Paired-Samples Sign Test

Statistics > Nonparametric Tests > Paired Sign Test


Performs Sign Test for Paired-Samples.


This test is a nonparametric procedure used with two related samples to test the hypothesis that two variables have the same distribution. The differences between the two variables for all cases are computed and classified as either positive, negative, or tied. If the two variables are similarly distributed, the numbers of positive and negative differences will not be significantly different.


Dialog box items

Samples in different columns:
Choose if you have entered raw data in two separate columns.

oFirst Sample: Enter the column containing one sample.

oSecond Sample: Enter the column containing the other sample

Samples in one column:
Choose if the sample data are in a single column, differentiated by factor levels in a second column.

oSamples: Enter the columns containing the sample data.

oFactor and Levels: Enter the columns containing the sample factor, and select the levels.

The display of outputs of VisualStat.



Data can be entered in one of two ways:

Both samples in a single numeric column with another grouping column (called factor) to identify the population. The grouping column may be categorical, numeric or text.

Each sample in a separate numeric column.

Each row contains the paired measurements for an observation. Paired observations where one of values is missing are ignored.



Use Exact Distribution:
Choose to use the exact distribution of the test statistic to compute the p-value.

Continuity Correction:
Choose to use a continuity correction in the normal approximation to the distribution of the test statistics. This correction is valid only for dichotomous categories and does not work for an exact distribution.

Alternative Hypothesis:
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level:
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.



A physiologist wants to know if monkeys prefer stimulation of brain area A to stimulation of brain area B. In the experiment, 14 rhesus monkeys are taught to press two bars. When a light comes on, presses on Bar 1 always result in stimulation of area A; and presses on Bar 2 always result in stimulation of area B. After learning to press the bars, the monkeys are tested for 15 minutes, during which time the frequencies for the two bars are recorded. The data are shown in a dataset.

1.Open the DataBook nonparam.vstz

2.Select the sheet brain

3.Choose the tab Statistics, the group Nonparametric Tests and the command Paired Sign Test

4.Select group Samples in different columns

5.In First Sample, select Bar 1. In Second Sample, select Bar 2.

6.Click OK


Report window output


Paired-Samples Sign Test


Test of concordance between two variables

null hypothesis: true The two variables have the same distribution

With continuity correction


              Bar 1 - Bar 2

Type of Test   Two-sided

+ Differences  3

- Differences  11

Ties           0

Z Statistic    3

Distribution   Exact

p-value        0.0574

alpha-level    0.05

Conclusion     Accept the Null Hypothesis




Interpreting the results

The sampling distribution of the statistic is the binomial distribution with N = 14 and p = .5. With this distribution, we would find that the probability of 3 or fewer + signs is .0287. But because the alternative is nondirectional, or two-tailed, we must also take into account the probability 11 or more + signs, which is also .0287. Adding these together, we find that the probability of (3 or fewer) or (11 or more) is .0574. Therefore, if our pre-determined alpha was set at .05, we would not have sufficient evidence to allow rejection of the null hypothesis.




See Also:

McNemar’s Chi-Square Test | Report | Numeric Formats

Web Resource: Non-parametric tests (PDF)