How to Read a Probit Table

Reading a probit table involves understanding how the results from a probit regression model are presented. A probit regression is used to model binary outcome variables, where the dependent variable is dichotomous. The probit model estimates the probability that the dependent variable equals one, given the values of independent variables. The results are presented in a table that includes coefficients, standard errors, z-values, and p-values, among other statistics. Here’s a detailed guide on how to interpret each component of a probit table.

Understanding the Probit Table Components

1. Coefficients (β)

The coefficients represent the estimated effect of each independent variable on the probability of the dependent variable being one. In a probit model, these coefficients are not in probability units but rather in terms of the z-score, which is the number of standard deviations away from the mean.

• Positive Coefficient: If the coefficient is positive, it implies that as the independent variable increases, the probability of the dependent variable being one increases.
• Negative Coefficient: Conversely, a negative coefficient means that an increase in the independent variable decreases the probability of the dependent variable being one.

2. Standard Errors

The standard error measures the variability or dispersion of the coefficient estimates. It is used to assess the precision of the estimated coefficients. A smaller standard error indicates a more precise estimate.

• Calculation: The standard error is usually computed as the square root of the variance of the coefficient.
• Interpretation: If the standard error is large relative to the coefficient, it indicates that the estimate is not very reliable.

3. Z-values

The z-value (or z-score) is calculated by dividing the coefficient by its standard error. It measures how many standard deviations the estimated coefficient is from zero.

• Formula: $Z=\frac{\text{Coefficient}}{\text{Standard Error}}$Z=Standard ErrorCoefficient​
• Interpretation: A higher absolute z-value suggests that the coefficient is significantly different from zero. In other words, it indicates the strength of the evidence against the null hypothesis that the coefficient is zero.

4. P-values

The p-value indicates the probability of observing the estimated coefficient, or one more extreme, if the null hypothesis were true. It helps in determining the statistical significance of the coefficient.

• Thresholds: Common thresholds for significance are 0.05, 0.01, and 0.10. A p-value less than 0.05 typically indicates statistical significance.
• Interpretation: A low p-value suggests that the coefficient is significantly different from zero and thus has a meaningful impact on the dependent variable.

5. Marginal Effects

Although not always included directly in the probit table, marginal effects are crucial for understanding the practical implications of the coefficients. They measure the change in probability of the dependent variable being one for a one-unit change in an independent variable, holding all other variables constant.

• Calculation: Marginal effects are derived from the coefficients and the estimated standard normal cumulative distribution function (CDF).
• Interpretation: They provide a more intuitive understanding of how changes in the independent variables impact the probability of the outcome.

Example of a Probit Table

Here is a simplified example of a probit table to illustrate these concepts:

Variable	Coefficient (β)	Standard Error	Z-value	P-value
Intercept	-1.234	0.456	-2.71	0.007
Variable X1	0.789	0.123	6.42	0.000
Variable X2	-0.345	0.210	-1.64	0.101

• Intercept: The negative coefficient suggests that, holding other variables constant, the baseline probability of the dependent variable being one is lower.
• Variable X1: The positive coefficient with a low p-value indicates that an increase in X1 is significantly associated with an increased probability of the outcome being one.
• Variable X2: Although the coefficient is negative, the higher p-value suggests that the effect is not statistically significant.

Conclusion

Reading and interpreting a probit table requires understanding how each component reflects the relationship between independent variables and the probability of a binary outcome. By analyzing coefficients, standard errors, z-values, and p-values, one can assess the significance and impact of each variable in the model. Marginal effects further aid in translating these findings into practical terms, enhancing the utility of the probit regression analysis.