2-Way Contingency Tables

Two-way contingency tables are used to compare two QUALITATIVE variables, such as gender versus political party, or uniform shirt color versus uniform pants color. We make the table and then find the totals for all variables by counting the number of observations in each.

This is an example of a 2-way contingency table. We can find the marginal distributions by looking to the row/column totals and dividing by the grand total. For example, if we wanted to find the marginal distribution of yes event observed, we would do 8/28. A conditional distribution is conditioned on one of the variables within the table. For example, if we said "find the conditional distribution of no event observed conditioned on yes event forecasted, we would do 16/18. Usually, we write these answers as a percentage rather than a fraction.

For five extra bonus points on your next problem set, find and interpret the conditional distribution of yes event forecasted conditioned on no event observed. I will take your submissions up until this Friday, August 31st.

Hints for Problem Set 1, Question 1

Problem 1, Part B, last part: Think about the type(s) of variables that Mrs. Long is measuring, and think about what type of information that a histogram contains (which we went over in class on Friday). Does it make sense to use a histogram given the types of random variables?

Problem 1, Part C: refer to the chart that we made in class on Friday. There is definitely more than one possible correct answer for each scenario, make sure you justify it properly. Complete sentences, please!

Problem 1, Part E: think about a variable that you would observe in real life where, if you made a graph of it, would be roughly distributed symmetrically or skewed.

Scatterplots

Scatterplots compare two bivariate variables. Our independent variable goes on the x axis and the dependent variable goes on the y-axis (think back to algebra 1, here). While we can't CUSS for a scatterplot in the exact same way, we do describe three aspects of the data:

1) Direction - do the observations appear to be going in a positive or negative direction?
2) Strength - are the observations close together? Far apart? Not correlated at all?
3) Linearity - do the data appear to be in the shape of a straight line?

Histograms

Histograms are used to graph univariate, quantitative data. We like to use these particularly when we have continuous data (data with decimals), but they can still be used for discrete data (whole numbers) as well.

NOTE: Histograms are NOT the same thing as a bar graph!! Bar graphs chart qualitative data while histograms chart quantitative data.

To make a histogram on the TI-84, enter your data into L1. Go to Stat Plot, turn the graph on, pick the one that looks like the histogram. Then press zoom - 9) Statistics.

Comparing Distributions

In the case of more than one graph, it makes sense to compare distributions of the same random variable. For example, we could compare the number of times girls can hop on one foot in a minute to the number of times boys could hop on one foot in a minute in terms of center, shape, spread, and outliers (CUSS). We did this today in class with two stem-and-leaf plots. Make sure to use comparative language such as "greater than," "smaller than," etc. and keep it in the context of the problem.

Shout out to Deja Collins for figuring out why it's not appropriate to CUSS when we're looking at a bar graph. Remember, you can only CUSS about QUANTitative data! Nice work!

Describing a Distribution

Today we learned how to describe distributions via dotplots. We need to CUSS when we do this - meaning, we need to mention Center, Unusual Observations, Shape, and Spread. BE SPECIFIC when you do this, putting everything in the context of the problem!

The first problem set was given out today. It is due Wednesday, August 28th.  Make sure that all of your graphs contain titles and labels.

Shout Out to Toni Clinton for calling me and asking a question about the problem set - way to go! VERY impressed that you started it already and I'm proud of your time management skills.

Monday August 19

Today was weird because we were cut short by a pep rally. The class went over the syllabus, expectations, and supplies for the class. We discussed the high expectations for this class - it is one of the most challenging in the school in terms of workload and dedication. However, the test is certainly passable with hard work and commitment to understanding the material.

All students in the class will take the AP Exam in May. This class is an ELECTIVE - it is a choice, not a requirement. If you don't want to be in the class or don't think that the workload is something that you can handle - that's fine - I won't be offended. Talk to your counselor about scheduling options that make sense for you.