Stat 226 - Lecture 3
01/21/13
Announcements
- Homework 1 is due by 5pm today. Homework 2 is now available (it requires JMP)!
- Your student/class number helps us alphabetize assignments (its not a grade). Use it!
- The reading quiz is now available. It is due Sunday!
- Find a group of 4 for the course project (and in-class help).
- Any questions???
- Take away: Don't mislead your audience!
Less is (often) more!
What's a 226 student to do?
- Identify the variable of interest.
- Identify whether the variable is categorical or quantitative.
- If variable is categorical (chapter 3), you're options are:
- Bar chart (recommended)
- Pareto chart (recommended)
- Pie chart (not recommended)
- If variable is quantitative (chapter 4), you're options are:
- Histogram (good for examining a single distribution)
- Boxplot (good for comparing multiple distributions)
Every pitch by Mariano Rivera in '11
description type start_speed month
1 Called Strike FC 91.3 04
2 In play, out(s) FF 91.5 04
3 Called Strike FC 91.8 04
4 Called Strike FC 91.8 04
5 Foul FC 92.0 04
6 Foul FC 92.0 04
7 Ball FC 89.5 04
8 Ball FC 89.5 04
9 Foul FC 91.0 04
10 Foul FC 91.0 04
11 Ball FC 90.5 04
12 Ball FC 90.5 04
13 In play, out(s) FC 90.8 04
14 In play, out(s) FC 90.8 04
15 Ball FC 90.5 04
16 Swinging Strike FC 90.6 04
17 Foul FC 90.4 04
18 Foul FC 91.5 04
19 Ball FC 90.6 04
20 Foul FC 91.6 04
21 Ball FC 91.0 04
22 Called Strike FC 90.3 04
23 In play, out(s) FC 89.8 04
24 Called Strike FF 90.3 04
25 Foul FC 89.4 04
26 Foul FC 90.8 04
27 Ball FC 90.7 04
28 Foul FC 90.3 04
29 In play, no out FC 90.9 04
30 Foul FF 91.0 04
31 Foul FF 91.9 04
32 Foul FC 91.6 04
33 Foul FC 91.2 04
34 Foul FF 91.5 04
35 In play, no out FC 89.9 04
36 Foul FC 91.3 04
37 Ball FF 91.3 04
38 Swinging Strike FF 91.1 04
39 Foul FF 92.1 04
40 Ball FC 92.5 04
41 Ball FC 91.9 04
42 Foul FC 92.4 04
43 Foul FC 91.4 04
44 Foul FC 93.2 04
45 Ball FC 90.0 04
46 Swinging Strike FC 89.9 04
47 Ball FC 88.6 04
48 Swinging Strike FC 89.3 04
49 Ball FC 90.7 04
50 Foul FC 90.6 04
51 Foul FC 89.9 04
52 Swinging Strike FC 89.6 04
53 Ball FC 90.1 04
54 Ball FC 89.9 04
55 Ball FC 89.4 04
56 Called Strike FC 90.6 04
57 In play, out(s) FC 91.2 04
58 Called Strike FC 91.0 04
59 Swinging Strike FC 90.3 04
60 Foul FC 90.8 04
61 Ball FC 89.9 04
62 Ball FC 90.1 04
63 Called Strike FC 90.7 04
64 Ball FC 91.3 04
65 Ball FC 91.1 04
66 Called Strike FC 89.9 04
67 Called Strike FC 90.9 04
68 Foul FC 91.7 04
69 Ball FC 91.2 04
70 Foul FC 90.1 04
71 Foul FC 90.1 04
72 Foul FC 90.5 04
73 In play, out(s) FC 90.3 04
74 Ball FC 90.5 04
75 Called Strike FC 90.8 04
76 In play, out(s) FC 90.5 04
77 Ball FC 91.1 04
78 Ball FC 91.2 04
79 Swinging Strike FC 90.6 04
80 Called Strike FC 91.8 04
81 In play, out(s) FC 91.8 04
82 Foul FC 90.4 05
83 In play, out(s) FC 90.6 05
84 Called Strike FC 92.4 05
85 In play, out(s) FF 90.9 05
86 Called Strike FC 90.6 05
87 In play, out(s) FC 91.3 05
88 Ball FC 92.0 05
89 Foul FC 90.8 05
90 Foul FC 91.1 05
91 Swinging Strike FC 92.4 05
92 Called Strike FC 89.1 05
93 Called Strike FC 90.4 05
94 Ball FC 89.7 05
95 Swinging Strike FC 89.8 05
96 Ball FC 91.0 05
97 Foul FC 90.2 05
98 Ball FC 89.5 05
99 Ball FC 89.1 05
100 In play, out(s) FC 88.9 05
Pitch Description
- What type of variable is the pitch description?
