be precise and don't use pronouns; verbalizing concepts help you learn them cognitively

central tendency:  the one number that best represents all the scores

frequency distribution; provide counts of the data (stem & leaf or graph)

• think qualitatively: where is the central tendency?

• sample: represented by roman characters (x)
• population parameters: represented by greek symbols (beta); usually not calculated because you limit to a sample
  • there is no guarantee that calculating a mean for a sample equals or is even close to the mean for a population.
  • (sampling error--each person is unique.)

mean  (average): conceptual & mathematical balancing point of the distribution (distribution being the set of data, arranged)

when in doubt, create a graph!

variance / variability ("spreadoutness"): tells us the difference between two classes with the same average--how spread out from that score is each class?

measures of variance: range, standard deviation, etc.

• range = highest score minus the lowest score (outliers can be a problem)
• sum of squares (SOS) = integral to regression (mucho importante!!);
  • subtract the mean from each score, then square them and sum those. it shows you how far from the middle each score is. :)  we could use other numbers to show the spreadoutness, but we use the main because it is the balancing point of the distribution.
  • if you subtract the mean from each score, and add the results (deviation scores), it always equals zero.
  • we square the deviation scores, then, to eliminate the negative score--here, negative is not a VALUE, but indicates a DIRECTION of spreadoutness in the distribution (distance from the mean).
  • SOS is hard to interpret because it's a squared (exponential) metric. We're trained to think in the power of 1.
  • now take sample size into account. There is more variance if there is less central tendency; 1, 2, 3 (more conceptual variance) VS 1, 2, 2, 2, 3 (stronger central tendency). BUT the SOS is the SAME for both sets of data--need to take sample size into account.  Remove the influence of n (sample size)--divide the SOS by n-1. We remove the influence of something by dividing by it. Variance of population: divide by N. Variance of sample: divide by n-1. Why divide by n-1? It's a degrees of freedom issue... there's a good reason, but it's complex.  :)
  • We're still in a squared metric, (even though variance is an adequate measure of spreadoutness)
  • Take the square root of the variance: that's the standard deviation. We unsquare it to get it back in the power (non-exponential metric) of the original scores. The standard deviation gives us something like the average spreadoutness of the scores around the mean. "How different are the scores around the mean?" Standard deviation is a good answer to that.
  • It's a product-moment leverage issue like in physics: the farther a weight on a scale is from the fulcrum, the heavier the weight near the fulcrum must be to balance it out. That's why we square and then unsquare, instead of simply using absolute values.
• individual differences: how different each person is from the other; differences in scores, etc. (why people score differently on measures); can we predict or explain that?

distributional shape

• skewness: how the scores tend to the positive or to the negative; does the tail (smaller end) go toward the higher numbers (or more positive numbers)? The mean gets pulled toward the outliers.
  • symmetrical: (has no skewness; the skewness should be 0 if the graph is symmetrical)
  • Z (standard scores): score minus the mean, divided by the standard deviation--remove the influence of the standard deviation.
  • difference between SCORES and MEASURES of variance/etc.; measures of variance are statistics; scores are the distance of ONE PERSON
• kurtosis: measures normality. distributional shape doesn't matter in normality; .... (GET THIS FROM ANNIE) 0 = a normal curve. positive # = taller & skinnier (leptocurtic). Negative # = platykurtic, wider, shorter.