More Chapter 3!

1. More Chapter 3! (or Chapter 4)

2. Brave New Data • We are no longer limited to charts which only work for categorical data. • We have three more charts at our disposal. • Even though I do not think the book stresses this enough, frequency tables and relative frequency tables are still useful for quantitative data. • Bar charts and pie charts, however, are not.

3. Just Kidding On The Bar Charts • We do not use bar charts (or column charts) for quantitative data. • We use histograms. • These are, as you can hopefully see, charts with bars. • Doesn’t that make them bar charts?

4. It Totally Should • Distinguishing between histograms and bar charts borders on obnoxiousness. • However, it is important to note that bar charts have gaps and histograms do not, and so we call them something different. • The primary purpose in the distinction is help reinforce that categorical data and quantitative data are different.

5. What Makes Histograms Special • Bar charts can show data in whatever order they like, but histograms need to go in order. • Since they are used with quantitative data, the order is built in. • If there is an interval with no data, you are still expected to have it in your graph as an empty space. • A gap on a histogram means there was a gap in the data.

6. Categorical vs. Quantitative • Sometimes the data can be made into either. • For example, scores and letter grades can both be found for the quiz.

7. Histograms FTW! • In later chapters, histograms will be the preferred plot for categorical data in general. • Dotplots are a fun way to amuse yourself…if you are into making charts and graphs. • Stem-and-leaf plots are useful, but can take forever and also require intense attention to detail. • They are very convenient for displaying two distributions side by side. • While not mentioned much in this chapter, there are also lineplots, which are like histograms, except instead of bars, there is a line connecting the frequencies.

8. Stem-and-leaf Diagrams • Also known as stemplots. • The stem contains the beginning of each data point (such as the tens place or hundreds place). • Each data point is called a leaf. • Each leaf needs to be the same number of characters. • If you have double-digit leaves, it is wise to leave a space after each one.

9. Stem-and-leaf Diagrams • The stem can be broken down into partial categories, such as high and low. • The stem can be surrounded on both sides with leaves, representing two distributions side by side. • The leaves need to all take up the same space. • On a computer, the Courier font ensures that all text takes up the same space left to right.

10. Stem-and-leaf Diagrams • The leaves should be in numerical order within each stem. • This means sorting the data first. • No stem should be left out, which means that if you do not have any leaves for a given stem, you still need it, but it just gets left empty. • Probably best done by hand, and for relatively small data sets (like 30 subjects or less).

11. Timeplots • These are the only lineplots mentioned in your book. • They are the most common kind of line plot. • You basically plot the dots and connect the dots. • They are not only really straightforward, but they are also intuitive, so regular people can look at them and see trends.

12. Back to Histograms • Histograms should be evenly scaled. • This means even class widths. • The book would say even bin sizes. • This also can be expressed as even intervals. • Histograms should include every interval between the start and stop of the data. • Even if they are empty. • Especially if they are empty.

13. Describing Distributions • There are three key areas to describe when discussing a distribution. • Shape – This usually means counting the high points, checking for symmetry, and looking for extreme values. • These high points are called modes. • Center – This will usually focus on an appropriate measure of central tendency. • The Mean and the Median are common. • Spread – This will usually mean giving an indication of how spread out the data is. • The Range and the Standard Deviation are common.

14. Shape • Within the shape category, there are three things we will tend to focus on. • First is known as modality. That is basically just how many bumps. • One exception is a uniform distribution. • The second is symmetry and skew. • A graph is considered skewed if it leans more towards one side of the mode than the other. • The third is outliers. • Next chapter we will learn how to identify them numerically, but for now, we will only focus on outliers that are obvious.

15. Center • Next chapter we will learn all about calculating centers. • For now, we will just rely mostly on intuition. • If the graph is skewed in a direction, the mean will be more in that direction than in the other direction, and might not match up perfectly with the mode.

16. Spread • We will learn how to calculate spread. • We will learn how to calculate spread by hand even. • Once we have finished that, you will understand spread really well. • For now, it just relates to how wide the graph is.

17. Comparing Distributions • A good rule of thumb is that if you have two distributions, graph them separately, but on the same scale as one another. • If you fix the scales, a more accurate picture of how they match up forms. • Comparing two distributions on a stem-and-leaf diagram is a bit different. • Comparing two sets of categorical variables on the same bar chart can be handy as long as they have the same categories. • It is common for bar charts to be used in place of histograms to compare two or more sets of quantitative data. • It is worth your while to see this kind of graph.

18. Assignments • Chapter 3: 5, 9, 19, 25, 33, 37 • Due Monday • Chapter 4: 4, 8, 11, 17, 18, 30, 33 • Due Tuesday • Read Chapter 4. • Make time to see or e-mail me with quiz questions. • Begin studying for Chapter 4 Quiz on Monday. • So maybe do the chapter 3 homework before Sunday so you have time to study.

19. Quiz Bulletpoints • Be familiar with the differences between a histogram and a bar chart. • Be familiar with the advantages and disadvantages of a stem-and-leaf diagram. • Be familiar with the what-not-to-do list in chapter 4. • Be familiar with the what-not-to-do list in chapter 4. • Know when and how to transform data.

20. But What If I Don’t Have A Book?!?! • Me memememe. • j/k lol :) • Here’s the list: • Don’t Make a Histogram of a Categorical Variable. • Don’t Look for Shape, Center, and Spread of a Bar Chart. • Don’t Use Bars in Every Display – Save Them for Histograms and Bar Charts. • Choose a Bin Width Appropriate to the Data. • Avoid Inconsistent Scales • Label Clearly