Null distribution refers to the distribution of a statistical measure under the assumption that the null hypothesis is true. In other words, it is the expected distribution of a statistical measure when there is no relationship between the variables being studied.

For example, consider a study examining the relationship between a person’s height and their risk of developing a particular disease. The null hypothesis in this case would be that there is no relationship between height and disease risk. If we were to plot the heights of a large group of people and the incidence of the disease in that group, we would expect to see no relationship between the two variables under the null hypothesis. This expected distribution is known as the null distribution.

Another example of a null distribution is in the context of a hypothesis test. Suppose we are testing the hypothesis that a coin is fair (i.e., has a 50% chance of landing on heads or tails). We could conduct an experiment by flipping the coin a large number of times and recording the number of heads and tails. Under the null hypothesis, we would expect to see an equal number of heads and tails. This expected distribution of heads and tails is the null distribution.

It is important to understand the concept of a null distribution because it helps us to interpret the results of statistical tests. If the observed distribution of a statistical measure is significantly different from the null distribution, it suggests that the null hypothesis is not true and that there is a relationship between the variables being studied.

For example, continuing with the coin flipping example, if we observed a significantly higher number of heads than tails in our experiment, this would suggest that the coin is not fair and that the probability of heads is greater than 50%. On the other hand, if the observed distribution of heads and tails is not significantly different from the null distribution, we would conclude that the coin is likely fair and that the null hypothesis is true.

In conclusion, a null distribution represents the expected distribution of a statistical measure under the assumption that the null hypothesis is true. Understanding the concept of a null distribution is important for interpreting the results of statistical tests and for determining the likelihood of a hypothesis being true.