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, H_{0} |
Alternate Hypothesis, H_{1} |
One-tailed |
m = m_{0} |
m < m_{0} or m > m_{0} |
Two-tailed |
m = m_{0} |
m ¹ m_{0} |
where m is the population median and m_{0} is the hypothesised population median.
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.
Interpretation
For a desired a = 0.05, since p = 0. 0385 < a, we will reject H_{0}. 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.