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Dec 15, 2016 2:00 PM
(3265 views)

Hey All,

I had a question about the R-square uncertainty ratio in Contingecy Tables (placed in same table as DOF and loglikelihood). I am currently doing research where I've found significance in my p-value (alpha=.05), but the R-square value is close to 0. Now, I am aware that in continuous vs continuous, an R-value is used to determine the correlation between the two variables.

My question is: What relevance does the Rsquare value in a contingecy table have on my conclusions?

I was able to reject the null hypothesis via my p-value, but as I previously mentioned, the Rsquare is very close to 0, which makes me unsure if I should proceed with the alternative hypothesis in mind.

Thanks in advance!

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Dec 16, 2016 7:15 AM
(6488 views)

Solution

You may interpret the **RSquare (U)** the same way as you would interpret the **RSquare** from a linear regression. The **RSquare** is based on sums of squares: **SS(model) / SS(total)**. **RSquare (U)** likewise is **-L(model) / -L(reduced)**. It tells you the proportion of the total uncertainty that is accounted for by the model, assuming it is the correct model.

This relationship is easier to see in **Logistic Fit** than in **Contingency** because **Contingency** only reports the **-L(model)**. This is the analysis of **age **by **weight **from **Big Class** sample data table:

The **-L(model)** above is labeled **Difference** here. The **-L(total)** above is labeled **Reduced** here. The **RSquare (U)** is therefore **Difference / Reduced = 5.037918 / 67.266350 = 0.0749**.

It is common for a statistically significant model of a categorical response to exhibit a very low **RSquare (U)** as this example demonstrates. Like its continuous model **RSquare **counterpart, it indicates the performance of the conditional prediction over the marginal prediction.

Learn it once, use it forever!

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Dec 16, 2016 7:15 AM
(6489 views)

You may interpret the **RSquare (U)** the same way as you would interpret the **RSquare** from a linear regression. The **RSquare** is based on sums of squares: **SS(model) / SS(total)**. **RSquare (U)** likewise is **-L(model) / -L(reduced)**. It tells you the proportion of the total uncertainty that is accounted for by the model, assuming it is the correct model.

This relationship is easier to see in **Logistic Fit** than in **Contingency** because **Contingency** only reports the **-L(model)**. This is the analysis of **age **by **weight **from **Big Class** sample data table:

The **-L(model)** above is labeled **Difference** here. The **-L(total)** above is labeled **Reduced** here. The **RSquare (U)** is therefore **Difference / Reduced = 5.037918 / 67.266350 = 0.0749**.

It is common for a statistically significant model of a categorical response to exhibit a very low **RSquare (U)** as this example demonstrates. Like its continuous model **RSquare **counterpart, it indicates the performance of the conditional prediction over the marginal prediction.

Learn it once, use it forever!

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Dec 16, 2016 11:35 AM
(3238 views)