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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

Binomial Logistic Regression

A binomial logistic regression (or logistic regression for short) is used when the outcome variable being predicted is dichotomous (i.e. yes/no, pass/fail). This model can be used with any number of independent variables that are categorical or continuous.

Assumptions

In addition to the two mentioned above:

  1. Independence of observations
  2. Categories of the outcome variable must be mutually exclusive and exhaustive
  3. Linear relationship between continuous variables and the logit transformation of the outcome variable

Running Logistic Regression in SPSS

  1. Analyze > Regression > Binary Logistic...
  2. Move the dichotomous outcome variable to the "Dependent" box.
  3. Move all predictor variables into the "Covariates" box (ignoring the "Previous" and "Next" options).
    • Click on the "Categorical" button to define the categories of any categorical predictor variables.
    • Click "Continue" to return to the main dialogue box.
  4. Click on the "Options" button to select additional statistics and plots you want included with your output.
    • Click "Continue" to return to the main dialogue box.
  5. Click "OK" to run the test. 

Interpreting Output

  • Model Summary
    • Cox & Snell R Square - a measure of variance explained - interpreted the same as R-square in linear regression
    • Nagelkerke R Square - preferred measure of variance explained - interpreted the same as R-square in linear regression
  • Ombinus Tests of Model Coefficients
    • Provides results of the Chi-Square Goodness-of-Fit test used to assess the significance of the overall model
  • Classification Table
    • Provides a measure of the accuracy of the model
      • percentage accuracy in classification (PAC) - the percentage of cases correctly classified with the predictor variables added
      • sensitivity - the percentage of cases that had the observed characteristic and were correctly predicted by the model
      • specificity - the percentage of cases that did not have the observed characteristic and were correctly predicted by the model
      • positive predictive value - the percentage of correctly predicted cases with observed characteristic compared to the total number of cases predicted as having the characteristic
      • negative predictive value - the percentage of correctly predicted cases without observed characteristic compared to the total number of cases predicted as not having the characteristic
  • Variables in the Equation
    • Provides a measure of the contribution of each predictor variable in the model (like the "Coefficients" output for a linear regression)
    • Wald test - used to determine the significance (sig.) for each predictor variable
    • Exp(B) is an odds ratio used to predict the probability of an event occurring based on a one-unit change in the predictor variable when all other predictors are kept constant.

Reporting Results in APA Style

A logistic regression was performed to assess the effects of age and gender on the likelihood of having cancer. The logistic regression model was statistically significant, χ2(4) = 17.313, p < .001. The model explained 42% (Nagelkerke R2) of the variance in cancer presence and correctly classified 73% of cases. Males were 7.02 times more likely to have cancer than females. Additionally, increasing age was associated with an increased likelihood of developing cancer. 

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