Statistical hypothesis testing · BEGINNER LESSON
Two-sided test
A two-sided test is a binary hypothesis test with a null hypothesis of the form H0: θ = θ0 and an alternative H1: θ ≠ θ0. It asks whether the unknown scalar parameter could be either above or below the null value.
What it is
A two-sided test is a way to decide between two hypotheses when the unknown parameter is a single number, called a scalar parameter. The null hypothesis says the parameter equals a specific value θ0, and the alternative says it is not equal to θ0. In other words, the alternative allows the true value to lie on either side of the null value. [0]
How it works
In hypothesis testing, data are summarized with a test statistic, and that statistic is compared with what would be expected if the null hypothesis were true. For a two-sided test, the rejection region is split across both tails of the null distribution, because unusually large positive or unusually large negative values can both count against H0. The p-value is the probability, under H0, of seeing a result at least as extreme as the one observed in either direction. [1,2]
[2] web.stanford.edu › class › bios221Modern Statistics for Modern Biology - 6 Testing [3] Empowering statistical methods for cellular and molecular biologists
Why it is used
Two-sided tests are used when the direction of a possible effect is not fixed in advance. For example, if a treatment could make a measured outcome larger or smaller, a two-sided test leaves room for both possibilities. In biology and other sciences, this helps quantify whether data support or refute a proposed effect without assuming the sign of the effect beforehand. [1,2]
[2] web.stanford.edu › class › bios221Modern Statistics for Modern Biology - 6 Testing [3] Empowering statistical methods for cellular and molecular biologists
Limitations and assumptions
Two-sided and one-sided tests are defined only for scalar parameter spaces, and at least one hypothesis must be composite. The results also depend on modeling assumptions such as randomization, exchangeability, and often independence of observations. If those assumptions do not fit the study design, the test may not be accurate. [0,2]
[1] Hypothesis Testing [3] Empowering statistical methods for cellular and molecular biologists
SEE THE IDEA
Two-sided test in a hypothesis-testing workflow
The parameter equals a chosen value θ0.
A number computed from the data to summarize evidence.
Extreme values on either side count against H0.
Reject H0 or do not reject H0 based on the p-value or critical region.
Data are summarized by a test statistic, which is compared with the null distribution; extremes in either tail can lead to rejection.
A two-sided test spreads evidence against H0 across both directions instead of only one.
TRY IT YOURSELF
Test your understanding
Choose an answer, then check the explanation.
PUT IT TOGETHER
Match each concept to its meaning
Drag a label onto its description, or select a label and then select a description. This also works with a keyboard.
4 pairs to match
Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.