1-Sample Sign

 

Overview  |  How to  |  Data  |  Example

 

 

 

Overview

 

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  ¹ 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.

 

 

 

 

 

Data

 

Variable: Numeric.

               

Test median: Numeric.

 

Confidence level: Numeric; Between 0 and 100.

 

 

 

 

 

Example

 

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.

 

 

 

 

Interpretation

 

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.

 

 

 

 

Interpretation

 

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.