Q 587. What are the key similarities and differences between the 1-sample Sign test and the 1-sample Wilcoxon test regarding their assumptions, advantages, limitations, and applications? Please include relevant examples to illustrate your response.

 

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1-sample Sign test 1-sample Wilcoxon test Assumptions In any 1sample sign T test all dependent variables (Y) should be continuous, normaly distributed In any 1 sample wilcoxon test all dependend variables should be continuos,but non normal Advantages As the data required is less for conducting the test, so data can be collected easily Ex. If we want to see that the mean of length of shaft manufactured matched the standard. As this test can be performed on datas which are non parametric also,so the range of this test is more comparing to 1 sample sign test. Limitations In case the sample size is ver less then using this test is not useful If many measurments have same values then this test will mislead in inference Application If the data is collected from a single group and we want to know that the mean of this data are different from that specified by standard Where the data's have failed the nomality test , and we want to compare the before and after condition of the score of the same individual

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%

Slightly difficult question. Sanuja Godaarawa has provided the best answer to this question by clearly highlighting the assumptions, advantages, limitations, and applications. 

 

P.S. Many answers have not been approved. Either they were high on AI generated content or were plagiarized.