ANOVA for test scores (range 0-100), but not percentages?

[jamiecr]

Hi,
I know ANOVA is not the best option for percentage data, mostly due to the lower and upper bounds at 0 and 100. However, what if the data were based on test scores that happened to be bound by 0 and 100? Is there a difference? Can ANOVA be used for the latter? Why or why not?

Thanks in advance for any help!

[Jon K Peck]

No, there is no difference.  Bounds are bounds, and they necessarily invalidate the usual assumptions about the error term and make a linear functional form unrealistic.  Whether this is a practical concern depends on how much data is near the bounds and the size of the error variance.

If you don't have data at the bounds, you could transform y (assumed to be in (0,1)) via
ln(y/(1-y)),
which is the logit model but run on a continuous variable.  If you have some boundary data, you could adjust like this:
(y * (N − 1) + 0.5)/N
where N is the number of cases.

You could also use proportional regression via the STATS PROPOR REGR extension command, which requires the R Essentials for Statistics.


Jon Peck (no "h") aka Kim
Senior Software Engineer, IBM
[hidden email]
phone: [phone]




From:        jamiecr <[hidden email]>
To:        [hidden email]
Date:        08/18/2014 02:54 PM
Subject:        [SPSSX-L] ANOVA for test scores (range 0-100), but not percentages?
Sent by:        "SPSSX(r) Discussion" <[hidden email]>

---

Hi,
I know ANOVA is not the best option for percentage data, mostly due to the
lower and upper bounds at 0 and 100. However, what if the data were based on
test scores that happened to be bound by 0 and 100? Is there a difference?
Can ANOVA be used for the latter? Why or why not?

Thanks in advance for any help!



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[jamiecr]

Interesting. Thanks, Jon, for your quick and informative reply! What if the data are only bound on one side (e.g., by 0, as in weight)? I have seen countless times where ANOVA has been used in these instances. I can see how data approaching either bound would result in nonlinearity, and I have heard that as long as the data fall in the range of 30-70% or even 20-80%, then ANOVA is acceptable (even on untransformed data). What are your thoughts?

[Ryan]

Depends on predictor(s)...Beta regression is a possible solution for such data tho that may be overkill depending on your design.

Ryan

Sent from my iPhone

> On Aug 18, 2014, at 3:54 PM, jamiecr <[hidden email]> wrote:
>
> Hi,
> I know ANOVA is not the best option for percentage data, mostly due to the
> lower and upper bounds at 0 and 100. However, what if the data were based on
> test scores that happened to be bound by 0 and 100? Is there a difference?
> Can ANOVA be used for the latter? Why or why not?
>
> Thanks in advance for any help!
>
>
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/ANOVA-for-test-scores-range-0-100-but-not-percentages-tp5727001.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> 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

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[Art Kendall]

How was your variable operationalized?

Is the underlying construct bound or just the operationalized measure?

If the potential range of the variable is 0 to 100, e.g., if the variable is a score based on the      number of 100 questions right, what was the range of the obtained score.

Is the score from a standardized well-developed instrument?Are there published norms?

[Jon K Peck]

In principle, any bound is a potential problem, but if the data are not near the theoretical bound(s), it is not likely to be a problem.  You can still use something like the logistic transform to see if it affects significance or the effects of the predictors in a meaningful way.  Of course, if the predicted values from a linear model go outside the bounds, that's a good clue that the model is not working.


Jon Peck (no "h") aka Kim
Senior Software Engineer, IBM
[hidden email]
phone: [phone]




From:        jamiecr <[hidden email]>
To:        [hidden email]
Date:        08/18/2014 10:07 PM
Subject:        Re: [SPSSX-L] ANOVA for test scores (range 0-100), but not percentages?
Sent by:        "SPSSX(r) Discussion" <[hidden email]>

---

Interesting. Thanks, Jon, for your quick and informative reply! What if the
data are only bound on one side (e.g., by 0, as in weight)? I have seen
countless times where ANOVA has been used in these instances. I can see how
data approaching either bound would result in nonlinearity, and I have heard
that as long as the data fall in the range of 30-70% or even 20-80%, then
ANOVA is acceptable (even on untransformed data). What are your thoughts?



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[jamiecr]

Thanks, Jon! Very helpful.

[jamiecr]

Hi Ryan,
Thank you for mentioning beta regression--I had heard about it, but didn't pursue it. I will definitely be doing some more research!