Likert scales as ordinal or interval levels? reference.

[crossover]

Hey,

I found this from Wikipedia

"Responses to several Likert questions may be summed, providing that all questions use the same Likert scale and that the scale is a defendable approximation to an interval scale, in which case they may be treated as interval data measuring a latent variable. If the summed responses fulfill these assumptions, parametric statistical tests such as the analysis of variance can be applied. These can be applied only when more than 5 Likert questions are summed."

Can some one give me reference of this? I have tried for a while. can't find it.
Is this method reliable?  I am thinking to use it.

Thank you.

[John F Hall]

In the real world, survey researchers do it all the time, despite objections from pedantic statisticians (none of those on the list as as far as I know) many of whom wouldn't recognise a decent survey question if it smacked them in the g*b.  The literature abounds with examples (likewise with quota versus probability sampling). 

 

If your questions make sense to your respondents and theoretical sense to you and your readers, go ahead.  Substantive content is much more important than statistical technique as John Tukey recognised when he said, "All the statistics in the world won't help you if you asked the wrong question in the first place."  Mind you it helps to have statisticians around when you need to search for structure and reliability in your data, especially if you're going to publish it or submit it for a diploma/degree.

 

John Hall
[hidden email]
http://surveyresearch.weebly.com

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Friday, October 15, 2010 3:06 PM

Subject: Likert scales as ordinal or interval levels? reference.

Hey,

I found this from Wikipedia

"Responses to several Likert questions may be summed, providing that all
questions use the same Likert scale and that the scale is a defendable
approximation to an interval scale, in which case they may be treated as
interval data measuring a latent variable. If the summed responses fulfill
these assumptions, parametric statistical tests such as the analysis of
variance can be applied. These can be applied only when more than 5 Likert
questions are summed."

Can some one give me reference of this? I have tried for a while. can't find
it.
Is this method reliable?  I am thinking to use it.

Thank you.


--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Likert-scales-as-ordinal-or-interval-levels-reference-tp3213610p3213610.html
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[zstatman]

Wouldn't this be more applicable after one has identified appropriate question "sets" from a factor analysis? Just doing it across a series of questions doesn't appear to me viable - Unless the FA is implied in the original post?

 

WMB
Statistical Services

============
mailto: [hidden email]
http:\\home.earthlink.net\~info.statman
Skype: zstatman
============

---

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of John F Hall
Sent: Friday, October 15, 2010 11:32 AM
To: [hidden email]
Subject: Re: Likert scales as ordinal or interval levels? reference.

In the real world, survey researchers do it all the time, despite objections from pedantic statisticians (none of those on the list as as far as I know) many of whom wouldn't recognise a decent survey question if it smacked them in the g*b.  The literature abounds with examples (likewise with quota versus probability sampling). 

 

If your questions make sense to your respondents and theoretical sense to you and your readers, go ahead.  Substantive content is much more important than statistical technique as John Tukey recognised when he said, "All the statistics in the world won't help you if you asked the wrong question in the first place."  Mind you it helps to have statisticians around when you need to search for structure and reliability in your data, especially if you're going to publish it or submit it for a diploma/degree.

 

John Hall
[hidden email]
http://surveyresearch.weebly.com

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Friday, October 15, 2010 3:06 PM

Subject: Likert scales as ordinal or interval levels? reference.

Hey,

I found this from Wikipedia

"Responses to several Likert questions may be summed, providing that all
questions use the same Likert scale and that the scale is a defendable
approximation to an interval scale, in which case they may be treated as
interval data measuring a latent variable. If the summed responses fulfill
these assumptions, parametric statistical tests such as the analysis of
variance can be applied. These can be applied only when more than 5 Likert
questions are summed."

Can some one give me reference of this? I have tried for a while. can't find
it.
Is this method reliable?  I am thinking to use it.

Thank you.


--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Likert-scales-as-ordinal-or-interval-levels-reference-tp3213610p3213610.html
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[John F Hall]

There's a detailed worked example using SPSS on my website. 

