These notes are not meant to be inclusive of all the information we will cover. I created a PowerPoint presentation to teach some of the concepts covered in this unit.
NOTE: We divide by number of scores if the data is from the entire population...we divide by the number of scores minus 1 (6-1=5) if the data is from a sample. If our data were from a sample the variance would be 52 divided by 5 (52 divided by 5 = 10.4)
YOU CAN EASILY CALCULATE THE MEAN AND STANDARD DEVIATION WITH EXCEL.
Visit http://davidmlane.com/hyperstat/z_table.html to use an on-line program that will calculate areas under the normal curve. I also have a PowerPoint presentation on how to use his z table program.
T score (transformed score -- a.k.a. Z score) --> multiple the z
score by 10 and add 50
(i.e., z score=-1.5 --> -1.5 X 10 = -15 --> -15 + 50 = 35)
The skew is the tail. If the tail (skew) is on the left (negative side), we have a negatively skewed distribution. That means that more of the subjects scored on the high end (because most of the people are not in the tail where the low scores are)..
If the skew (tail) is on the right (positive side), we have a positive skew. That means more people scored low (because most of the people are not in the tail where the high scores are).
Sometimes most of the scores are in the middle, we then have a leptokurtic distribution.
Sometimes the scores have a large spread without a lot of people in the middle, we then have a platykurtic distribution.
If a set of scores does not form a normal distribution (skewed), then the characteristics of the normal curve do not apply. For example, 68% of the scores would not fall within one standard deviation of the mean if the distribution were negatively skewed.
Del Siegle, Ph.D.
Neag School of Education - University of Connecticut