The 1-Sample Sign is a nonparametric test of population location (median) and also calculates the corresponding point estimate and confidence interval. Its parametric counterpart is the 1-sample Z and 1-sample t tests. Nonparametric tests do not make assumptions that the population is from a specific distribution. Therefore its results are more robust than a parametric test when such assumptions are violated.
| Test | Null Hypothesis, H0 | Alternate Hypothesis, H1 |
| One-tailed | m = m0 | m < m0 or m > m0 |
| Two-tailed | m = m0 | m <> m0 |
where m is the population median and m0 is the hypothesised population median
At the Excel Menu (For Excel 2007, go to Add-ins first)
Choose ProcessMA > Statistics > Nonparametric > 1-Sample Sign
In Variable, select the column containing the data (Numeric)
In Test Median, enter hypothesized population median (Numeric)
In Alternate, select the appropriate alternate test
In Confidence Level, enter value for confidence level (Numeric, >0 & <1)
Click OK
You are a school teacher and you want to find out if the median score for the English test has improved and you also want to obtain a 90% confidence interval for the population median. Past records show that the population median for similar English tests of the same grade was 68.
Open data worksheet by choosing ProcessMA > Tools > Data
Choose ProcessMA > Statistics > Nonparametric > 1-Sample Sign
In Variable, select BN - Score
In Test Median, enter 68
In Alternate, select Greater than
Click OK
For a desired a = 0.05, since p = 0.0192 < a, we will reject H0. Therefore, we conclude that there is significant evidence that the median score for the English test has improved. The 90% confidence interval of the median is (69.82, 82) and it is interpolated from the confidence levels below and above the requested level.
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