2_Distributions_Graphs

2_Distributions_Graphs - Distributions & Graphs...

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Unformatted text preview: Distributions & Graphs Distributions & Graphs Variable Types Variable Types Discrete (nominal) Sex, race, football numbers Continuous (interval, ratio) Temperature, Test score, Reaction time Frequency Distributions Frequency Distributions Graphic representation of data Basic kinds of frequency distributions Easier to understand than raw numbers Helps communicate to others Ungrouped – simple tally Grouped – used to simplify Uses Relative and cumulative frequency Shape Common of Graphs Common of Graphs Bars show counts 6 Bar Chart (discrete) Frequency 4 2 0 f 4 e ee e e 40 30 20 3 e e e ee e ee e e e e ee e e eee eee eee ee e e e eee eee e e e ee e e e e e e ee e e eeeee e e ee e e eee e e e e ee ee e eee e e e e ee e e e ee e e e e eeee ee e ee e e e eeee ee e e e eeee e e ee ee e e e e e ee e e e ee e e e e eeeee eeee e e e ee e e e e e eeee ee e e e e eee e e e e e ee ee e eee e e ee eee e ee e e e e eee e e e e e eee ee e e e ee e ee e e eee eee e ee e e e e e e e e ee e e e e e ee e e e ee e e ee e ee e ee e eeee ee eee e e e e e e ee e e e 10 2 1 e e ee e ee ee eee e e e e e e ee e e e ee ee e e e e 59.00 50 m Sex Frequency Histogram (continuous) Scatterplot (2 variables) Miles per Gallon 100 150 Horsepower 60.00 61.00 62.00 200 Height Inches 63.00 64.00 Distribution Shapes Distribution Shapes Normal Center Spread Shoulders Skew There will be numerical ways to describe all these, but for now, just consider the shape visually. Normal Normal Central Tendency Central Tendency Variability (spread) Variability (spread) Central tendency and Variability Skew Skew The tail! Kurtosis ­ shoulders Kurtosis ­ shoulders Odd Shapes Odd Shapes Modern Stat Graphs Modern Stat Graphs Box plot Stem­leaf Boxplot Boxplot Boxplot for a normal distribution 9 Largest C ase not an Outlier 8 7 Whisker or tail 75 %tile 6 5 Middle 50 Perc ent Median 25 %tile 4 3 2 Whisker or tail Smallest C ase not an Outlier 1 N= 17 D1 Same distribution as a (sort of) histogram Boxplot with outliers Boxplot with outliers 20 22 10 20 19 0 21 -10 N= 21 Extreme Outlier Outlier Outlier Extreme Outlier Boxplot with Skewed Distribution Boxplot with Skewed Distribution 30000 20000 224 225 226 223 227 222 10000 0 10000 N= 227 volcano heights Exam and Course Distributions Psych Stats Fall 2007 Course Grades Sp 2008 Course Grades Sp 2008 Stem­leaf diagram Stem­leaf diagram Frequency Stem & Leaf 1.00 2 . 0 2.00 3 . 00 3.00 4 . 000 4.00 5 . 0000 3.00 6 . 000 2.00 7 . 00 1.00 8 . 0 Stem width: 1.00 Each leaf: 1 case(s) Normal distribution Stem­leaf of volcano heights Stem­leaf of volcano heights Frequency Stem & Leaf 8.00 0 . 25666789 8.00 1 . 01367799 23.00 2 . 00011222444556667788999 21.00 3 . 011224445555566677899 21.00 4 . 011123333344678899999 24.00 5 . 001122234455666666677799 18.00 6 . 001144556666777889 26.00 7 . 00000011112233455556678889 12.00 8 . 122223335679 14.00 9 . 00012334455679 13.00 10 . 0112233445689 10.00 11 . 0112334669 9.00 12 . 111234456 5.00 13 . 03478 2.00 14 . 00 3.00 15 . 667 2.00 16 . 25 2.00 17 . 29 6.00 Extremes (>=18500) Stem width: 1000.00 Each leaf: 1 case(s) Final Grade Pct Sp 08 Final Grade Pct Sp 08 TotPct08 Stem­and­Leaf Plot Frequency Stem & Leaf 12.00 Extremes (=<.48) 3.00 5 . 669 12.00 6 . 011333344444 18.00 6 . 555566677777889999 28.00 7 . 0000111122222223333333444444 34.00 7 . 5555555566666667777777888888889999 29.00 8 . 00000111111112222223333344444 13.00 8 . 5555566667788 16.00 9 . 0000011111123344 Note that SPSS has the boxplot 3.00 9 . 566 with larger numbers at the top, Stem width: .10 Each leaf: 1 case(s) but the stem­leaf shows larger numbers at the BOTTOM, so one is backwards from the other. Definition Definition Political party is an example of what kind of variable? 1 continuous 2 discrete 3 intensity 4 objective Definition Definition A distribution with a long tail to the right (high) end is called ________ 1 leptokurtic 2 negatively skewed 3 platykurtic 4 positively skewed Graphs Graphs Which boxplot shows a skewed distribution? 2 1 4 3 8 12 10 6000 7 5000 10 8 6 4000 5 8 6 4 3000 6 4 3 2000 2 4 2 1000 2 N= 24 VAR00001 1 0 0 N= 406 Vehicle Weight (lbs. N= 0 19 VAR00002 N= 19 VAR00001 Discussion Question Discussion Question When might you prefer a graph to a table of numbers for presenting a result? Name a variable you think would be interesting for college students to see as a graph. What kind of data would you put in the graph? Why would it be of interest? ...
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