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Unformatted text preview: Exam 2 Study Guide Statistics of variability (provide info about degree to which scores in a dataset differ from one another) • Summarize and describe the extent to which scores in a distribution differ from each other • How consistent the scores are • How accurately the measure of central tendency describes the distribution Range : high score minus low score • Crude measure • Only use it as the sole measure of variability when using nominal or ordinal data Deviation : index of distance of score from sample mean (score minus sample mean) • Indicates how much the score is spread out from the mean Variance : reveals degree to which scores are spread out or clustered together • The average of the squared deviations of scores around the mean • Can also be the error variance o Refers to the differences between the scores and the mean that produce the error in our predictions • 2 Problems o Variance is unrealistically large o Variance is measure in squared units Standard Deviation : square root of variance • The average amount that scores deviate around the mean • Should equal 1/6 of the range Requirements for application of sample variance, sample standard deviation statistics: 1) Interval or ratio scale 2) Reasonably normal distribution Sample Symbols N = number of scores in sample S = sample X = score in sample X bar = sample mean = M (in APA style) S 2 x = sample variance Σ (X – X bar ) 2 /N S x = sample standard deviation = SD (in APA style) To gain an estimate of the degree to which scores vary from the mean, one might consider calculating the average of the deviations for each score in the sample: ( ∑ X – X bar ) ∕ N Problem: the average of deviations = 0 (positive and negative deviation scores cancel each other out) Calculating sample variance Because we cannot simply calculate the average deviations of scores around the mean, we have to take another approach: square the deviations Variance = average of squared deviations of scores around the mean Sample Variance = S 2 x = ( ∑ X – X bar ) 2 ∕ N Sample variance and standard deviat ion sample variance good for comparing the relat ive variability of two samples: sample with highest variance has more variability (more spread) …but averaging squared deviat ions exaggerates the size of the deviat ion scores solut ion: take square root of sample variance SD = S x = square root of ( ∑ X – X bar ) 2 ∕ N Standard deviation sample standard deviation allows us to determine exactly how deviant a single score really is sample SD allows us to determine what percentage of scores fall above or below a particular point on the distribution. Standard deviation applied to the normal curve Approximately 68% of scores fall in the range between 1 and +1 standard deviations from the mean Approximately 95% of scores fall in the range between 2 and +2 standard deviations from the mean Relationship between SD and proportion of scores in a normal distribution Estimating population variance/...
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This note was uploaded on 01/24/2010 for the course PSYC 2401 taught by Professor Wallace during the Fall '08 term at Trinity University.
 Fall '08
 Wallace
 Psychology

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