- description is a nominal variable. Here is it's distribution (shown as a frequency table):
description
Ball :98
Foul :71
Called Strike :67
In play, out(s):39
Swinging Strike:23
In play, no out:11
(Other) : 6
Relative Frequencies
- Now, here is the relative frequency:
[,1]
Ball 0.311
Called Strike 0.213
Foul 0.225
Foul (Runner Going) 0.003
Foul Tip 0.006
In play, no out 0.035
In play, out(s) 0.124
In play, run(s) 0.010
Swinging Strike 0.073
- There were 315 pitches, so divide every number in the frequency table by this number to get the relative frequencies.
Bar Chart
Pareto Chart
- Pareto charts always place the mode as the left-most category.
- If the variable is nominal, pareto charts are preferred! Why?
- Resist the temptation to pie charts and use bar charts instead.
- Why are they bar charts so much better than pie charts?
- month is a ordinal variable. Here is it's distribution (shown as a frequency table):
month
04:81
05:29
06:13
07:52
08:60
09:79
10: 1
- You probably shouldn't change the ordering of an ordinal variable.
- In other words, a pareto chart of an ordinal variable might be misleading!
Pitch speed
- start_speed: The speed of the pitch as it left the hand. This is quantitative.
- To visualize the distribution a single quantitative variable, use a histogram.
- Since quantitative variables don't have “categories”, we have to create them!
- Although histograms look similar to bar charts, histograms deceivingly hard.
Choosing binwidths
- Notice that all the 'binwidths' (within each plot) are equal!
- Which do you think looks best?
- When doing this in practice, trial and error is essential!
Frequencies when binwidth is 1
[,1]
[88,89) 2
[89,90) 23
[90,91) 57
[91,92) 100
[92,93) 100
[93,94) 32
[94,95) 1
Numerical summaries
- Often times you'd like to report numerical summaries in addition to graphics.
- Numerical summaries could be grouped into measures of center and measures of spread.
- The mean, median, and mode are all measures of center.
- The mean (91.6565 MPH) is obtained by adding all the values of start_speed and dividing by the number of pitches.
- The median (91.8 MPH) is obtained by:
- Rank all of the values from highest to lowest: 88.6, 88.9, 89.1, 89.1, …, 93.6, 93.7, 94.3
- Find the middle value. See pg 56 the lecture notes for more details on how to find this…
Mean vs. median
- The mean is influenced by outliers, but the median is robust to outliers.
- In other words, the mean is dragged towards the more unusual values.
- Thus, we sometimes compare these values to assess the direction of skew in a distribution.
- If mean < median, then the mean is dragged to the left (skewed left)
- If mean > median, then the mean is dragged to the right (skewed right)
- If mean = median, the distribution is symmetric (in a perfect world)
Visual representation
- The mean corresponds to the red line below. The median corrresponds to the green line.
- What is the overall shape of the distribution?
Boxplot vs Histogram
- A boxplot is another visual representation of a distribution, but instead of a frequency table, it uses the 5 number summary.
- All of these numbers can be thought of as percentiles.
- The median is also known as the 50th percentile.
- What percentile is the minimum? Maximum?
- Q1 is the median of the first half of the distribution.