The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Avoidance learning and learned helplessness are critical concepts in understanding behavioral responses to negative stimuli.
Avoidance learning occurs when an organism learns that a specific behavior can prevent an unpleasant outcome. For example, a student who receives a bad grade may start studying harder to avoid future poor grades. This behavior persists even when the negative outcome is no longer present. Avoidance learning is powerful because it maintains behavior in the absence of the...

Albert Bandura's observational learning, also known as imitation or modeling, occurs when a person observes and imitates another's behavior. It is a quicker process than operant conditioning. A well-known example is the Bobo doll study, where children who saw an adult acting aggressively towards the doll were more likely to act aggressively when left alone, compared to those who observed a nonaggressive adult. Many psychologists view observational learning as a form of latent learning...