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# TAMU PSYC 203 - "Z" scores

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PSYC 203 1st Edition Lecture 5Outline of Last Lecture I. Review of last classII. MedianIII. VariabilityIV. Range without reference to real limits V. Standard deviation and variance VI. Standard deviation VS. variance Outline of Current Lecture I. Outliers II. Review (Variance & Standard Deviation)III. Z Scores & LocationIV. Visual Approaches to Understanding Datasets a. Frequency distributionV. In class exampleCurrent LectureI. Outliers a. To find outliers follow: xbar +/- (c*s) with c being the cutoff value of interest (1,2,3, etc)b.c. in the graph above, the outliers are 32 and 40 because, as the formula states, xbar+/- (c*s) gives us:i. 36+/-(1*4)=32 and 40, assuming we wanted to make c, the cutoff, 1d. Ways to deal with this include:i. deletion, ii. trimming, iii. Winzorizing (setting ur own extreme value to a less extreme value), transformation (a mathematical constant applied to all data )1. Used to “pull in ends” of distributione. The key, however, is to tell the reader what you did and let them decide whether you made the right decision or not These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.II. Review (Variance & Standard Deviation)a. Variance and Standard Deviationb. Population versus Sample Formulasc. SS computation is the samed. Difference: Dividing by N (Population) versus n-1 (Sample) to compute Variancee. Outliers and the 2 or 3 SD rule of thumbIII. Z Scores & Locationa. Knowing your “Z” score is often more meaningful because they tell you how far away you are from the mean. b. The sign (+ or -) tells you if you are above or below the mean IV. Visual Approaches to Understanding Datasets a. Grouped Frequency distributioni. 10 rows s a good rule of thumb ii. this is used because people usually cant take in massive amounts of information at once b. Bar graphs i. They have the spaces because it enforces the idea that they aren’t continuous, as opposed to histograms ii. Bar graphs are used when there are categories or types c. The skew statistic i. Kurtosis measures the height of the graph1. If a graph is mesokurtic: there is a normal dist. d. Frequency distribution: method of tallying and representing how often scores occur e. 2 types of descriptive stats: central tendency & variability f. class interval: range of numbers g. midpoint the middle point in an interval h. tallyho model i. uses tallies instead i. distributions can be very different V. In class example: a. Assume you are looking at the number of pushups certain age groups can make and you have the following data:i. Age group xbar σ (pop. SD) Xbar +/-(c*σ) [c=2]20-29 17 7 17 +/-(2*σ) 0-3130-39 15 8 15+/-(2* σ) 0-3840-49 15 9 15+/-(2* σ) 0-3350-59 10 9 10+/-(2* σ) 0-2860-69 9 6 9+/-(2* σ) 0-2170+ 8 10 8+/-(2* σ) 0-28ii. Note that the range becomes 0 because you cant have negative

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