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Hypothesis: Framing Null Hypothesis and Alternative Hypothesis


A hypothesis (plural: hypotheses), in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. In a scientific experiment or study, the hypothesis is a brief summation of the researcher’s prediction of the study’s findings, which may be supported or not by the outcome. Hypothesis testing is the core of the scientific method.

The researcher’s prediction is usually referred to as the alternative hypothesis, and any other outcome as the null hypothesis — basically, the opposite outcome to what is predicted. (However, the terms are reversed if the researchers are predicting no difference or change, hypothesizing, for example, that the incidence of one variable will not increase or decrease in tandem with the other.) The null hypothesis satisfies the requirement for falsifiability: the capacity for a proposition to be proven false, which some schools of thought consider essential to the scientific method. According to others, however, testability is adequate, on the grounds that if there is sufficient support for a hypothesis it is not necessary to be able to conceive of a contrary outcome.

Framing Null Hypothesis

The null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups. Testing (accepting, approving, rejecting, or disproving) the null hypothesis—and thus concluding that there are or are not grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science; the field of statistics gives precise criteria for rejecting a null hypothesis.

A null hypothesis is a precise statement about a population that we try to reject with sample data.

We don’t usually believe our null hypothesis (or H0) to be true. However, we need some exact statement as a starting point for statistical significance testing.

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Null Hypothesis Examples

Often -but not always- the null hypothesis states there is no association or difference between variables or subpopulations. Like so, some typical null hypotheses are:

  • The correlation between frustration and aggression is zero (correlation-analysis);
  • The average income for men is similar to that for women (independent samples t-test);
  • Nationality is (perfectly) unrelated to music preference (chi-square independence test);
  • The average population income was equal over 2012 through 2016 (repeated measures ANOVA).

“Null” Does Not Mean “Zero”

A common misunderstanding is that “null” implies “zero”. This is often but not always the case. For example, a null hypothesis may also state that

The correlation between frustration and aggresion is 0.5.

No zero involved here and -although somewhat unusual- perfectly valid.

The “null” in “null hypothesis” derives from “nullify”: the null hypothesis is the statement that we’re trying to refute, regardless whether it does (not) specify a zero effect.

Null Hypothesis – Limitations

Thus far, we only concluded that the population correlation is probably not zero. That’s the only conclusion from our null hypothesis approach and it’s not really that interesting.

What we really want to know is the population correlation. Our sample correlation of 0.25 seems a reasonable estimate. We call such a single number a point estimate.

Now, a new sample may come up with a different correlation. An interesting question is how much our sample correlations would fluctuate over samples if we’d draw many of them. The figure below shows precisely that, assuming our sample size of N = 100 and our (point) estimate of 0.25 for the population correlation.

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Framing Alternative Hypothesis

An alternative hypothesis is one in which a difference (or an effect) between two or more variables is anticipated by the researchers; that is, the observed pattern of the data is not due to a chance occurrence. This follows from the tenets of science, in which empirical evidence must be found to refute the null hypothesis before one can claim support for an alternative hypothesis (i.e. there is in fact a reliable difference or effect in whatever is being studied). The concept of the alternative hypothesis is a central part of formal hypothesis testing.

An alternative hypothesis states that there is statistical significance between two variables. In the earlier example, the two variables are Mentos and Diet Coke. The alternative hypothesis is the hypothesis that the researcher is trying to prove. In the Mentos and Diet Coke experiment, Arnold was trying to prove that the Diet Coke would explode if he put Mentos in the bottle. Therefore, he proved his alternative hypothesis was correct.

The alternative hypothesis is generally denoted as H1. It makes a statement that suggests or advises a potential result or an outcome that an investigator or the researcher may expect. It has been categorized into two categories: directional alternative hypothesis and non-directional alternative hypothesis.

Key Differences between Null and Alternative Hypothesis

The important points of differences between null and alternative hypothesis are explained as under:-

  1. A null hypothesis is a statement, in which there is no relationship between two variables. An alternative hypothesis is a statement; that is simply the inverse of the null hypothesis, i.e. there is some statistical significance between two measured phenomenon.
  2. A null hypothesis is what, the researcher tries to disprove whereas an alternative hypothesis is what the researcher wants to prove.
  3. A null hypothesis represents, no observed effect whereas an alternative hypothesis reflects, some observed effect.
  4. If the null hypothesis is accepted, no changes will be made in the opinions or actions. Conversely, if the alternative hypothesis is accepted, it will result in the changes in the opinions or actions.
  5. As null hypothesis refers to population parameter, the testing is indirect and implicit. On the other hand, the alternative hypothesis indicates sample statistic, wherein, the testing is direct and explicit.
  6. A null hypothesis is labelled as H0 (H-zero) while an alternative hypothesis is represented by H1 (H-one).
  7. The mathematical formulation of a null hypothesis is an equal sign but for an alternative hypothesis is not equal to sign.
  8. In null hypothesis, the observations are the outcome of chance whereas, in the case of the alternative hypothesis, the observations are an outcome of real effect.


There are two outcomes of a statistical test, i.e. first, a null hypothesis is rejected and alternative hypothesis is accepted, second, null hypothesis is accepted, on the basis of the evidence. In simple terms, a null hypothesis is just opposite of alternative hypothesis.


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