 

http://surveyresearch.weebly.com/51-introduction-to-count-and-compute.html 

 

and following pages.  It's from a survey done to professional standards under my supervision by three of my sophomore students in 1981 for their second year group research project.  I later prepared the data and documentation for use in teaching, but my tutorials don't show the preliminary analysis (correlation, cluster, reliability etc) which led to the selection of 9 items to measure "sexism" from a longer list of 14.  I also use a shorter 4-item scale developed by Hilde Himmelweit to measure "Attachment to status-quo" in teenagers.  The set of seven tutorial, questionnaire, user manual, raw data and SPSS saved file are all on the site and freely downloadable.

 

There are several other sets of items, some composed by the students themselves, some replications of other work (eg Wilson-Patterson Neo-conservatism scale and various items from the British Social Attitudes surveys) which have never been analysed except by the students as single items in their dissertation.  Open invitation to all budding analysts!

 

John Hall
[hidden email]
http://surveyresearch.weebly.com

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Friday, October 15, 2010 6:00 PM

Subject: Re: Likert scales as ordinal or interval levels? reference.

Wouldn't this be more applicable after one has identified appropriate question "sets" from a factor analysis? Just doing it across a series of questions doesn't appear to me viable - Unless the FA is implied in the original post?

 

WMB
Statistical Services

============
mailto: [hidden email]
<A href="file://\\home.earthlink.net\~info.statman">http:\\home.earthlink.net\~info.statman
Skype: zstatman
============

---

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of John F Hall
Sent: Friday, October 15, 2010 11:32 AM
To: [hidden email]
Subject: Re: Likert scales as ordinal or interval levels? reference.

In the real world, survey researchers do it all the time, despite objections from pedantic statisticians (none of those on the list as as far as I know) many of whom wouldn't recognise a decent survey question if it smacked them in the g*b.  The literature abounds with examples (likewise with quota versus probability sampling). 

 

If your questions make sense to your respondents and theoretical sense to you and your readers, go ahead.  Substantive content is much more important than statistical technique as John Tukey recognised when he said, "All the statistics in the world won't help you if you asked the wrong question in the first place."  Mind you it helps to have statisticians around when you need to search for structure and reliability in your data, especially if you're going to publish it or submit it for a diploma/degree.

 

John Hall
[hidden email]
http://surveyresearch.weebly.com

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Friday, October 15, 2010 3:06 PM

Subject: Likert scales as ordinal or interval levels? reference.

Hey,

I found this from Wikipedia

"Responses to several Likert questions may be summed, providing that all
questions use the same Likert scale and that the scale is a defendable
approximation to an interval scale, in which case they may be treated as
interval data measuring a latent variable. If the summed responses fulfill
these assumptions, parametric statistical tests such as the analysis of
variance can be applied. These can be applied only when more than 5 Likert
questions are summed."

Can some one give me reference of this? I have tried for a while. can't find
it.
Is this method reliable?  I am thinking to use it.

Thank you.


--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Likert-scales-as-ordinal-or-interval-levels-reference-tp3213610p3213610.html
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[crossover]

Hi,
Thank you so much for this information.

I will have a look in details.

My design is a within-subject design with three conditions.  32 participants
I treat the scores of the 15-item emotional responses from the self-rated scale as ordinal data to compare individual item differences in these three conditions (by using Friedman and Wilcoxon signed-rank test. Am I using this right?
Moreover, I am exploring the different nature of these 15 emotional responses and hope to group them into 4 different categories based on my theoretical assumptions for further comparisons.  
I have tired to factor analysis to group a 15-item self-rated scale into 4 categories and found that the statistical results are aligned with my theoretical prediction with small differences.
I then want to group these.  Can I sum these similar items, based on the results showed from factor analysis, and take the average of these items in each group to make comparison between conditions for further analysis?  In this case, can the summed scores of several items be treated as interval data?
I appreciate very much for your reply and your knowledge.
 
 

[Art Kendall]

"they" is a little ambiguous.  The scale score is very often held to be not too discrepant from interval level.
Individual items are also often treated as not too discrepant from interval level.

In instances where there is a single item as the DV, categorical regression can be used to see how much substantive difference it makes in the conclusions to treat the variable as ordinal vs interval level.  I cannot not recall any instances where it has made a difference in the substantive conclusions, but I have not tried this on a wide number of studies.

Have other members of this list found instances where there was a different substantive conclusion when the DV was considered ordinal and when it was considered interval?


Of course it is important to use good scale construction practices in deciding what items to sum(average).

