Similarities and differences between null and alternative hypotheses

by Posted on

Similarities and differences between null and alternative hypotheses

Null and alternative hypotheses are similar in some ways:

  • They’re both answers to the research question.
  • They both make claims about the population.
  • They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

Null hypotheses (H0) Alternative hypotheses (Ha)
Definition A claim that there is no effect in the population. A claim that there is an effect in the population.
Also known as H0 Ha 

H1
Typical phrases used
  • No effect
  • No difference
  • No relationship
  • No change
  • Does not increase
  • Does not decrease
  • An effect
  • A difference
  • A relationship
  • A change
  • Increases
  • Decreases
Symbols used Equality symbol (=, ≥, or ≤) Inequality symbol (≠, <, or >)
p ≤ α Rejected Supported
p > α Failed to reject Not supported

Here’s why students love Scribbr’s proofreading services

Discover proofreading & editing

How to write null and alternative hypotheses

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

General template sentences

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable?

  • Null hypothesis (H0): Independent variable does not affect dependent variable.
  • Alternative hypothesis (Ha): Independent variable affects dependent variable.

Test-specific template sentences

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Statistical test Null hypothesis (H0) Alternative hypothesis (Ha)
Two-sample t test  

or

One-way ANOVA with two groups

 The mean dependent variable does not differ between group 1 (µ1) and group 2 (µ2) in the population; µ1 = µ2. The mean dependent variable differs between group 1 (µ1) and group 2 (µ2) in the population; µ1 ≠ µ2.
One-way ANOVA with three groups The mean dependent variable does not differ between group 1 (µ1), group 2 (µ2), and group 3 (µ3) in the population; µ1 = µ2 = µ3. The mean dependent variable of group 1 (µ1), group 2 (µ2), and group 3 (µ3) are not all equal in the population.
Pearson correlation There is no correlation between independent variable and dependent variable in the population; ρ = 0. There is a correlation between independent variable and dependent variable in the population; ρ ≠ 0.
Simple linear regression There is no relationship between independent variable and dependent variable in the population; β1 = 0. There is a relationship between independent variable and dependent variable in the population; β1 ≠ 0.
Two-proportions z test The dependent variable expressed as a proportion does not differ between group 1 (p1) and group 2 (p2) in the population; p1 = p2. The dependent variable expressed as a proportion differs between group 1 (p1) and group 2 (p2) in the population; p1 ≠ p2.

Note: The template sentences above assume that you’re performing one-tailed tests. One-tailed tests are appropriate for most studies.

Published by Henry