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Odds Ratio in Logistic Regression Quantitative Research

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Updated: Aug 12th, 2019

In logistic regression, odds ratio indicates the nature and the degree of association between a dependent variable and independent variables. Macdonald (2015) states that odds ratio applies to the prediction of a dependent variable using independent variables in logistic regression analysis. In this case, the dependent variable is burnout while the independent variables are coping style and stress from teaching.

The dependent variable is a binary categorical variable because it comprises burnout and no burnout. The independent variables contain continuous data, which indicate the degree of coping style and stress from teaching. High scores and low scores of coping style indicate high and low ability to cope with stress respectively.

Similarly, high scores and low scores of stress from teaching show high and low levels of stress that emanate from teaching. The odds ratio in this case originates from the comparison of the probability of burnout and the probability of no burnout. In this view, the logistic analysis applies these variables in demonstrating odds ratio.

Table 1 indicates that there is significant difference between logistic regression model with a constant only and the logistic regression model with all independent variables, namely, coping style and stress from teaching, (χ2(2) = 137, p = 0.000).

Table 1

Omnibus Tests of Model Coefficients
Chi-square df Sig.
Step 1 Step 137.015 2 .000
Block 137.015 2 .000
Model 137.015 2 .000

Table 2

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 393.092 .254 .375

The model summary table (Table 2) shows that coping style and stress from teaching explain 25.4% (Cox & Snell R Square) or 37.5% (Nagelkerke R Square) of the variation in burnout. The explanatory power is important in interpreting odds ratio, which describe the nature and the strength of the relationship between burnout, the dependent variable, and coping style and stress from teaching, the independent variables.

Table 3

Classification Table
Observed Predicted
Burnout Percentage Correct
Not Burnt Out Burnt Out
Step 1 Burnout Not Burnt Out 320 28 92.0
Burnt Out 65 54 45.4
Overall Percentage 80.1

Table 3 is a contingency table, which shows the distribution for 80.1% of the total lecturers (N = 467). In this view, the table suggests that the model can predict 80.1% of the total lecturers, which is very significant.

From the logistic regression model, it is evident that coping style (Wald χ2(1) = 71.287, p = 0.000) and stress from teaching (Wald χ2(1) = 5.760, p = 0.016) are significant predictors of burnout. Thus, the statistical significance of coping style and stress from teaching validates the use of these predictors in the analysis of odds ratio.

In interpreting odds ratio, Field (2013) states that odds ratio greater than one indicates that a predictor variable increases a criterion variable while odds ratio less than one indicates that the predictor variable reduces criterion variable. From Table 4, the odds ratio for coping style and burnout is 1.111 (95% CI, 1.084 to 1.138).

The odds ratio suggests that a unit increase in coping ability increases burnout by 11.1%. The odds ratio for stress from teaching and burnout is 0.968 (95% CI, 0.943 to 0.994). The odds ratio suggests that a unit increase in stress from teaching results in a reduction of burnout by 3.2%.

Table 4

Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I. for EXP(B)
Lower Upper
Step 1a cope .105 .012 71.287 1 .000 1.111 1.084 1.138
teaching -.032 .013 5.760 1 .016 .968 .943 .994
Constant -2.077 .592 12.308 1 .000 .125
a. Variable(s) entered on step 1: cope, teaching.

References

Field, A. (2013). Discovering statistics using SPSS (4th ed.). London: SAGE Publisher.

Macdonald, S. (2015). Essentials of Statistics with SPSS. Raleigh: Lulu.com Publisher.

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