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1-sample Sign test and the 1-sample Wilcoxon test both are non-parametric test. This is used to compare the median of the sample to determine whether there is statistically difference with a standard value. 1-sample Sign test 1-sample Wilcoxon test Assumptions Applicable when data are Non – Normal Applicable when data are Non – Normal The variable data are continuous. The variable data are continuous. Data distribution is non-symmetric and can be left skewed or right skewed. Data distribution is symmetric. Observations are independent. Observations are independent. Sample Size More powerful with large sample size since the statistic is followed the binomial distribution and can be used for small sample size. More powerful with large sample size Power Low powerful than 1-sample Wilcoxon test More powerful than 1-sample sign test since it considers the magnitude of differences. Outliers Not sensitive to outliers More robust against outliers Limitation Required paired data for the calculations but always it may not available. Data taken from random samples from the population hence the correct sample may not capture. Less powerful and it may not detect the difference between paired data. Eg: Manager of the ABC insurance company shows that the median of new life insurance customers per day is 50. The agent of the same insurance company claim that it is more than 50. To analyze whether this is true or wrong we can use 1-Sample sign test and the hypothesis is as follows. Ho: median of new life insurance customers per day = 50 Ha: median of new life insurance customers per day > 50 In a term text of grade 10, it is required to check the median marks for the mathematics is greater than 70%. Then we can apply 1-samaple Wilcoxon test by selecting few marks randomly, Ho: The population Median value = 70% Ha: The population Median value >70%

Thanks a lot, Mayank.