# Require help and advice in Wilcoxon Signed rank test

#### Rita08

##### New Member
Hello everyone,

Here is my problem statement:

I have 5 products namely Product A, Product B, Product C , Product D, Product E.

A survey was conducted on these products. The sample size of the responses is 150. The data is of ordinal- likert scale ranging from 1-7 and also paired since the responses for all 5 products were from the same respondents.

My objective was to determine whether the mean of each product is statistically higher than a hypothesised value , i.e. a one sample t test.
But since the data I have is ordinal, according to me, a one sample t test wouldn’t be suitable as it’s mainly used for the data that is continuous and is not suitable for data which is likert scale.

I found out that an alternative approach of one sample t test is one sample wilcoxon signed rank test. Before using this test, one of the assumptions of wilcoxon signed rank is that the data should be symmetrical in nature, I found out that my data is not at all symmetrical. I really don’t know whether I am going in a right direction to solve this problem statement.

My question is :
1) Is Wilcoxon signed rank test a better option to use rather than one sample t test according to my problem statement mentioned above??

2) If yes, since my data is not symmetrical and is violating the assumption of wilcoxon signed rank test, how should I solve this? Should I use log transformation on ordinal data?? Please suggest.
Thank you!

#### Karabiner

##### TS Contributor
A survey was conducted on these products. The sample size of the responses is 150. The data is of ordinal- likert scale ranging from 1-7
Just to be sure, is this really a Likert scale (consisting of sveral Likert-type items which are summed up?
Or is this just 1 Likert-type item (ordinal scaled)?
I found out that an alternative approach of one sample t test is one sample wilcoxon signed rank test.
The Wilcoxon signed rank test requires interval scaled data. If you just have one Likert-type item,
then you could use the Friedman test as global test, and the sign test for pairwise comparisons.

With kind regards

Karabiner

#### Rita08

##### New Member
Hello

1) The survey was associated with 7-point likert scale. The respondents had to choose from a scale of 1(poor) to 7 (excellent).

2) Is wilcoxon signed rank test only applicable for interval data?? When I searched it’s also includes ordinal data as well.

3) How can I use Friedman test for my above problem? My problem statement is like one sample test. I need to compare it with a hypothesised value.

4) I can use sign test but according to my knowledge, does it have a less statistical power compared to wilcoxon signed rank?

Please correct me if I am wrong.

Thank you!

#### Karabiner

##### TS Contributor
1) The survey was associated with 7-point likert scale. The respondents had to choose from a scale of 1(poor) to 7 (excellent).
Sorry, but I am still not sure. Did you use just 1 single item, or did you use a Likert scale
(= a measurement instrument consisting of several Likert-type items which are summed up)?
The description is mixing both.
If you have a Likert scale, then you can consider it as quasi interval scaled. If you only have one
Likert type item, then you have ordinal data (although such single item measures are often
treated as if they are interval scaled).
2) Is wilcoxon signed rank test only applicable for interval data?? When I searched it’s also includes ordinal data as well.
The formula shows that it cannot be used on ordinal data, since differences are calculated and
compared. That requires interval data. And you discussed symmetry, this requires interval data.
If you decide that Wilcoxon can be used, you could use t-test as well.
3) How can I use Friedman test for my above problem? My problem statement is like one sample test. I need to compare it with a hypothesised value.