I have a logistic regression model, where a binary response variable is being explained by a categorical variable which has three classes.
When we look at the 95% confidence intervals of the odds ratios of the three classes, two of them differ in a statistically very significant way (p<0,001).
But when I calculate predicted values which results in 3 means of predicted values for members of the three categories, the plusminus (standard error * 2) from the means gives much larger confidence intervals, such that all the intervals of the three means of the three categories are overlapping.
Can anyone explain to me why is this happening, if it is true, that some of the categories differ in a statistically significant way?