Reminders. Homework is due at 9:30am tomorrow morning in the catalyst dropbox.
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1 Reminders Homework is due at 9:30am tomorrow morning in the catalyst dropbox. You have to make some plots and charts in this homework. You can mastermind a way to do this in word/excel/whatever you use, or you can do it by hand and take pictures or scan them If you do them by hand, make sure you only hand in 1 file into dropbox. For instance, you can embed all your pictures into a word document. 1
2 Warm Up After WWII, people studied the accuracy of strategic bombing with statistics. Some things made sense (different types of bombers had different accuracy levels, higher altitude meant less accuracy). But one variable that they measured was whether enemy fighters opposed the bombers, and this had the opposite effect from what anyone would expect (they found that when there were opposing fighters the bombers were more accurate). They were eventually able to figure out what the lurking variable was. What was the lurking variable? 2
3 Chapter 10 and 11: Graphs Aaron Zimmerman STAT Summer 2014 Department of Statistics University of Washington - Seattle 3
4 Class Data Grainne and I collected some data from you: age, gender, major, amount of coffee you drink daily Here it is: Age Gender Major Coffee/Day 18 F Bio F Med. Tech F Bio M Social Work F Bio F Bio F Bio F Pub. Health M Business F Accounting
5 Summarizing Data The problem is, showing a big table full of data isn t easy for anyone understand The goal in this course is give you two sets of tools: 1) The ability to think critically about results that people present to you 2) The ability to start putting together your own results A good graph can go a long ways towards meaningful summaries of data and understanding what makes a good (or a bad) graph is a key step for both of these goals. 5
6 Terminology The distribution of a variable tells us what values it takes and how often it takes those values A categorical variable places an individual into one of several groups or categories In the survey, gender is a categorical variable A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense The average number of cups of coffee you drink per week is a quantitative variable 6
7 Pie charts A pie chart shows how a whole is divided into parts The area of each wedge represents the percent for each value of the variable Pie charts work best for categorical variables The percents must add to 100%! Percent of English-speaking people in the world who live in different countries 7
8 Pie chart of Majors Pie Chart of Majors in Stat 220 Bio BioChem Bus. Admin Business Accounting CS Econ English Env. Studies GWSS Informatics Med. Tech. Non Matric Social Work Soc Pub. Health Nursing Cleveland (1985), page 264: Data that can be shown by pie charts always can be shown by a dot chart. This means that judgements of position along a common scale can be made instead of the less accurate angle judgements. This statement is based on the empirical investigations of Cleveland and McGill as well as investigations by perceptual psychologists. 8
9 Dot Chart of Majors Dot Chart of Majors in Stat 220 Social Work Soc Pub. Health Nursing Non Matric Med. Tech. Informatics GWSS Env. Studies English Econ CS Business Bus. Admin BioChem Bio Accounting If you can make a dot chart, you can also make a bar chart. 9
10 Bad pie chart #1 10
11 Bad pie chart #2 11
12 Bad pie chart #2 12
13 Bar charts A bar graph shows the percent or count for each variable The height of the bar represents the percent or count Bar graphs are best with a small number of categorical variables Values do not need to be part of a whole! 13
14 Bar Chart Bar Chart of Majors in Stat Accounting Bio BioChem Bus. Admin Business CS Econ English Env. Studies GWSS Informatics Med. Tech. Non Matric Nursing Pub. Health Soc Social Work 14
15 Bar Chart Homicide By Firearm Rate per 100, All countried are High Income OECD' USA Switzerland Italy Belgium Luxembourg Ireland Canada Sweden Finland Portugal Netherlands Greece Denmark Estonia New Zealand Spain Germany Austria Czech Repub Slovakia Norway Israel United Kingdom Hungary Poland France Australia Slovenia Iceland S. Korea Japan 15
16 Bad bar graph #1 16
17 Bad bar graph #2 17
18 Line graphs A line graph of a variable plots each observation against the time at which it was measured Always put time on the horizontal scale of your plot and the variable you are measuring on the vertical scale 18
19 Line Graphs Smoothed Average amount of Coffee Consumption in Stat 220 Average Coffee Age 19
20 Bad line graph #1 20
21 Bad line graph #2 21
