y axis: Frequency or Density x axis: binned variable bins defined by: lower & upper limits midpoint bin width = upper-lower Histogram Frequency

Transcription

1 Part 3 Displaying Data Histogram requency y axis: requency or Density x axis: binned variable bins defined by: lower & upper limits midpoint bin width = upper-lower Density area of each rectangle equals proportion of measures falling in a bin density = (frequency/total) / binwidth = proportion / binwidth Histogram Body Weight Body Weight Note dip in distribution. Histogram requency requency requency requency Weight (lbs) Weight (lbs) Bin widths are crucial! Too wide and you can obscure important details. Bins that are too narrow and can obscure important trends.

2 requency Stem-and-Leaf Displays Stem: vertical pieces (leading digits) are analogous to midpoints bin lower limit in histogram The decimal point is 1 digit(s) to the right of the Leaves: horizontal pieces (trailing digits) provide information about data points within each bin Reading a stem-and-life display > stem(dat,scale=1) The decimal point is at the > stem(dat,scale=2) The decimal point is at the sorted data Bar Graphs Line Graphs Canada Student Loan Balance ( ) New York City Temperature 2013 New York City Temperature 2013 Percent ean Weight Temperature () Temperature () < > 30 emale ale Debt (thousands of dollars) Gender Week Week Value of interest is represented by height of bars. X-axis usually consists of levels on a qualitative/nominal variable. Typically have quantitative variables on X and Y axes.

3 Scatter Plots height (inches) weight (lbs.) Value of homes in aplewood, NJ 1970 (thousands $) 2000 (thousands $) 2000$ = 1970$ reference line regression line Useful for visualizing the association between quantitative variables Pie Charts Left Right ixed ade Proportion of Rivalry Percept Time Left Right ixed ade Proportion of Rivalry Percept Time Graph Rules Graphs complement and add to quantitative analyses Graphs are essential for seeing patterns/trends in data - and checking validity of assumptions underlying analyses Keep things simple - label axes - start axes at zero whenever possible - avoid empty frills (e.g., 3D displays) - avoid plotting different units/quantities in single graph isleading with Bad Graphs Times Telegraph Sales (1000 $) Times leaves competition behind!

4 Dramatic tax increase! Expanding y-axis to accentuate differences Dramatic increase in # of welfare recipients! What s wrong with this figure? 11Q2 11Q1 10Q4 10Q3 10Q2 10Q1 09Q4 09Q3 09Q2 0 09Q1 Number of Americans (x 100,000) ederal Welfare Recipients What does y-axis stand for?

5 Different scales and units! 2,007, , , ,573 Line graph suggests quantitative x variable What is this x axis?

6 Pie chart by.c. Escher: Distribution Shapes Unimodal vs ulti-modal Symmetric vs Skewed Light vs. Heavy tails (kurtosis) Unimodal Distributions Bimodal Distributions 1000 rolls of 2 six sided dice Housefly Wing Length Body Weight Old aithful Eruptions Old aithful Intervals requency requency requency requency requency Dice Sum Wing length (0.1 mm) Weight (lbs) duration (sec) interval (min)

7 ultimodality population mixtures? Unimodal or ultimodal? Correct Reaction Times (Table 3.1) requency requency requency Are these bumps real? x x Reaction Time (sec) Symmetrical Distributions Skewed Distributions unimodal & symmetrical bimodal & symmetrical Binocular Rivalry (Young Adults) 2012 Australian Deaths (males) Housefly Wing Length 1000 random t values (df=22) requency requency requency requency count Wing length (0.1 mm) t x percept duration (sec) age at death (years) Sokal, R.R. and P.E. Hunter Ann. Entomol. Soc. Amer. 48: positive skew negative skew

8 Kurtosis Kurtosis example: frequency highest kurtosis Votes High or Low Kurtosis? IDb User Ratings of Inconvenient Sequel ean Rating = x lowest kurtosis Rating Part 3 Summary Graphs: - Histogram lower & upper limits; midpoints; frequency vs density - Stem-and-Leaf Display stem, leaves, leading/trailing digits, relation to histogram - Bar graphs - Line graphs - Scatter plots - Pie Charts (bad!) Distribution Shapes symmetric, bimodal, unimodal (modality), positive & negative skew, high & low kurtosis