List the two conditions that must be met in order to use the paired-sample sign test.

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1. The first condition for using the paired-sample sign test is that the data must consist of paired observations. This means that each observation in one sample is uniquely matched to an observation in the other sample, often representing measurements taken on the same subject under two different conditions or at two different times.
2. The second condition is that the paired observations must be ordinal or at least capable of being ranked. The sign test does not require interval or ratio-level data, but it does require that the differences between paired observations can be classified as positive, negative, or zero.

Key Concepts

Paired Samples

Paired samples refer to two sets of related observations, where each observation in one sample is uniquely matched with an observation in the other sample. This relationship is crucial for the paired-sample sign test, as it assesses the differences between these matched pairs rather than treating the samples as independent. Examples include measurements taken before and after a treatment on the same subjects.

Non-Normality of Differences

The paired-sample sign test is a non-parametric method used when the differences between paired observations do not follow a normal distribution. This condition is essential because the test relies on the ranks of the differences rather than their actual values, making it suitable for data that may be skewed or ordinal in nature. It allows for valid statistical inference without the assumption of normality.

Symmetry of Differences

For the paired-sample sign test to be valid, the distribution of the differences between paired observations should be symmetric around the median. This condition ensures that the test accurately reflects the central tendency of the differences, allowing for reliable conclusions about the population from which the samples are drawn. If the differences are highly skewed, alternative methods may be more appropriate.