Alternative Hypothesis-Definition, Types and Examples

Edited By Team Careers360 | Updated on Jul 02, 2025 05:16 PM IST

A hypothesis is a working assertion based on scant data. As a result, there arises a requirement for additional testing. A statistical hypothesis test is a technique for determining if the available data are sufficient to support a given hypothesis. Hypothesis testing can be used to make probabilistic claims about the characteristics of the population. There are two types of hypotheses:

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Alternative hypothesis
Types of alternative hypothesis
Null hypothesis
Differences and similarities between null and alternative hypothesis
Examples

Null hypothesis
Alternative hypothesis

Alternative hypothesis

The alternative hypothesis is a hypothesis under which a statistically significant association exists between two variables. It is denoted by Ha or H1. It is also called the research hypothesis. The alternative hypothesis is typically a claim that a researcher believes to be true and that rejects the null hypothesis. An alternative hypothesis is complementary to the null hypothesis and thus, only one of them can be true at a time. Suppose, your null hypothesis is ‘Harry will get more than 20 marks in the test’ then the alternative hypothesis will be ‘Harry will get less than or equal to 20 marks in the test’.

Types of alternative hypothesis

There are three types of alternative hypotheses:

Left-tailed: In this type of hypothesis, the sample proportion (ᴨ) is less than a specific value (ᴨ0).

Ha : ᴨ < ᴨ0

Right-tailed: In this type of hypothesis the sample proportion (ᴨ) is greater than a specific value (ᴨ0).

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Ha : ᴨ > ᴨ0

Two-tailed: In this type of hypothesis the sample proportion (ᴨ) is not equal to a specific value (ᴨ0).

Ha: ᴨ ≠ ᴨ0

Null hypothesis

A null hypothesis is a hypothesis in which there is no statistically significant relationship between two variables. It is denoted by the symbol H0. Researchers try to reject the null hypothesis and always write the null hypothesis in terms of ‘no effect’, ‘no difference’, or ‘no relation’. One should never prove or accept the null hypothesis.

Differences and similarities between null and alternative hypothesis

Differences between null and alternate hypothesis:

NULL HYPOTHESIS	ALTERNATIVE HYPOTHESIS
It states there is no statistical relationship between two variables.	It states there is a statistically important relationship between two variables.
A claim that effects on the population don’t exist.	A claim that there is an effect on the population.
The researcher tries to reject this hypothesis.	The researcher assumes this hypothesis to be true.
It is denoted by H0.	It is denoted by Ha.

Similarities between null and alternative hypotheses:

They are both solutions to research problems.
Statistical tests are used to examine them.

Examples

We want to determine if the mean salary of employees in an office is different from $75,000. The null and alternative hypotheses are:

H0: ᴨ = $75,000

Ha: ᴨ ≠ $75,000

Let us take a decision in a court as a statistical hypothesis test. The null hypothesis is that the defendant is assumed to be innocent while the alternative hypothesis states that the defendant is guilty. The defendant is innocent until proven guilty likewise it is presumed that the null hypothesis is true in a hypothesis test until proven otherwise. There must be sufficient evidence to prove the alternative hypothesis true that is to prove the defendant guilty.

Only legitimate evidence may be used in a court as the basis for a trial. To determine the statistical significance of the null hypothesis in hypothesis testing, an acceptable test statistic should be used. If the null hypothesis is proven wrong at a particular level of significance, evidence would back up the alternative hypothesis.

Frequently Asked Questions (FAQs)

1. What are the two types of hypotheses?

Null hypothesis and alternative hypothesis are the two types of hypothesis.

2. What are null and alternative hypotheses?

The null hypothesis states that there’s no relationship between variables while the alternative hypothesis states that there’s a statistically important relation between variables. The researcher tries to reject the null hypothesis while the alternative hypothesis is assumed to be true.

3. Which symbol is used to represent alternative hypothesis?

Alternative hypothesis is denoted by Ha or H1.

4. What is another name for the alternative hypothesis?

Alternative hypothesis is also called the research hypothesis.

5. Which hypothesis is true in the researcher’s view?

The alternative hypothesis is assumed to be true by the researcher.

6. What is an alternative hypothesis in statistics?

An alternative hypothesis, often denoted as H1 or Ha, is a statement that contradicts the null hypothesis in statistical testing. It represents the possibility that there is a significant effect, relationship, or difference in the population being studied. The alternative hypothesis is what researchers are typically trying to provide evidence for in their studies.

7. What is the importance of clearly stating the alternative hypothesis before conducting a study?

Clearly stating the alternative hypothesis before conducting a study is crucial for several reasons:

8. How does the concept of effect size relate to the alternative hypothesis?

Effect size is closely related to the alternative hypothesis. While the alternative hypothesis states that there is an effect or difference, the effect size quantifies the magnitude of this difference. In power analysis, the alternative hypothesis often includes an assumption about the expected effect size, which helps determine the sample size needed for the study.

