Test 2 Flashcards
Problem with range
based on just 2 scores, can be inflated if there are extreme scores
Interquartile range
difference between the 75 percentile and 25 percentile
Advantage: not influenced by extreme scores
Problems: difficult to determine, based on only 50% of data
Variance
- derived from SS
- get pop. variance by dividing SS by n
- pop. variance is a biased estimator
Why is variance a biased estimator? and solution
- if all samples obtained, and variance calculated for each sample dividing by n, the mean of sample variances would underestimate value of pop. variance
- Solution: divide SS by n - 1, and get s^2
Why is SS divided by n-1 (not n) when calculating s^2?
- n - 1 are degrees of freedom when calculating sample variances
- mean of sample variances would equal value of pop. variance if you divinde by n - 1 (so unbiased)
Degrees of freedom
the number of ways the scores that are needed to calculate a statistic are free to vary
- deviations from the mean are free to vary n - 1 ways
Standard deviations
Provides a measure of the typical (standard) amount of deviation of a score from the mean
- Still a problem with σ2and s2: Inflated because all deviations are squared
- solution: take square root of variance
- s is preferred because it is the unbiased estimate of pop. SD
Which is usually the preferred measure of variability?
Standard deviation (usually sample)
Sum of Squared Deviations formula
SS = ∑(x - M)^2
Why do we square deviations from the mean?
because ∑(x - M) = is always 0
No matter how much variability there is
Sum of squared deviations conceptual formula
can be derived from understanding concept
- difficulty: requires means (often decimals)
X
Sum of squared deviations computational formula
easier for calculations
X
Central tendency
To provide info about the avg, middle, or most frequent score
Mean
average score
PPT def
M = ∑ x / n
Median
middle score
- point that cuts distribution in 1/2 (half greater, half less than)
- advantage: not influenced much by extreme values (skew)
