Using Two Way Tables

Two way tables describe data relationships in two dimensions between two different types of items. Also called a contingency table, the table provides the frequency of the occurrence, how often both items occur or do not occur.

Example 1

Here a survey of 250 students in the school cafeteria created the following results.

	Likes Bananas	Does Not Like Bananas	Total
Takes Band Class	72	16	88
Does Not Take Band Class	145	17	162
Total	217	33	250

A rectangular table provides data horizontally and vertically allowing analysis in both directions.

The table below is another two way table, but there are more than two items vertically and horizontally. The categories of team data is compared with each student providing the frequency of occurrence. This table describes some basic ideas in a softball game in terms of statistics that would be kept on each player over 1 or more games. The statistics shown are the number of times an item occurs at each intersection horizontally and vertically across the table.

Example 2

Describe some basic statistics of three players on ABC Softball Team.

ABC Softball Team		Students Playing Softball

	Student A	Student B	Student C
Hits	3	2	4
At Bats	7	8	10
Runs	0	2	1
Walks	1	4	0
Outs at Bat	3	1	6

Notice that information is easily organized in the table. Student A had 3 hits batting and had a total of 7 at bats. This is a frequency table, how many.

Let's review some questions concerning this table. The table provides lots of thought which poses many questions. Review the questions in the ABC Softball Analysis below.

Obviously data and statistics provide information, sometimes not enough to know the whole picture. Analyzing what is given can be done and sometimes a conjecture may be made based on the data provided, sometimes more information is needed.

Clearly we can compare the batting averages of the students, but is a better comparison the times on base? Some of the students appear to be able to walk on base, and that is just as good if getting on base earns a run in the future.

Student A on base average = (3 + 1)/7 = .5714 or 57.14%.
Student B on base average = (2 + 3)/8 = .625 or 62.5%.
Student C on base average = (4 + 0)/10 = .4 or 40%.

Now examining the data gathered from the statistics, Student B appears to be more productive for the team, although Student A is a close second.

What we do not know is whether Student C is causing the hits to earn the runs for the team with students on base. Value is hard to measure without more data. However we can say that at the current time Student C either gets a hit or strikes out. There are no walks (base given for 4 balls that are not over the plate).

Watch the following video to learn how to convert the ABC Softball Table above to a Relative Frequency Table.

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