Statistics > Nonparametrics > 2-Sample Matched-Pair Sign Test
This utility performs calculations for testing claims about two population
means for the case when the type of
population distribution cannot be assumed, except that the population
of the pairwise differences is symmetric.
The null hypothesis H0 of a claim is
μ1= μ2.
The alternative
hypothesis H1
can be one of the following:
μ1 < μ2,
μ1 > μ2, or
μ1 ≠ μ2.
A positive difference is assigned a positive (+) sign.
A negative difference is assigned a negative (-) sign.
The test statistic is computed as follows:
- Left-tailed (H1: μ1 < μ2):
s = the number of positive (+) signs
- Right-tailed (H1: μ1 > μ2):
s = the number of negative (-) signs
- Two-tailed (H1: μ1 ≠ μ2):
s = the minimum of the number of (+) signs and the number of
(-) signs
The p-value for a one-tailed test (left-tailed or right-tailed) is
P(X ≤ s) where X is a random variable representing the number
of positive signs. The-value for a two-tailed test is
2P(X ≤ s).
If the sample size n (excluding values that are equal to the hypothesized
mean) is not more than 50, exact binomial probability calculations
are used to compute the p-value. If the sample size is greater than
50, the normal distribution is used as an approximation to binomial:
To use the utility, follow these steps:
- If individual samples are entered in two columns of the
Datasheet, select the Samples in column: radio button, and
select the column names in the drop-down menu.
- To use summary statistics of the sample data, select the
Summarized sample data: radio button, and input the number
of positive signs and the number of negative signs in the provided text fields.
- Select the form of the alternative hypothesis in the
Alternative Hypothesis: drop-down menu.
- Click the OK button to perform the computation. The
results will be displayed in the log window.