Null hypothesis

Dina statistik, **hipotesis kosong** (Ing: *null hypotesis*) nyaéta hipotesis nu mibanda anggapan awal bener lamun kajadian statistik dina bentuk tes hipotesis nunjukkeun sabalikna. Hipotesis kosong nyaéta hiji hipotesis yén urang mikaresep kana hiji hal nu nembongkeun hal éta téh palsu atawa salah! Salawasna ieu katangtuan téh ngeunaan hiji parameter nu ngagambarkeun sifat tina hiji populasi, nu mana sakabéh populasi ieu teu katalungtik, sarta tes dumasar kana sampel acak tina populasi ieu. Nu dimaksud sababaraha paraméter ieu, ilaharna nu dipaké nyaéta méan jeung simpangan baku.

Not unusually, such a hypothesis states that the parameters, or mathematical characteristics, of two or more populasi 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 méan score in the male population from which the first sample was drawn was the same as the méan score in the female population from which the second sample was drawn:

:H_0: \mu_1 = \mu_2

where:
:*H*0 = the null hypothesis
:&mu;1 = the mean of population 1, and
:&mu;2 = the mean of population 2.

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

:H_0: \mu_1 - \mu_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 méan as sample B, the alternative hypothesis is that they come from populations with *different* méans (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 méan is no lower than the méan of the population from which sample B is drawn, the alternative hypothesis is that sample A comes from a population with a *larger* méan 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 paraméters 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 méans 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 incréasing the number of trials. However, accepting the alternative hypothesis only commits us to a difference in observed paraméters; it does not prove that the théory 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 théory.

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 maké 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 modél 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.  http://www.jasnh.com/ 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 gréater divorce avoidance from Thomas Théory than from Edgar Théory, 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 Théory is indeed more effective.

Tempo oge: tes hipotesa statistik.