# Thread: one sample t-test --> nonparametric equivalent?

1. ## one sample t-test --> nonparametric equivalent?

Dear all,

this is my first post in this forum, in which it seems many people find help and share insights . Working on my MBA thesis, I might need some as well. I searched the forum, but did not find anything specific relating to my question, which is in short:

Is there a nonparametric equivalent to the one sample t-test?

My case: I gathered data on a question such as "At what level do people "A" exhibit skills compared to the average level exhibited by all people (B)?"

It was coded on a 5-point Likert scale, anchored by 1 = extremely poor and 5 = excellent, with 3 = average. Since this is ordinal data, I prefer to use nonparametric tests (I know that in spite of this, parametric tests are sometimes used with such data).

Unfortunately, I was not able to construct a decent pair of questions that ask for A and B separately, in which case I would have been able to use the Mann-Whitney test (right?).

Now I have a known population mean of 3 (set by 3 = average) and want to test whether the mean of my data about "A" is significantly different from the known population mean. For parametric data I would simply use a one sample t-test, and all would be well.

My question: Is there a nonparametric test to compare a one sample mean to a known mean?

I did not find anything on that. My current goofy "solution": I experimented with SPSS and used my one sample data and generated a dummy variable which I set at "3" for all respondents and then ran the Mann-Whitney test to compare means. Of course, the second sample has a mean of 3 with a SD of 0. The Mann-Whitney significance here is the same (very close) to when I run a one sample t-test with the data, so I guess the result is "correct".

I would highly appreciate any help or advice on this issue. Many thanks in advance,

Anatol

2. Originally Posted by Astro Boy
Unfortunately, I was not able to construct a decent pair of questions that ask for A and B separately, in which case I would have been able to use the Mann-Whitney test (right?).

Now I have a known population mean of 3 (set by 3 = average) and want to test whether the mean of my data about "A" is significantly different from the known population mean.Anatol
Ummm...stupid fundamental question here, but if you don't have a good set of data on "B", how do you know the population mean (or median) is 3?

3. Originally Posted by JohnM
Ummm...stupid fundamental question here, but if you don't have a good set of data on "B", how do you know the population mean (or median) is 3?
Hi John, thank you for your comment.

Well the thing is the question in my survey is like this:

"At what level do people "A" exhibit skills compared to the average level exhibited by all people ("B")?"

1. "From your experience, how good are the CAR driving skills of people who also have a motor cycle driver's license compared to the average level of car driving skills for people who do NOT have a motor cycle license (but of course a car license)?"

1 extremely poor
2 below average
4 above average
5 excellent

So I am asking for a comparison of the skills of "A" to the average. That is why I assumed I know the population mean because I defined it as the "average".

I know it is somewhat long-winded, but in my current view it is the better alternative to asking the following two questions, which would target the same but enabled me to do Mann-Whitney:

2a. "From your experience, how good are the car driving skills of people with a car license but WITHOUT a motorcycle license?"

2b. "From your experience, how good are the car driving skills of people with a car license and WITH a motorcycle license?"

1 extremely poor
2 poor
3 fair
4 good
5 excellent

My feeling, and the prevailing feeling of my pilot testers, is that questions 2a and 2b are more confusing and overall weaker than question 1 above.

I am open for suggestions and comments, but still my question remains about the one-sample t-test (could I use it for question 1 if it were parametric data?) and a possibility to test the same for nonparametric data.

Anatol

4. I like your argument about question quality, but I'm not aware of a 1-sample nonparametric test.

5. Originally Posted by JohnM
I like your argument about question quality, but I'm not aware of a 1-sample nonparametric test.
Thanks John, me neither...that's the problem

So supposed I gather data on the one sample about deviation from average and want to test whether that is statistically significant.

If distribution is normal and interval, I can use the one-sample t-test.

I could argue for interval from the Likert scale from literature sources (even though it is an ongoing debate).

I can test for normality with the Kolmogorov-Smirnov test. Now WHAT IF K-S is significant, i.e., my distribution is NOT normal?

Then, strictly speaking, I cannot use the t-test because of violation of parametric assumptions? I cannot use a non-parametric one sample test because there is none?

Hmmm.... which way to go?

Anatol

6. I would just use the 1-sample t-test, since there aren't any other options, and it's pretty robust to departures from normality.

7. Originally Posted by Astro Boy
Thanks John, me neither...that's the problem

So supposed I gather data on the one sample about deviation from average and want to test whether that is statistically significant.

If distribution is normal and interval, I can use the one-sample t-test.

I could argue for interval from the Likert scale from literature sources (even though it is an ongoing debate).

I can test for normality with the Kolmogorov-Smirnov test. Now WHAT IF K-S is significant, i.e., my distribution is NOT normal?

Then, strictly speaking, I cannot use the t-test because of violation of parametric assumptions? I cannot use a non-parametric one sample test because there is none?

Hmmm.... which way to go?

Anatol

edit: Found the naunce! The naunce is about whether or not it even make sense to say your data has a mean. It would be like a weighted average of A, B, C. I get it now.

end edit!

8. ## Re: one sample t-test --> nonparametric equivalent?

Hi, I know your question is no more actual, but the test you were looking for is named "One Sample Wilcoxon Signed Rank test" It is an alternative to One sample T test and is used mostly when the data have not normal distribution Maybe, it will help other people...

Stanka

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