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,
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")?"
It would be like asking:
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
3 about average
4 above average
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
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.
Many thanks in advance,
I like your argument about question quality, but I'm not aware of a 1-sample nonparametric test.
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?
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.
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...
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