9. How does the alternative hypothesis relate to confidence intervals?

The alternative hypothesis and confidence intervals are complementary ways of presenting statistical results. While hypothesis testing gives a binary decision (reject or fail to reject the null), confidence intervals provide a range of plausible values for the parameter. If a confidence interval doesn't include the null hypothesis value, it supports the alternative hypothesis.

10. How does the formulation of the alternative hypothesis affect the p-value interpretation?

The formulation of the alternative hypothesis affects how you interpret the p-value. For a two-tailed test, the p-value represents the probability of obtaining a result as extreme as or more extreme than the observed result in either direction. For a one-tailed test, it represents this probability in only one direction, as specified by the alternative hypothesis.

11. How does the alternative hypothesis differ from the null hypothesis?

The alternative hypothesis is the opposite of the null hypothesis. While the null hypothesis typically assumes no effect or relationship, the alternative hypothesis suggests that there is an effect, relationship, or difference. The goal of statistical testing is often to gather evidence to reject the null hypothesis in favor of the alternative hypothesis.

12. Can an alternative hypothesis ever be proven true?

No, an alternative hypothesis cannot be proven true in the strict sense. Statistical tests can only provide evidence in support of the alternative hypothesis by rejecting the null hypothesis. This is why we say we "fail to reject" the null hypothesis rather than "accept" the alternative hypothesis. Science operates on the principle of falsification, not proof.

13. What is the role of the alternative hypothesis in power analysis?

In power analysis, the alternative hypothesis helps determine the effect size, which is crucial for calculating statistical power. The alternative hypothesis specifies the magnitude of the effect you expect to detect, allowing you to estimate the sample size needed to achieve a desired level of power in your study.

14. How does the alternative hypothesis relate to Type II errors?

The alternative hypothesis is directly related to Type II errors. A Type II error occurs when we fail to reject the null hypothesis when the alternative hypothesis is actually true. The probability of a Type II error (β) is used to calculate statistical power (1 - β), which is the probability of correctly rejecting the null hypothesis when the alternative is true.

15. What is the relationship between the alternative hypothesis and the significance level (α)?

The significance level (α) is used in conjunction with the alternative hypothesis to make decisions in hypothesis testing. It represents the probability of rejecting the null hypothesis when it's actually true (Type I error). The alternative hypothesis helps determine the critical region in the sampling distribution, which is based on the chosen significance level.

16. Can you provide an example of a left-tailed alternative hypothesis?

A left-tailed alternative hypothesis states that the effect is less than a specific value. For example, if a company claims that its new production method reduces defects to less than 5%, the alternative hypothesis could be: H1: p < 0.05, where p represents the proportion of defects.

17. How does the alternative hypothesis influence the choice of statistical test?

The alternative hypothesis helps determine the appropriate statistical test by specifying the nature of the relationship or difference you're looking for. For example, a two-tailed alternative hypothesis about comparing two group means might lead you to use a two-sample t-test, while a hypothesis about the relationship between two variables might lead to a correlation or regression analysis.

18. Can you have multiple alternative hypotheses for a single null hypothesis?

While it's common to have one alternative hypothesis for each null hypothesis, it's possible to have multiple alternative hypotheses. This is often seen in ANOVA (Analysis of Variance) where you might have several group means to compare. However, it's important to adjust for multiple comparisons to control the overall Type I error rate.

19. What is the difference between a point alternative hypothesis and an interval alternative hypothesis?

A point alternative hypothesis specifies a single value for the parameter of interest, such as H1: μ = 10. An interval alternative hypothesis specifies a range of values, such as H1: μ > 10 or H1: 5 < μ < 15. Interval alternative hypotheses are more common in practice as they allow for a range of possible effects.

20. Can you explain the concept of the "region of rejection" in relation to the alternative hypothesis?

The region of rejection, also known as the critical region, is the set of values for the test statistic that leads to rejecting the null hypothesis in favor of the alternative hypothesis. The shape and location of this region depend on whether the alternative hypothesis is one-tailed or two-tailed and on the chosen significance level (α).

21. What are the three main types of alternative hypotheses?

The three main types of alternative hypotheses are:

22. When would you use a two-tailed alternative hypothesis?

A two-tailed alternative hypothesis is used when you want to test for a difference in either direction, without specifying whether the effect will be positive or negative. For example, if you're testing whether a new teaching method affects test scores, but you're not sure if it will increase or decrease them, you would use a two-tailed hypothesis.

