I found a figure as follows, showing distributions of some scores at three time points:
Considering the with of 25th-75th percentiles, how can 95% CIs be so narrow? Is this erroneous?
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Confidence intervals represent a type of confidence in knowing the mean value in the underlying population, based on your data sample. They are often calculated from the estimated standard error of the mean, which decreases with the square root of the number of observations. Even though the widths of the distributions are themselves large, with enough data points (sampled from a distribution that meets certain requirement) you can still get a very precise estimate of the mean value in the population.