Distributions:
Normal distribution is where the mean, median, and mode are identical; is symmetrical; and tails never touch x-axis. Characteristics in nature are thought to be normally distributed. Parametric statistics are appropriate.
Non-Normal distributions is not symmetical; is either positively skewed (tailed) or negatively skewed; and is peaked (leptokurtic or less variability) or flat (platykurtic or more variability). Non-parametric statistics are appropriate.
Population vs. Sample (subset of population)
Sample statistic vs. population parameter (like "x bar" and "mew" for mean). If you know parameters, you do not need statistics.
Variability:
Variability is the spread or dispersion of scores in a distribution.
1. Range is highest score value minus lowest score value. Range is not sensitive to inside variability. Two sets of data can have the same range, but very different standard deviations.
2. Variance is an index that considers all scores (including inside variability). Sample is read as "s squared" and population is read as "sigma squared". Variance is the average distance of all the scores from the mean of the scores. Sum of (x - mean) squared/(n - 1) = s squared. Variance squares the distance from the mean because without squaring it, the answer would be zero.
3. Standard deviation is the square root of variance. Standard deviation is an index of variability that is expressed in the original counting units (variance is expressed in squared counting units). It is known as the "spread-out-ness". It is read as "s" for samples and "sigma" for population.
(On exam: A calculation of standard deviation will be required by hand)
4. Median Absolute Deviation is used for ordinal (ranked) data and skewed data (see pg. 103).
*If you have scaled (interval) data, then use mean and standard deviation. If you have ranked (ordinal) data, then use median and median absolute deviation. If you have nominal data, then use mode and a frequency comparison. (See table 5.5 page 107).
No comments:
Post a Comment