Sign test

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This page was translated from the Dutch-language original using AI and has not been fully reviewed. Where the two differ, the Dutch version takes precedence.

The sign test is a simple non-parametric technique based on the median of the sample distribution. Suppose that the gross median annual income of a Dutch household is €30,000. The sign test examines how many observations in a sample lie above (+) or below (-) the assumed value of €30,000. A random sample of 9 households shows that 7 households have a higher income than €30,000 and that 2 households have a lower income. Is there now sufficient evidence to reject the claim (the H0 hypothesis) that H0: median = €30,000? If H0 is correct, i.e. half of Dutch households have an income higher than €30,000, this does not imply that this would be exactly the case in the sample as well (tossing a coin 10 times will not automatically give 5 heads). It does mean that, if every observation is a random draw from the Dutch population of households, there is a 50% chance that it is above €30,000. If H0 is true, then a binomial distribution can be used to calculate the probability of finding 7 households with an annual income higher than €30,000 in a sample of 9 observations. That probability turns out not to be significant: p = 0.09 = 9%. In other words, there is currently insufficient evidence to reject H0 in favor of the alternative hypothesis H1 that the median annual income differs from €30,000.

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