## Normal Probability PlotsDetecting normality from a histogram is a difficult job when data sets are not large. Here we view 4 large data sets and corresponding "normal probability plots." If we see how they relate when histograms are easily described (because of the large amounts of data) we can infer how they relate when histograms are not so easy to parse (because of small amounts of data). ## Normal Probability PlotsThe basic premise is that the plot compares the data
with what would be expected of data that is perfectly
normally distributed. Then two quantities are compared:
The data and idealized normally distributed data. If the
two generally agree that means the data agrees with what
would be expected from a normal distribution. The normal
probability plot is then ## Data Sampled From a Normal DistributionHere's a histogram of 100 observations that were
randomly sampled from a normal distribution. Below the
histogram you see the normal probability plot of the data
(generated used the Notice that the normal probability plot (NPP) is
basically ## Data Sampled From a Left Skewed DistributionFor left skewed data, the normal probability plot is generally not straight. In general this sort of curvature in the NPP evinces left skew. ## Data Sampled From a Right Skewed DistributionFor right skewed data, the normal probability plot is generally not straight. In general this sort of curvature in the NPP evinces right skew. ## Data Sampled From a Bimodal DistributionFor bimodal (two distinct peaks) data, the normal probability plot is generally not straight. In general this sort of curvature evinces bimodality. Want to see how this works in making conclusions about the normality of small samples? |