Wilcoxon/ t-test, z-standardization

[Tom]

Hello

 

I’m confused about the right proceeding: I got two variables, “time” measuring the amount of time for a task (5-point Likert-scale) , the other (“benefit”, 4-point Likert scale) is the estimated benefit of the used time. If the difference between “benefit” and “time” is positive, the time spent on the task is a somehow efficient investment, if the difference is negative, the time spent on the task doesn’t worth the investment.

So far my intention.

 

My first idea was to calculate a paired t-Test (N= 150), but I’v got a problem with the different scales.

My second idea was to do a z-transformation and then to do the t-test with the z-standardized variables.

My third idea was to run a nonparametric analysis, Wilcoxon (just in case, ).

My forth idea is to run a t-test on the new variable “difference” (“z-benefit” – “z-time”) to test, if “difference” differs significantly from zero (zero means, that the time spent is in accordance with the benefit).

 

Now my results:

-       Paired T-test with the z-standardized variables: no significance.

-       Wilcoxon with original variables: no significance.

-       Wilcoxon with the z-standardized variables: significance!

 

Which requirements I have to look at in order to decide for a certain test in this case? What about my considerations? I appreciate any help, thanks.

Tom

 

[Genevieve Odoom]

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[Rich Ulrich]

Start over.

a) Since the original Likert scaling uses categories of Agree/ Don't Agree,
I think you should not use that name.  You might say something like
"a Likert-type scaling" if your measure of Time (say) was from "too little"
to "too much".  But that would place "most benefit" - I presume - in the
middle. 

What you have, it seems, is a 4 (and 5) point scale from "xxx" to "yy".
If you have a number of items, they make up a summative scale of parallel
items.

b) You should not apply a paired t-test to these measures, Time and
Benefit, which *seem*  so naturally incommensurable.  A z-transformation
has no chance of equalizing anything.  If your anchor points/ labels  were
carefully chosen, you might have been able to chose some apparent
equivalence between certain levels.  But apparently, that is not the case.

Look at your cross-tabulation.  What can you say about the extreme
corners?  How many are "extremely good" versus "extremely bad"?
You might argue that there are more of one than the other, applying
McNemars test to the two numbers (basically, the sign test).

--
Rich Ulrich

---

Date: Fri, 24 Aug 2012 12:24:53 +0000
From: [hidden email]
Subject: Wilcoxon/ t-test, z-standardization
To: [hidden email]

Hello

 

I’m confused about the right proceeding: I got two variables, “time” measuring the amount of time for a task (5-point Likert-scale) , the other (“benefit”, 4-point Likert scale) is the estimated benefit of the used time. If the difference between “benefit” and “time” is positive, the time spent on the task is a somehow efficient investment, if the difference is negative, the time spent on the task doesn’t worth the investment.

So far my intention.

 

My first idea was to calculate a paired t-Test (N= 150), but I’v got a problem with the different scales.

My second idea was to do a z-transformation and then to do the t-test with the z-standardized variables.

My third idea was to run a nonparametric analysis, Wilcoxon (just in case, ).

My forth idea is to run a t-test on the new variable “difference” (“z-benefit” – “z-time”) to test, if “difference” differs significantly from zero (zero means, that the time spent is in accordance with the benefit).

 

Now my results:

-       Paired T-test with the z-standardized variables: no significance.

-       Wilcoxon with original variables: no significance.

-       Wilcoxon with the z-standardized variables: significance!

 

Which requirements I have to look at in order to decide for a certain test in this case? What about my considerations? I appreciate any help, thanks.

Tom

 

[Kornbrot, Diana]

Ordinal regression is analysis of choice for ordinal level data, this included ALL Likert type single items
To be found under regression, ordinal. Note although under regression one can insert categorical predictors
Also goes under name PLUM – its a peach
Best
Diana


On 24/08/2012 18:16, "Rich Ulrich" <rich-ulrich@...> wrote:

Start over.

a) Since the original Likert scaling uses categories of Agree/ Don't Agree,
I think you should not use that name.  You might say something like
"a Likert-type scaling" if your measure of Time (say) was from "too little"
to "too much".  But that would place "most benefit" - I presume - in the
middle.  

What you have, it seems, is a 4 (and 5) point scale from "xxx" to "yy".
If you have a number of items, they make up a summative scale of parallel
items.

b) You should not apply a paired t-test to these measures, Time and
Benefit, which *seem*  so naturally incommensurable.  A z-transformation
has no chance of equalizing anything.  If your anchor points/ labels  were
carefully chosen, you might have been able to chose some apparent
equivalence between certain levels.  But apparently, that is not the case.

Look at your cross-tabulation.  What can you say about the extreme
corners?  How many are "extremely good" versus "extremely bad"?
You might argue that there are more of one than the other, applying
McNemars test to the two numbers (basically, the sign test).

---

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email:  d.e.kornbrot@...    
web:    http://dianakornbrot.wordpress.com/
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School of Psychology
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---

[Rich Ulrich]

Diane,
This is a puzzling post to be in this thread, citing my post.

The Original Poster does not have a regression problem;
I have implied that the problem probably does not have
Likert-type items.

Further, it is my own impression that there is a pretty broad
consensus that actual Likert items are designed to be interval
and additive, and are therefore safe to use in ordinary ANOVA. 

Your serious testing ordinarily will be performed on the actual
total scores (or means) of the designed sets of items.

--
Rich Ulrich

---

Date: Sat, 25 Aug 2012 08:52:53 +0100
From: [hidden email]
Subject: Re: Wilcoxon/ t-test, z-standardization
To: [hidden email]

Ordinal regression is analysis of choice for ordinal level data, this included ALL Likert type single items
To be found under regression, ordinal. Note although under regression one can insert categorical predictors
Also goes under name PLUM – its a peach
Best
Diana


On 24/08/2012 18:16, "Rich Ulrich" <rich-ulrich@...> wrote:

Start over.

a) Since the original Likert scaling uses categories of Agree/ Don't Agree,
I think you should not use that name.  You might say something like
"a Likert-type scaling" if your measure of Time (say) was from "too little"
to "too much".  But that would place "most benefit" - I presume - in the
middle.  

What you have, it seems, is a 4 (and 5) point scale from "xxx" to "yy".
If you have a number of items, they make up a summative scale of parallel
items.

b) You should not apply a paired t-test to these measures, Time and
Benefit, which *seem*  so naturally incommensurable.  A z-transformation
has no chance of equalizing anything.  If your anchor points/ labels  were
carefully chosen, you might have been able to chose some apparent
equivalence between certain levels.  But apparently, that is not the case.

Look at your cross-tabulation.  What can you say about the extreme
corners?  How many are "extremely good" versus "extremely bad"?
You might argue that there are more of one than the other, applying
McNemars test to the two numbers (basically, the sign test).

... snip sig.