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by: kgottuk

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# PSYCH 315 Week 3 Notes Psych 315

kgottuk
UW

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These notes go over variance, standard deviation, and other topics we have gone over in week 3.
COURSE
Statistics of Psychology
PROF.
Dr. Dana Nelson
TYPE
Class Notes
PAGES
6
WORDS
CONCEPTS
standard deviation, Statistics, variance
KARMA
25 ?

## Popular in Psychology (PSYC)

This 6 page Class Notes was uploaded by kgottuk on Sunday October 16, 2016. The Class Notes belongs to Psych 315 at University of Washington taught by Dr. Dana Nelson in Fall 2016. Since its upload, it has received 4 views. For similar materials see Statistics of Psychology in Psychology (PSYC) at University of Washington.

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Date Created: 10/16/16
1 Week 3 Notes Measure of Variability/Dispersion: single summary figure that describes spread of observation within a distribution - Distributions will vary in shape, central tendency, and variability - Types: o Range = highest score – lowest score = distance between them  Often paired with mode (least stable across samples; strongly affected by extreme scores)  Only descriptive (sometimes used) o Interquartile Range (IQR): range of middle 50% of observations (IQR= Q – Q ) 3 1  1, 2 ↓ 3, 4 ↓ 5, 6 ↓ 7, 8 IQR= 6.5 - 2.5 = 4 Q 1 Q 2 Q 3  Not affected by extreme scores and reported with the median  Only descriptive (not often used, but can be for open-ended distributions) Deviation-Based Measures of Variability - Deviation score (x - x): difference of each score(x) from the mean (x) ̅ ̅ o If the mean is balanced  ∑ = 0 o Can’t calculate average distance of all scores from mean since all scores = 0  Other ways: ∑(x - x)̅and sometimes absolute value - Variance (ϭ, s x S x: variability = mean of squared deviation scores o Population variance ϭ x ϭ = ∑ (x - µ) = SS x N N 2 Σ(????−????) 2 ???????????? - Estimate of population variance (Howell’s sample variance): s = x ????−1 =????−1 o Underestimates true population variance (to compensate, divide by (n-1) as deg. of freedom) o Sample variance used to estimate population variance *mean for chart x = ̅* 2 ???? ???? x x - ̅ (x - ̅) Ϭ = ???? ????−????) S =2 ????(????−????) x ???? x ????−???? 2 -3 9 18 / 4 = 4.5 18 / (4-1) = 6 4 -1 1 Avg. sq. distance of 7 2 4 each score 7 2 4 from the mean. ∑ = 18  SS (sum of all squares) 2 o Standard deviation: sq. root of variance  used most and reported with mean  used for descriptive and inferential Normal Distribution: bell-shaped; basis of many stat. procedures (samp. dist.); based on mathematical function Standard Normal Distribution: normal distribution, mean of 0, SD of 1 Standard Deviation Units: SD used as unit of measurement; makes norm. dist.  stand. norm. dist. Inflection point - Standard score: value of how far score is from mean using standard deviation units o Z-score: type of standard score; indicates how many SD above or below a score is  Raw score  z-score  z = X     to convert z-score  raw score, rearrange equation Examples: 55 70 85 100 115 130 145 Raw  z- score: z = score – mean = 85 - 100 = -15 = -1 St. dev. 15 15 Finding the area of a normal distribution with a score when mean = 100 and SD = 15 Area above 110 Z = 110 – 100 / 15 = .67 Smaller = .2514 P x 100 Area below 80 Z = 80 – 100 / 15 = -1/33 Smaller = .0918 P x 80 Area between 90 and 105 Z = 90 – 100 / 15 = - .67 Mean to Z = .2486 .2486 - .1293 = .1193 Z = 105 – 100 / 15 = .33 Mean to Z = .1293 P 90x < P 105 3 Getting a score from a percentage when mean = 100 and SD = 15 Score corresponding to the top 5% 1. .05 (change percentage to proportion) 2. z = 1.64 (found by seeing which score on left side of z-chart matched up closest to .05) 3. x = 100 + 1.64 (15) = 124.6 Score corresponding to the bottom 1% 1. .01 2. z = - 2.33 (negative because it is on the left side of the middle of the distribution) 3. x = 100 + (-2.33)(15) = 65.05 Score corresponding to middle 10 % 1. .05 (5% on right side and 5% on left side to create middle 10%) 2. z = ± .13 3. x = 100 ± .13 (15) = 98.05 and 101.95 4 5 6

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