# Can SPSS produce a confidence interval for a binomial proportion?

## Problem

I'm looking for the standard large sample normal theory confidence interval on a binomial proportion, and I don't see it in SPSS. Is it available?

## Resolving The Problem

The "standard" large sample normal theory confidence intervals for binomial proportions are also known as Wald confidence intervals. The GENLIN procedure (Analyze>Generalized Linear Models>Generalized Linear Models) can produce Wald and likelihood ratio confidence intervals on binomial proportions. You simply fit an intercept-only model with an identity link and a binomial distribution to a binary 0-1 dependent variable using the first category of the response as the reference category (the DESCENDING option in command syntax). The parameter estimate for the intercept will be the observed proportion. The default confidence intervals are 95% Wald intervals. You can specify likelihood ratio intervals instead by specifying profile likelihood for the confidence interval type on the Statistics tab in the dialog boxes. These intervals have better coverage properties than the Wald intervals, which even in large samples can have coverage levels well below the nominal level.

Command syntax for likelihod ratio intervals might be:

GENLIN y (REFERENCE=FIRST)
/MODEL INTERCEPT=YES
/CRITERIA CILEVEL=95 CITYPE=PROFILE(.0001)
/PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.

If you would like to obtain confidence intervals that match those used in charts, which are known as equal tailed Jeffreys prior intervals, you can use the NPTESTS procedure via Analyze>Nonparametric Tests>One Sample (NPTESTS offers Jeffreys, likelihood ratio, and Clopper-Pearson "exact" intervals). On the Fields tab, select Use custom field assignments and specify the binary variables of interest. On the Settings tab, select Customize tests, Compare observed binary probability to hypothesized (Binomial test), click Options, select the type(s) of intervals desired, and specify the response category of interest, click OK, then click Run. The command might look like:

NPTESTS
/ONESAMPLE TEST (y) BINOMIAL(TESTVALUE=0.5 CLOPPERPEARSON JEFFREYS LIKELIHOOD
SUCCESSCATEGORICAL=LIST(1) SUCCESSCONTINUOUS=CUTPOINT(MIDPOINT))
/CRITERIA ALPHA=0.05 CILEVEL=95.

By default, the output from NPTESTS is in a interactive Model Viewer rather than in pivot tables. In your output window, you will see an object labeled Hypothesis Test Summary. Double click on this object to activate the Model Viewer, then from the dropdown on the left side, select Confidence Interval Summary View in order to see the confidence intervals.

Beginning with Version 22, you can opt to get pivot table output instead of Model Viewer output. Under Edit>Options select the Output tab. Under Output Display, change the selection from Model Viewer to Pivot tables and charts and click Apply or OK.

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Modified date:
16 June 2018

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