Null and alternative hypotheses are important parts of scientific papers and in college projects involving psychological research or data analysis.
This article explains how to write about both types of hypotheses in your academic essays.
Definition: Null and alternative hypotheses
These two hypotheses are used in statistical testing to prove or disprove a theory.
- The null hypothesis always states that there’s no statistically significant relationship between variables.
- The alternative hypothesis states the opposite.
Null/Alternative hypotheses: Research questions
These hypotheses function as tentative answers to research questions. Therefore, you can’t have an answer to your research questions without confirming or rejecting either hypothesis.
Both hypotheses are tested using statistical tests that compare two population samples/groups. Testing confirms or rejects the hypotheses, by showing whether there’s a relationship between an independent variable and a dependent variable.
The null hypothesis (H0)
The null hypothesis states that there’s no statistically significant relationship or effect between variables.
Based on test results, the null hypothesis can be rejected, which means there is a significant relationship between the variables – one affects the other.1
When writing about null hypotheses, you can only reject them or fail to reject them. Don’t use expressions like accepting, proving, or disproving.
Depending on sample size and testing method, you can incur errors when determining the validity of null hypotheses.
- A Type I error happens if you reject H0 and claim there’s a significant relationship between the variables, even though test results don’t support this claim.
- A Type II error happens if you fail to reject H0 and claim there’s no relationship between variables, even though testing proves otherwise.2
Examples of null hypotheses
|Does exercise lower the risk of heart disease?||Exercise has no effect on heart disease risk|
|Does age affect employability?||Age has no effect on employability|
The alternative hypothesis (Ha)
The alternative hypothesis (Ha or H1) claims there’s a statistically significant relationship between variables.
Because Ha is the opposite of what the null hypothesis claims, accepting Ha means rejecting H0 and vice versa.3
When reporting alternative hypotheses, you can only say that Ha is supported or not supported by test data. Don’t use expressions like accept, reject, disprove, confirm, etc.
Examples of alternative hypotheses
|Does exercise lower the risk of heart disease?||Exercise has an effect on heart disease risk|
|Does age affect employability?||Age has an effect on employability|
Null hypothesis vs. alternative hypothesis
Both hypotheses provide possible but mutually exclusive answers to a research question. They can only be rejected or supported through statistical testing.
The differences between them are:
|Null hypothesis (H0)||Alternative hypothesis (Ha)|
|Claims there’s no relationship between variables.||Claims there isa relationship between variables.|
|Common expressions used to write it include no relationship, no effect, no difference, no increase, no decrease, and no change.||Common expressions used to write it include a relationship, an effect, a difference, an increase, a decrease, and a change.|
|If testing shows there’s a relationship, this is reported as p ≤ α, therefore H0 is rejected.||If testing shows there’s a relationship,
this is reported as p ≤ α, therefore Ha is supported.
|If testing shows there’s no relationship, this is reported as p > α, therefore we fail to reject H0.||If testing shows no relationship, this is reported as p > α, therefore Ha is not supported.|
Writing null and alternative hypotheses correctly
To write these hypotheses correctly in your essay, make sure you:
- Write your research question, mentioning both independent and dependent variables
- State the null hypothesis
- State the alternative hypothesis.
For specific tests, use the following wording:
|Two-sample t test||The mean dependent variable has no effect on sample 1 (µ1) and sample 2 (µ2); µ1 = µ2||The mean dependent variable has an effect on sample 1 (µ1) and sample 2 (µ2); µ1 ≠ µ2.|
|One-way ANOVA||The mean dependent variable has no effect on sample/group 1 (µ1) and sample/group 2 (µ2); µ1 = µ2||The mean dependent variable (µ1) and sample/group 2 (µ2) are not all equal; µ1 ≠ µ2 ≠ µ3.|
|Pearson correlation||There’s no correlation between the independent variable and the dependent variable: ρ = 0.||There's a correlation between
the independent variable and ρ = 0 the dependent variable; ρ ≠ 0.
|Simple linear regression||There’s no relationship between the independent variable and the dependent variable; β1 = 0.||There’s a relationship between the independent variable and
the dependent variable; β1 ≠ 0.
|Two proportions||The dependent variable expressed as a proportion doesn’t differentiate between sample/group 1 (ρ1) and sample/group 2 (ρ2); ρ1 = ρ2.||The dependent variable expressed as proportion differentiates between sample/group 1 (ρ1) and sample/group 2 (ρ2); p1 ≠ p2.|
They’re unproven statements about a research question.
The null hypothesis says there’s a relationship between variables, and the alternative hypothesis claims there isn’t one.
No, these hypotheses are competing statements, so when you test one hypothesis, you automatically test the other.
The mathematical symbol used to write H0 is =
For Ha, the symbol is ≠
In most cases, one-tailed tests are best.
1 Glen, Stephanie. “Null Hypothesis Definition and Examples, How to State.” StatisticsHowTo.com. Accessed 9 December 2022. https://www.statisticshowto.com/probability-and-statistics/null-hypothesis/.
2 McLeod, Dr. Saul. “What are Type I and Type II Errors?” Simply Psychology. July 4, 2019. https://www.simplypsychology.org/type_I_and_type_II_errors.html.
3 Glen, Stephanie. “Alternate Hypothesis in Statistics: What is it?” StatisticsHowTo.com. Accessed 9 December 2022. https://www.statisticshowto.com/what-is-an-alternate-hypothesis/.