Art Kendall


On 10/15/2010 9:06 AM, crossover wrote:

Hey,

I found this from Wikipedia

"Responses to several Likert questions may be summed, providing that all
questions use the same Likert scale and that the scale is a defendable
approximation to an interval scale, in which case they may be treated as
interval data measuring a latent variable. If the summed responses fulfill
these assumptions, parametric statistical tests such as the analysis of
variance can be applied. These can be applied only when more than 5 Likert
questions are summed."

Can some one give me reference of this? I have tried for a while. can't find
it.
Is this method reliable?  I am thinking to use it.

Thank you.


--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Likert-scales-as-ordinal-or-interval-levels-reference-tp3213610p3213610.html
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[hidden email] (not to SPSSX-L), with no body text except the
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[Gosse, Michelle]

Hi all, interesting answers to this so far.

 

The only points/questions I have are:

1.       Why a minimum of 5 Likert questions? My impression was that the argument tended to be around whether there were sufficient response options on the scale, so for example one would have difficulty arguing that a 3-point scale is interval but a 5-point scale or 7-point scale can be argued to perform much more like an interval (or even ratio) level measure. I’ve not seen the argument for the minimum number of questions to sum/average before. I think this is similar  to Art’s point below.

2.       I was taught (but no references) that if one argues that a Likert scale is interval, then if one gets a mean of say 3.2,  one should be able to explain what 3.2 is given that it falls between two scale points. If a result such as 3.2 is meaningless, then the argument for an interval level scale fails. I like this approach as I feel it gives the correct emphasis to the theory underpinning how the scale was developed in the first place.

 

Wouldn’t the main issue with the ordinal versus interval question be around  the use of parametric techniques that rely on comparisons of group variances – where an ordinal scale could be argued to constrain variance more than an interval/ratio scale? To use a trivial example, I can ask people how much they think their income has changed in the past year using a 5-point or even 7-point scale, or I could do this with tax returns (say) and measure to the cent what the real change has been (I realise income is ratio, but I can’t think of an interval scale off hand other than temperature...). Obviously, the level of variance in people’s incomes is going to be more accurately reflected with the tax information, and it is going to be much greater than that captured by the Likert scale. While this is probably a strawperson argument, and I realise that there are many constructs where an interval or ratio level is not available, I think the main issue is the mathematically constrained variance that comes from using Likert scales. Following on this argument, is there an issue that Likert scales could inflate the Type II error rate because the constraints to variance mean that groups will tend to have artificially similar responses?

 

Cheers

Michelle

 

Michelle Gosse

Consumer and Social Sciences

Food Standards Australia New Zealand

email: [hidden email]

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Art Kendall
Sent: Saturday, 16 October 2010 8:28 a.m.
To: [hidden email]
Subject: Re: Likert scales as ordinal or interval levels? reference.

 

"they" is a little ambiguous.  The scale score is very often held to be not too discrepant from interval level.
Individual items are also often treated as not too discrepant from interval level.

In instances where there is a single item as the DV, categorical regression can be used to see how much substantive difference it makes in the conclusions to treat the variable as ordinal vs interval level.  I cannot not recall any instances where it has made a difference in the substantive conclusions, but I have not tried this on a wide number of studies.

Have other members of this list found instances where there was a different substantive conclusion when the DV was considered ordinal and when it was considered interval?


Of course it is important to use good scale construction practices in deciding what items to sum(average).

Art Kendall


On 10/15/2010 9:06 AM, crossover wrote:

Hey,

I found this from Wikipedia

"Responses to several Likert questions may be summed, providing that all

questions use the same Likert scale and that the scale is a defendable

approximation to an interval scale, in which case they may be treated as

interval data measuring a latent variable. If the summed responses fulfill

these assumptions, parametric statistical tests such as the analysis of

variance can be applied. These can be applied only when more than 5 Likert

questions are summed."

Can some one give me reference of this? I have tried for a while. can't find

it.

Is this method reliable?  I am thinking to use it.

Thank you.

--

View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Likert-scales-as-ordinal-or-interval-levels-reference-tp3213610p3213610.html

Sent from the SPSSX Discussion mailing list archive at Nabble.com.

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[hidden email] (not to SPSSX-L), with no body text except the

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For a list of commands to manage subscriptions, send the command

INFO REFCARD

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD