Psychology 202a Advanced Psychological Statistics September 8, 2015

What can we say about the Peabody distribution? The Peabody distribution is centered in the 80s and 90s. The distribution tends to pile up in one place. There is substantial variation in the scores. The distribution is not symmetric: there may be some negative skew. Extreme low and high scores are much less frequent than central scores.

Aspects of shape Those points correspond to the basic aspects of shape: –central tendency –modality –variability –symmetry or skew –kurtosis

Numerical Methods descriptive statistics measures of central tendency: –mean –median –mode central tendency in R: –mean(Peabody)‏ –median(Peabody)‏

Choosing measures of central tendency geometric interpretations –mean = balance point –median = halfway point your purpose may govern choice –cereal box examplecereal box principle of “resistance” may govern choice

Stem and Leaf Plot of Peabody 5|7 6|14 6| |12 7|6679 8| | | |556 10|0

Descriptive Statistics for Variability skipping over modality (why?)‏ The measure of variability is pretty much determined by the measure of central tendency. median  interquartile range mean  standard deviation

The interquartile range Considerations that make the median a reasonable choice for central tendency (e.g., resistance) may apply just as well to measuring variability. Interquartile range = the difference between the median of the upper half of the data and the median of the lower half. These “medians” are actually quartiles.

Stem and Leaf Plot of Peabody 5|7 6|14 6| |12 7|6679 8| | | |556 10|0

The standard deviation When the mean is the chosen measure of central tendency, a measure of variability that is something like average distance from the mean is a reasonable way of describing variability. Digression in R.

The standard deviation (cont.) The conceptual formula for the sample variance is The standard deviation is just the square root of the variance.

Simple descriptive statistics in SAS proc univariate proc means

Extending R Writing a simple function. An IQR function that does what we want it to do.