Null Distribution
- The null distribution is the expected distribution of a statistic when there is no relationship between the variables.
- It provides a baseline to compare observed data and assess whether a result is unusual under the null hypothesis.
- A large deviation from the null distribution suggests the null hypothesis may not hold.
Definition
Section titled “Definition”Null distribution refers to the distribution of a statistical measure under the assumption that the null hypothesis is true — that is, the expected distribution of the measure when there is no relationship between the variables being studied.
Explanation
Section titled “Explanation”Under the null hypothesis, data are assumed to follow the null distribution for the statistic of interest. By comparing the observed distribution or observed statistic to the null distribution, analysts determine whether the observed outcome is consistent with the null hypothesis. If the observed result is significantly different from the null distribution, this suggests the null hypothesis may be false; if it is not significantly different, the null hypothesis is more plausible.
Examples
Section titled “Examples”Height and disease risk
Section titled “Height and disease risk”Consider a study of height and the risk of a particular disease. The null hypothesis is that there is no relationship between height and disease risk. Under this null hypothesis, the expected joint distribution of heights and disease incidence shows no relationship between the two variables — that expected distribution is the null distribution for this scenario.
Coin flips
Section titled “Coin flips”When testing whether a coin is fair (has a 50% chance of heads or tails), one can flip the coin many times and record counts of heads and tails. Under the null hypothesis of fairness, the expected distribution of heads and tails (equal numbers on average) is the null distribution. Observing a substantially higher number of heads than expected would suggest the coin is not fair.
Use cases
Section titled “Use cases”- Interpreting the results of statistical hypothesis tests.
- Determining whether an observed result is unlikely under the null hypothesis (assessing the likelihood of a hypothesis being true).
Notes or pitfalls
Section titled “Notes or pitfalls”- The null distribution is a baseline; conclusions depend on how unusually the observed data deviate from that baseline.
- A result significantly different from the null distribution suggests the null hypothesis may not be true; a result not significantly different supports the null hypothesis.