23. What is the difference between a one-tailed and a two-tailed alternative hypothesis?

A one-tailed alternative hypothesis (either left-tailed or right-tailed) specifies the direction of the effect or relationship being tested. It states that the effect is either greater than or less than a certain value. A two-tailed hypothesis, on the other hand, doesn't specify a direction and simply states that there is a difference or effect, regardless of its direction.

24. What does a right-tailed alternative hypothesis look like?

A right-tailed alternative hypothesis states that the effect is greater than a specific value. For instance, if a researcher believes that a new drug increases average lifespan by more than 2 years, the alternative hypothesis could be: H1: μ > 2, where μ represents the mean increase in lifespan.

25. How do you choose between a one-tailed and a two-tailed alternative hypothesis?

The choice between a one-tailed and two-tailed alternative hypothesis depends on your research question and prior knowledge. Use a one-tailed hypothesis when you have a specific directional prediction based on previous research or theory. Use a two-tailed hypothesis when you're unsure about the direction of the effect or when you want to test for differences in both directions.

26. How does the formulation of the alternative hypothesis affect the interpretation of results?

The formulation of the alternative hypothesis directly impacts how you interpret your results. For a one-tailed hypothesis, you're only considering effects in one direction, which can lead to more powerful tests but may miss effects in the opposite direction. For a two-tailed hypothesis, you're considering effects in both directions, which is more conservative but allows for unexpected findings.

27. What is the difference between a simple and composite alternative hypothesis?

A simple alternative hypothesis specifies a single, exact value for the parameter being tested. For example, H1: μ = 10. A composite alternative hypothesis specifies a range of values. For example, H1: μ > 10 or H1: μ ≠ 10. Most alternative hypotheses in practice are composite.

28. What is the relationship between the alternative hypothesis and the concept of statistical significance?

The alternative hypothesis is central to the concept of statistical significance. A result is considered statistically significant if it provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The threshold for significance is determined by the chosen significance level (α), which is compared to the p-value of the test.

29. How does the alternative hypothesis influence the interpretation of confidence intervals?

The alternative hypothesis helps interpret confidence intervals by providing context. If the confidence interval doesn't include the null hypothesis value but includes values consistent with the alternative hypothesis, it supports the alternative. The width of the interval also gives information about the precision of the estimate, which is related to the effect size specified in the alternative hypothesis.

30. What is the role of the alternative hypothesis in meta-analysis?

In meta-analysis, the alternative hypothesis guides the overall research question and the selection of studies to include. It also influences the choice of effect size measure and the interpretation of the pooled results. Meta-analyses often use more complex alternative hypotheses that account for heterogeneity across studies.

31. How does the concept of statistical power relate to the alternative hypothesis?

Statistical power is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. It's directly related to the alternative hypothesis because the power calculation requires specifying an effect size, which is essentially a more precise version of the alternative hypothesis. Higher power increases the likelihood of detecting a true effect as specified by the alternative hypothesis.

32. Can you explain the concept of the "least favorable configuration" in relation to composite alternative hypotheses?

The least favorable configuration refers to the specific value within a composite alternative hypothesis that is closest to the null hypothesis. This configuration is used in power calculations because it represents the most challenging scenario for rejecting the null hypothesis. By ensuring adequate power for the least favorable configuration, you ensure power for all other values in the alternative hypothesis.

33. How does the alternative hypothesis relate to the concept of practical significance?

While the alternative hypothesis and statistical significance focus on whether an effect exists, practical significance considers whether the effect is large enough to be meaningful in real-world terms. The alternative hypothesis can incorporate practical significance by specifying an effect size that is considered meaningful, rather than just statistically different from zero.

34. What is the relationship between the alternative hypothesis and the concept of a minimum detectable effect?

The minimum detectable effect (MDE) is the smallest true effect size that a study can reliably detect given its sample size and chosen significance level. It's closely related to the alternative hypothesis, as the MDE is essentially the smallest effect size for which the study has adequate power to support the alternative hypothesis over the null.

35. How does the alternative hypothesis influence the design of experimental studies?

The alternative hypothesis plays a crucial role in experimental design by:

36. What is the difference between a precise and an imprecise alternative hypothesis?

A precise alternative hypothesis specifies an exact effect size or a narrow range of values, such as H1: μ = 10 or H1: 9 < μ < 11. An imprecise alternative hypothesis is less specific, such as H1: μ ≠ 0 or H1: μ > 0. Precise hypotheses allow for more powerful statistical tests but require stronger prior knowledge or theoretical justification.

37. How does the concept of effect size estimation relate to the alternative hypothesis?

Effect size estimation is closely tied to the alternative hypothesis. While the alternative hypothesis posits the existence of an effect, effect size estimation quantifies the magnitude of this effect. After rejecting the null hypothesis, researchers often estimate and report effect sizes to provide a more nuanced understanding of their findings, which relates back to the original alternative hypothesis.

