Chapter 3

Data and Dirty Laundry Laundry needs to be separated into loads for a machine to handle it. Laundry should be sorted by color (and other factors potentially) for best results. Data likewise needs to be organized into manageably small clusters or portions. Data likewise needs to be sorted in some specific, useful way for best results.

Where to Start When Analyzing Data Step 1: Draw a picture. Humans are a visual species, and by seeing the data we are better able to think about it. Step 2: Draw a picture. With a properly selected picture, we are better able to demonstrate our reasoning and our process. Step 3: Draw a picture. Once a conclusion has been reached it is often best expressed as a picture. Note: On some problems step 1, 2, and 3 might each require their own pictures.

Frequency Vocabulary Frequency – The number of times a value occurred. Relative Frequency – The number of times a value occurred divided by the total number of cases collected. Often expressed as a percent. Frequency Table – A table that displays frequencies. Relative Frequency Table – A table that displays relative frequencies.

Step 1 – Draw a Picture With categorical data, we want to start with a frequency chart. Your book gave you some examples, but we will use some hypothetical favorite color data.

Step 1 – Draw a Picture ColorFrequency Black2 Blue20 Green14 Pink8 Purple5 Red5 Yellow6 ColorFrequency Blue20 Green14 Pink8 Yellow6 Purple5 Red5 Black2 Vs.

Frequency vs. Relative Frequency With a small data set like 60, these raw counts are not a problem. If you had a data set where 1472 people contributed a favorite color, you would generally be better off getting the relative frequency.

Frequency vs. Relative Frequency ColorFrequency Blue20 Green14 Pink8 Yellow6 Purple5 Red5 Black2 ColorFrequency Blue33.3% Green23.3% Pink13.3% Yellow10% Purple8.3% Red8.3% Black3.3% Vs.

Step 2 – Draw a Picture If all you are doing is describing the data, then a frequency table or relative frequency table will cover steps 1 and 2. The same picture that helps you think about what is going on also helps to show what is going on. We will come back to what happens when you are doing more than just describing data.

Step 3 – Draw a Picture Even if you are describing the data with a frequency chart to show what is going on, you should use an additional picture to showcase your findings. Two popular choices (for categorical data) are bar charts and pie charts. Bar charts are best when the categories can be put in some sensible order, such as months. They can basically always be used Pie charts are best when the categories do not have a natural order, such as colors. Pie charts can only be used when your data adds up to 100% of the data

Bar Charts and Pie Charts Bar charts are super crazy easy on Excel once you get the hang of it. Pie charts are also easy. Creating a pie chart by hand is much trickier than a bar chart, so if you are having to work by hand you might do a bar chart instead of a pie chart.

Step 1 – Draw a Picture When we want to look at the relationship between two variables, we will use a contingency table instead of a frequency chart. A contingency table is a table where the rows are categories for one variable and where the columns are categories for the other variable.

Contingency Table Once we have determined the columns and the rows, we fill the table with the frequencies. Each value represents the frequency of the category for that row happening at the same time as the category for that column.

Contingency Table Next we will total each row and total each column. Then we will total the whole table. To do this we total the row totals and total the column totals to make sure they match.

Contingency Tables Relative values get trickier. In a frequency table, there is only one total. In a contingency table there is a row total and a column total and a table total.

Example Time! If you missed class today, this was the really sad part to miss. You should get notes from someone who was here.

Assignments Read Chapter 3 for tomorrow if you haven’t already. The Chapter 1-3 Quiz will be Friday. Chapter 3: 5, 9, 19 (This is the first half, more will be added before a due date is set) Chapter 2 homework is due tomorrow. Problems 2-7, 25, 26 I will not be actively lecturing over the Area Principle. Instead, if you have questions about it, you should bring those tomorrow so that when I ask “Are there any questions about the Area Principle?” you have a good answer. I will not answer the question, “What even is the Area Principle?” Nor will I answer any of its ilk.

More Unsupporting Cast On yesterday’s episode we talked about Mr. Cheeseburger and then need for ridiculously levels of clarity. Today we will focus on the Casual Observer, the Hasty Generalizer and the Exemplar, which might seem like the same at first, but are actually three very differently flawed archetypes. They do, however, have in common that they come to their conclusions far too easily.

The Casual Observer This phrase normally refers to a person who is looking at the situation, but does not have any particularly strong background in what is going on and who does not look any deeper than what is on the surface. We are using it to refer to someone who does exactly that with exactly the same restrictions. Casual Observers are easily swayed by misleading pictures and misinformation because they are only looking at what is immediately available.

The Casual Observer The reason it is important to be aware of these observers is that the reason we must be concise is because if we take yawn-worthy lengths of time to get to our true point, some people will have totally tapped out by then. We need to get to our points in a timely manner so that a casual observer gets the information before they would otherwise give up.

The Hasty Generalizer A hasty generalization is when a person assumes that something which is/seems true in some situation is also actually true in many, if not all, similar situations. The person I refer to here is a little different than that, though. In this context I am referring to a person who just wants you to get to the conveniently digested point, not really caring how you got there, so they can get on with their day.

The Hasty Generalizer Such a person will typically latch on the first solid point you make and assume that the rest of what you said is meaningless, unless a better point comes along. At which point they tend to abandon the original point in favor of the new one. It is important to be complete while being concise in order to get around this. Your entire point needs to be visible in a relatively concise and clear manner for someone trying to breeze through it to get the full effect.

The Exemplar Normally an “exemplar” would be someone who has done things in a way that sets a superior example for others to follow. In this case, though, I am referring to a person who fixates on a specific example of something happening, and assumes that it is way more important than it is. Interestingly enough, that is actually closer to a hasty generalization, most of the time, than it is to anything else.

The Exemplar For example, this person assumes that “9 out of 10 dentists” approving of a particular dental product means that 1 of them did not…and that it should be closely investigated as to exactly why. This kind of person also assumes that there is genuine scientific controversy as to the existence of global warming because there are scientists which are unconvinced. This kind of person might get pulled over once for running a stop sign and then immediately decides that cops will always pull you over for running stop signs.

The Exemplar This sort of person tends to believe that one rather unlikely example should hold just as much weight as the ongoing, consistent outcome…which is the opposite of that example. It is very important that we address any and all unusual results in our efforts to avoid someone taking them and running with them, metaphorically, which means taking time to explore possible reasons that strange results occurred.

Quiz Bulletpoints Know what T-S-T stands for and what each one means. Know how to identify the 5 W’s and How in a study. Know the difference between a qualitative and quantitative variable. Know how to find percentages from a contingency table. Know the area principle.