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Assessing Linearity - What is the difference between the "Deviation from Linearity" Statistic and the "Linearity" Statistic

  • 1.  Assessing Linearity - What is the difference between the "Deviation from Linearity" Statistic and the "Linearity" Statistic

    Posted Tue July 19, 2022 10:45 AM
    I'm trying to assess the linearity of a variable on the DV. However, the scatterplots are hard to decipher due to a weak relationship. As I couldn't tell whether it was linear from the scatterplot, I found a linearity test on SPSS. 

    This test is accessible through SPSS (Compare Means> Means> Options [Select "Test for Linearity"]> Run).

    I'm just a bit confused on the difference between "Linearity" and the "Deviation from linearity" in this test. 

    If I'm looking to pass the linearity assumption, do I need a non-significant deviation from linearity? Or do I need a significant Linearity? 



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    Simone David
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    #SPSSStatistics


  • 2.  RE: Assessing Linearity - What is the difference between the "Deviation from Linearity" Statistic and the "Linearity" Statistic

    Posted Tue July 19, 2022 11:13 AM
    Edited by System Test Fri January 20, 2023 04:15 PM
    Here's an example to clarify.

    data list free /dv x1 x2 group.
    begin data.
    12 8 1 1
    13 9 3 1
    10 7 4 1
    11 8 3 1
    12 6 4 1
    22 8 5 2
    24 9 6 2
    21 7 6 2
    28 5 5 2
    24 4 7 2
    09 5 8 3
    10 6 8 3
    10 7 9 3
    12 8 9 3
    08 5 8 3
    end data.

    MEANS TABLES=dv x1 x2 by group
    /CELLS=MEAN COUNT STDDEV
    /STATISTICS ANOVA LINEARITY.

    When you look at the results, you see:

    1. dv has a significant deviation from linearity test.
    2. x1 has neither a significant linear relationship or non-linear one to group membership.
    3. x2 has a linear relationship; as group membership changes, x2 increases on average.

    So, the "linearity" test looks at the strength of the linear relationship, the "deviation from linearity" test the non-linear one.

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    Rick Marcantonio
    Quality Assurance
    IBM
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    Original Message


  • 3.  RE: Assessing Linearity - What is the difference between the "Deviation from Linearity" Statistic and the "Linearity" Statistic

    Posted Tue July 19, 2022 11:33 AM
    This was answered on the original Reddit post.

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    Original Message


  • 4.  RE: Assessing Linearity - What is the difference between the "Deviation from Linearity" Statistic and the "Linearity" Statistic

    Posted Tue July 19, 2022 03:53 PM
    Edited by System Test Fri January 20, 2023 04:48 PM
    In MEANS procedure, Combined effect is a one-way ANOVA with the grouping variable as the factor (nominal predictor). Linearity component is when the grouping variable is taken for the scale predictor (covariate). Deviation from linearity component is the difference "Combined minus Linear" and hence discovers the presence of dependency above just linear one.

    If both Linear and Deviation from linearity are significant, one can conclude of monotonic nature of dependency. If of the two only Deviation from linearity is significant, one can speak of nonmonotonic character of dependency. If only Linear is significant of the two, one can speak of prevailing linear character of dependency.

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    Kirill Orlov
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    Original Message