38. What is the role of the alternative hypothesis in sequential analysis or interim analyses?

In sequential analysis or interim analyses, where data is analyzed multiple times during a study, the alternative hypothesis helps define stopping rules. These rules determine when to stop the study early, either for efficacy (if strong evidence supports the alternative hypothesis) or futility (if it's unlikely that continued data collection will support the alternative hypothesis).

39. How does the formulation of the alternative hypothesis affect the choice between parametric and non-parametric tests?

The alternative hypothesis can influence the choice between parametric and non-parametric tests. Parametric tests often have more specific alternative hypotheses about population parameters (e.g., means, variances), while non-parametric tests may have more general alternative hypotheses about distribution shapes or ranks. The nature of your alternative hypothesis should align with the assumptions and capabilities of your chosen test.

40. What is the relationship between the alternative hypothesis and the concept of statistical models?

The alternative hypothesis is an integral part of statistical modeling. In model comparison approaches, different models often represent different alternative hypotheses. The process of model selection can be seen as choosing between different alternative hypotheses about the underlying data-generating process. The chosen model then becomes the basis for inference and prediction.

41. How does the alternative hypothesis relate to the concept of false discovery rate in multiple hypothesis testing?

In multiple hypothesis testing, the false discovery rate (FDR) is the expected proportion of false positives among all rejected null hypotheses. The alternative hypothesis is crucial here because the FDR depends on both the number of true null hypotheses and the number of true alternative hypotheses. Methods for controlling the FDR often make assumptions about the proportion and effect sizes of true alternative hypotheses.

42. What is the role of the alternative hypothesis in Bayesian hypothesis testing?

In Bayesian hypothesis testing, the alternative hypothesis is explicitly modeled and assigned a prior probability. The analysis computes the posterior probabilities of both the null and alternative hypotheses given the data. This approach allows for statements about the relative evidence for the alternative hypothesis compared to the null, rather than just rejecting or failing to reject the null.

43. How does the concept of equivalence testing relate to traditional alternative hypotheses?

Equivalence testing flips the traditional roles of null and alternative hypotheses. In equivalence testing, the null hypothesis is that there is a meaningful difference, while the alternative hypothesis is that any difference is too small to be practically significant. This approach is useful when the goal is to demonstrate that two treatments or groups are sufficiently similar, rather than different.

44. What is the relationship between the alternative hypothesis and the concept of statistical learning in machine learning?

In statistical learning and machine learning, the alternative hypothesis can be seen as analogous to the model or algorithm being trained. Just as a statistical alternative hypothesis proposes a specific relationship or effect, a machine learning model proposes a specific mapping from inputs to outputs. The process of model training and validation is similar to testing and refining alternative hypotheses in traditional statistics.

45. How does the alternative hypothesis relate to the concept of effect size heterogeneity in meta-analysis?

In meta-analysis, effect size heterogeneity refers to the variation in true effect sizes across studies. The alternative hypothesis in a meta-analysis often needs to account for this heterogeneity. Instead of a simple alternative hypothesis of a single true effect size, meta-analyses often use more complex alternatives that model the distribution of effect sizes across studies, such as random-effects models.

46. What is the role of the alternative hypothesis in defining and interpreting confidence intervals?

The alternative hypothesis provides context for interpreting confidence intervals. While confidence intervals are often associated with null hypothesis testing, they can be viewed as a range of plausible values for the parameter of interest under the alternative hypothesis. If a confidence interval excludes the null hypothesis value but includes values consistent with the alternative hypothesis, it provides support for the alternative.

47. How does the concept of clinical significance relate to statistical alternative hypotheses?

Clinical significance focuses on whether an effect is large enough to be meaningful in practice, which may differ from statistical significance. When formulating alternative hypotheses for clinical research, it's important to consider not just whether an effect exists (statistical significance) but whether it meets a threshold of clinical importance. This can be incorporated into the alternative hypothesis by specifying a minimum clinically important difference.

48. What is the relationship between the alternative hypothesis and the concept of statistical bias?

The alternative hypothesis can influence statistical bias in several ways. Researchers might be biased towards finding evidence for their alternative hypothesis, leading to issues like p-hacking or selective reporting. Additionally, if the alternative hypothesis is incorrectly specified (e.g., assuming a linear relationship when the true relationship is non-linear), it can lead to biased estimates and incorrect conclusions.

49. How does the alternative hypothesis relate to the concept of statistical efficiency?

Statistical efficiency refers to how well a statistical method uses the available data to estimate parameters or test hypotheses. A well-specified alternative hypothesis can lead to more efficient statistical tests. For example, if you have a directional alternative hypothesis and use a one-tailed test, it will be more efficient