reducing the file drawer problem, and reducing the bias in psychological literature. Without such a resource researchers could be wasting their time examining empirical questions that have already been examined. We collect these articles and provide them to the scientific community free of cost."

For example, if you want to see if there is greater divorce avoidance from Thomas Theory than from Edgar Theory, so your Null Hypothesis would be, "Thomas Theory is no more effective than Edgar Theory." If the probability of the observed results is under the null hypothesis is sufficiently low, you can accept the alternative hypothesis that Thomas Theory is indeed more effective.