- Nonparametric implies that there is no assumption of a specific distribution for the population
- The advantage of nonparametric test is that the test results are more robust against violation of the assumptions
- Use 1-Sample Sign to estimate the population median and to compare it to a target value or a reference value.
- The sign test is named from the model based on data recorded as plus and minus signs instead of numerical magnitude.
- The 1 sample sign test is a non-parametric hypothesis test that determines whether there is a statistically significant difference between a nonnormally distributed continuous data set's median and a standard median value.
- The 1 sample sign test is also considered as a nonparametric version of the 1 sample t-test.
-
Assumptions of 1 sample sign test includes:
- Data must be continuous but non-normal
- It must contain non-symmetric data i.e., either left skewed or right skewed
1 Sample Sign Test
1 Sample Sign Test Example
- The median time to resolve the IT ticket was 5 hours in an organization. But the IT manager claims that it is less than 5 hours after the software upgradation. Manager randomly collected 20 resolved ticket samples. With 95% confidence level, is there any evidence that the median resolving time is less than 5 hours.
- Let us conduct one sample sign test to find out if the difference is significant enough
-
Step 1.a: Conduct Normality test
Note: You can also evaluate the normality test by selecting
Minitab -> Stats -> Basic Statistics -> Normality Tests
(or)
Minitab -> Graph -> Probability Plot -
Step 1.b:Normality Check and Interpret
Interpret:
- As P-value (0.017) is less than 0.05, we can conclude that the data aren’t normal and doesn’t have any outliers. Also the skewness (0.848) is greater than 0.5, i.e. it is Right Skewed. So we choose 1 Sample Sign test. -
Step 2: Hypothesis
- Null Hypothesis Ho: The median ticket resolving time is 5 hours i.e. η = 5 hours
- Alternate Hypothesis Ha: The median ticket resolving time is less than 5 hours i.e. η < 5 hours
Note: 5 hours was the original resolution time prior upgradation and η is the current population median of resolution time post upgradation -
Step 3: Conduct 1 Sample Sign Test
-
Step 4: Interpretation
- Median = 2.56 hours
- At 95% confidence level, the number of samples less than 5 hours is 15, the number of samples more than 5 hours is 5
- The hypothesized median (5 hours) is greater than sample median (2.56 hours) and p-value (0.021) is less than alpha (0.05), we can reject the null hypothesis
- Therefore the new system has ticket resolving median time less than 5 hours.
- P value 0.021 means that there is 2.1% chance that the population mean will be equal to or more than 5 hours