22 Histograms The most common way to display a large amount of quantitative data is with a histogram The height of each bar represents the number or percent of observations between two values of the variable Histograms are most often used when you have repeated measurements about the same value 22
23 Interpreting Histograms Step 1 : Look at the overall pattern Describe the shape A distribution is symmetric if the right and left sides of the histogram are approximately mirror images of each other A distribution is skewed to the right if the right side of the histogram extends much farther out than the left side A distribution is skewed to the left if the left side of the histogram extends much farther out than the right side Describe the center What value has roughly 50% of the data on either side? Describe the spread What are the smallest and largest values? Step 2 : Look for striking deviations from that pattern An outlier in any graph of data is an individual observation that falls outside the overall pattern of the graph 23
24 Histogram of Coffee Histogram of Coffee Consumption in Stat 220 Frequency # Coffee per Day Right Skewed Center around 1 The spread is from is a borderline outlier 24
25 Histogram of Black Cherry Heights Symmetric Center around 75 The spread is from There are no outliers 25
26 Your turn - Obama Rating You have estimated the percent of Democrats, Republicans, and Independents who approve of President Obamas job performance. What type of figure would you use to display these statistics? Bar Graph Histogram Line Graph Pie Chart Party Rating Dem 0.82 Rep 0.10 Ind 0.38 From Gallup - First week of July
27 Your turn - Obama Rating You have estimated the percent of Democrats, Republicans, and Independents who approve of President Obamas job performance. What type of figure would you use to display these statistics? Bar Graph Histogram - No repeated counts to bin Line Graph - No measurements over time Pie Chart - Aren t parts from a whole Obama Approval July 2014 D R I 27
28 Your turn - World Cup Semi-Final You have estimated the percent Americans who think Argentina will win, and the percent who think the Netherlands will win the world cup semi-final this afternoon. What type of graph would you use to display these statistics? Bar Graph Histogram Line Graph Pie Chart Team Chance Argentina 0.47 Netherlands
29 Your turn - World Cup Semi-Final You have estimated the percent of Democrats, Republicans, and Independents who approve of President Obamas job performance and are interested in his approval across the country. What type of figure would you use to display these statistics? Bar Graph Histogram - No repeated counts to bin Line Graph - No measurements over time Pie Chart Argentina Netherlands Argentina Netherlands 29
30 Your turn - Obama Rating You have estimated the percent of Americans in each of the 50 states who approve of President Obama s job performance. What type of figure would you use to display these statistics? Bar Graph Histogram Line Graph Pie Chart State Rating ME NH VT MA RI CT
31 Your turn - Obama Rating You have estimated the percent of Americans in each of the 50 states who approve of President Obama s job performance and are interested in his approval across the country. What type of figure would you use to display these statistics? Obama Approval Rating Across States Bar Graph Histogram - No repeated counts to bin Line Graph Pie Chart - No parts of a whole Frequency Approval Approval Rating Obama Approval Rating Across State ME NH VT MA RI CT NY NJ PA MD DE WV DC OH MI IN IL WI MN IA MO ND SD NE KS VA NC SC GA FL KT TN AL MS AR LA OK TX MT AZ CO ID WY UT NV NM CA OR WA HI AK
32 Your turn - Australian Population You have estimated the number of Australian residents for 90 different quarters. What type of figure would you use to display the statistics? Bar Graph Histogram Line Graph Pie Chart Quarter Pop Q Q Q Q Q Q
33 Your turn - Australian Population You have estimated the number of Australian residents for 90 different quarters. What type of figure would you use to display the statistics? Australian Population Bar Graph Histogram - No repeated counts to bin Line Graph Pie Chart - No parts of a whole Population Quarter Australian Population
34 Homework Read Chapters 10 and 11 (skip stemplots in Chapter 11) Do problems 10.1 (add Why? ), 10.3, 10.8, 10.23, 11.2, 11.3, 11.5, and 11.6 Add part b to the following questions: 11.2: In how many states is over 2% of the population 85 and older? 11.3: In how many days was the first lightning strike before 9:30 AM? 11.5: Approximately how many universities had between 6 and 15 engineering doctorates earned by minorities? Watch this TED talk: the_best_stats_you_ve_ever_seen 34
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