Converting to log-odds, for the practice reading log-odds units...
In bits, we have:
90% initial confidence = lg(90%/10%), which is about 3.2 bits likely
30% final confidence = lg(30%/70%), which is about −1.2 bits likely, or 1.2 bits unlikely
total evidence needed to shift our view that far: 4.4 bits
In decibels:
90% initial confidence = 10 log(90%/10%), which is about 9.5 decibels likely
30% initial confidence = 10 log(30%/70%), which is about −3.7 decibels likely, or 3.7 decibels unlikely
total evidence needed to shift our view that far: 13.2 decibels of evidence
Converting to log-odds, for the practice reading log-odds units...
In bits, we have:
90% initial confidence = lg(90%/10%), which is about 3.2 bits likely 30% final confidence = lg(30%/70%), which is about −1.2 bits likely, or 1.2 bits unlikely total evidence needed to shift our view that far: 4.4 bits
In decibels:
90% initial confidence = 10 log(90%/10%), which is about 9.5 decibels likely 30% initial confidence = 10 log(30%/70%), which is about −3.7 decibels likely, or 3.7 decibels unlikely total evidence needed to shift our view that far: 13.2 decibels of evidence