1-Sample Sign


Overview | How to | Data | Example






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.



Null Hypothesis, H0

Alternate Hypothesis, H1


m = m0

m < m0 or m > m0


m = m0

m m0


where m is the population median and m0 is the hypothesised population median.






How to


1.     Choose ProcessMA > Statistics > Nonparametric > 1-Sample Sign.


2.     In Variable, select the column containing the sample.


3.     In Test, choose the type of test you want to run.


         If you choose to test median:


-         In Test median, enter the hypothesised population median.


-         In Alternate, select the type of test.


         If you choose to find confidence interval:


-         In Confidence level, enter the desired confidence level for the confidence interval.


4.     Click OK.



Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.








Variable: Numeric.

Test median: Numeric.


Confidence level: Numeric; Between 0 and 100.








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.


1.     Open worksheet ProcessMA > Tools > Data Files > Stat.xls.


2.     Choose ProcessMA > Statistics > Nonparametric > 1-Sample Sign.


3.     In Variable, select V Score.


4.     In Test, choose Test median.


5.     In Test median, enter 68.


6.     In Alternate, select Greater than.


7.     Click OK.







For a desired a = 0.05, since p = 0. 0385 < a, we will reject H0. Therefore, we conclude that there is significant evidence that the median score for the English test has improved.






Part 2


1.     Choose ProcessMA > Statistics > Nonparametric > 1-Sample Sign.


2.     In Variable, select V Score.


3.     In Test, choose Find confidence interval.


4.     In Confidence level, enter 90.


5.     Click OK.







The 90% confidence interval of the median is (71.374, 82) and it is interpolated from the confidence levels below and above the requested level.