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# Psy 202 Week 3 Lecture Notes Psy 202

OleMiss

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This 7 page Class Notes was uploaded by Anna Ballard on Monday September 12, 2016. The Class Notes belongs to Psy 202 at University of Mississippi taught by Mervin R Matthew in Fall 2016. Since its upload, it has received 18 views. For similar materials see Elementary Statistics in Psychology at University of Mississippi.

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Date Created: 09/12/16

Lecture 4 9/7 Ch. 3 –> Describing Quantitative Data w/ Summary Statistics Deviations from the Mean - Figure out average distance from the average Average Deviation - ADy = ∑|Yi – µy| ÷ n o Absolute value bars prevent cancelling out i Y µy Y - µ |Y - µ| (Y - µ)^2 1 6 5.67 0.33 0.33 0.11 2 3 5.67 -2.67 2.67 7.13 3 4 5.67 -1.67 1.67 2.79 ***Average Deviation is super 4 2 5.67 -3.67 3.67 13.47 sensitive to 5 7 5.67 1.33 1.33 1.77 sample size *** 6 12 5.67 6.33 6.33 40.07 ∑ 34.0 34.0 -0.02 16 65.34 2 2 Rounding errors The Variance: Definitional Formula • Squared average deviation y ∑ [(Y - µi) ÷ y 2 - squared means variance! ** try to avoid rounding errors because in the grand scheme, after squaring, you are only making those errors bigger! The Variance: Computational Formula Squared Sum of Y The Standard Deviation 2 2 Sum of y = ∑ Y i Square of – (∑Y 1 /n Ys n *** PREFERRED *** Square root of variance 2 gives variability in[∑ (Y – 1 ) ÷ y ] original units Interpreting the Standard Deviation CV = / y Coefficient of µ y Variation The Variance of a Sample: - uses sample to describe population Degrees of Freedom Sample mean We want sample to 2 approximat s = ∑ (Y 1 e total – Y) 2 population! n- Sample Variance Degrees of Freedom Computational Formula 2 2 The Shape Distribution∑ Y i – (∑Y 1 /n • Measure distribution – Skewness - no skew –> mean = median = mode Extreme Score Effects: - median - mean (moreso than median) Measure of Curvature (Kurtosis) Leptokurti c Ç√ K>0 Mesokurtic Ç√ K=0 Ç√ Platykurt ic K<0 Box and Whisker Plots - give us measure of central tendency and measure of variance - allows us to see distance Lecture 7 9/9 Ch. 4 –> Describing Categorical Data Intro – there is no natural ordering for categorical form - any order you put them in works Frequency Table Y F(Y) Rf(Y) • Almost always going to be ungrouped Baseball 31 0.207 • Order does not matter # of scores incause you cannot have Basketb 26 # of 0.173 scoresgroup are below a certain all categories level Football 29 0.193 Hockey 30 0.200 Bar Graph *Example does not use same data* Soccer 34 0.227 • When dealing with categorical scores there is no skewness or kurtosis • Bars do not touch – scores are discrete Pie Chart • Slices can be in any order • rf or percentage used more often than f • harder to read (bar chart is easier) • good to use when dealing with budget information Central Tendency • Mean – there is no scores to average – CANNOT USE • Median – there is no order – CANNOT USE • Mode – the only measure of central tendency you can use for categorical cases! Variability c IQVJ= 1 (n2 – ∑ nj2) Group index n2 (c–1) Index of Qualitative Variation Total # of scores c IQV = c (n2 – ∑ nj2) J= 1 1502 (5–1) IQV = 5 [• If all the scores are in 1 group IQV is ZERO • The closer you are to zero, the more scores are only in 1 group • When they are spread out evenly then IQV will come out to equal 1 • The closer you are to 1 they are almost evenly distributed IQV = 0.998 Lecture 8 9/12 Ch. 5 –> Describing the Position of a Case within a set of Scores Expressing the Ordinal Position of a Score • Percentile and percentile rank –> give ordinal only * Percentile Rank : raw scores –> cumulative relative frequency - used more often because of an easier conversion • Percentile : cumulative relative frequency –> raw scores Z i (Y – µi) / y y *** Cumulative relative frequency (CRF) is always written in decimal form *** - use that to figure out % at or below your level - CRF = 0.63 –> 63 percentile rank - Always round down to chop off extra decimal places (AKA no fractions @ percentiles) Interpreting Percentile Rank - Can tell you if someone is above or below someone else but not by how much - Aka no distance info! Misinterpretations of Percentile Rank Scores • “Lowest earning workers can’t afford median rents” - Invalid statement because if lowest earning’s pay increases, the median will also increase because the median is always in the middle. The Position of a Score Relative to the Mean - Checking deviation scores and determining if large or small Setting Standard: Normal distribution - How many standard deviations is it above/below mean? - These are standardized (z) scores Y iraw score) – µ y Ç√ 0 Renames scores but does not change score itself or distribution shape 2 i Y µy Y - µ y y Z i (Z i y 1 6 5.67 0.333 3.30 0.100 0.010 2 3 5.67 -2.667 3.30 -0.808 0.653 3 4 5.67 -1.667 3.30 -0.505 0.255 4 2 5.67 -3.667 3.30 -1.111 1.234 5 7 5.67 1.333 3.30 0.404 0.163 6 12 5.67 6.333 3.30 1.919 3.683 ∑ 34 34.002 -0.002 -0.001 5.998 • Absolute value of standard deviation tells you how much above/below - Signs tell you direction Using Z-scores to Derive New Metrics • Converting raw scores to standard scores and comparing distributions Z scores always sum to 0, so mean = 0 Ç√ Variance always equals 1! (must divide this number by 6 because n = 6 Test X 80 120160 200 240280 320 Test Test Y 40 6080 100 120140 160 Test Y µy 200 100 x 40 20 Which is better, 230 on test X or 117 on test Y? Zi= (Y –iµ ) y y Test X: Z = i230 – 200) /40 = 0.75 deviations above mean Test Y: Z =i(117 – 100) /20 = 0.85 so this is better choice!

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