Re: Ordinal ratings and relationship to continuous measurement variables

On Apr 1, 10:46 am, "mora...@xxxxxxxxxxx" <mora...@xxxxxxxxxxx> wrote:
I have 143 images with a square in the middle, generated by an
image generator. The image has some lines and "fuzziness" added
to the top of it, extending over the top of the square.
A rater rates the severity of the lines/fuzziness over the square
subjectively as "none" (0), "a little" (1), or "a lot" (2)
The depth of the fuzziness is then measured from the top of the
square.

The data looks like this:
Fuzziness Depth
row 1: 0 0.2
row 2: 1 1.3
row 3: 0 0.5
row 4: 1 0.9
row 5: 2 3.2
row 6: 2 2.4
row 7: 1 2.2
......
row143: 1 2.1

The question I want to know is: Is subjective rating correlated
to actual measured depth?

I haven't been able to find the best measure for this type of
question. What statistic(s) could I use to answer this question?

You say "correlated", but that doesn't mean that the answer you seek
is a "correlation". This is a regression problem: the independent
variable is Depth, the dependent variable is Subjective Fuzziness.
I would fit an ordinal logistic model.

If you must have a correlation-like statistic then you can get a
pseudo-R^2 from the logistic results, but be aware that it, like
correlations in general, is not a structural parameter and will vary
depending on the distribution of the i.v. In other words, if you
repeated the experiment, with the same (or an equivalent) subject but
a different distribution of Depths, you would get a different R^2;
the difference between the R^2's would be an artifact, not an
experimental finding.
.

Relevant Pages

  • Re: Ordinal ratings and relationship to continuous measurement variables
    ... If you have not yest gathered the data, I would strongly recommend a finer grained response scale, i.e., more possible values for a respondent to choose. ... A rater rates the severity of the lines/fuzziness over the square ... The depth of the fuzziness is then measured from the top of the ... is a "correlation". ...
    (sci.stat.math)
  • Re: Sum of squared semi-partial correlations
    ... squared semi-partial correlation PLUS the shared variance, ... square. ... The semi-partial correlation of a predictor with the d.v. ... of squared semi-partials only if all the predictors are mutually ...
    (sci.stat.consult)
  • Re: Ordinal ratings and relationship to continuous measurement variables
    ... A rater rates the severity of the lines/fuzziness over the square ... The depth of the fuzziness is then measured from the top of the ... actual measured depth? ...
    (sci.stat.math)
  • Re: Adjusted R2 (R Bar Squared)
    ... Correlation can be negative and can take the values anywhere from -1 ... it’s square also by definition cannot be greater ... Adjusted r-square and r are related. ... into account the strength of the correlation and the sample size. ...
    (sci.stat.math)
  • Ordinal ratings and relationship to continuous measurement variables
    ... I have 143 images with a square in the middle, ... generator. ... The depth of the fuzziness is then measured from the top of the ... actual measured depth? ...
    (sci.stat.math)