The Coach then sorts the 25 players into separate teams and positions
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1 Section 4 A: Contingency Tables Introduction A local school has a Varsity and Junior Varsity basketball team. No player plays on both teams and no player plays at more than one position. The coach writes down the team and position for each of the players on the teams. Varsity Guard Jr. Varsity Forward Jr. Varsity Guard Varsity Forward Jr. Varsity Guard Varsity Forward Jr. Varsity Forward Varsity Forward Varsity Center Jr. Varsity Forward Varsity Forward Jr. Varsity Guard Jr. Varsity Center Jr. Varsity Guard Varsity Center Jr. Varsity Forward Jr. Varsity Guard Varsity Guard Varsity Forward Jr. Varsity Forward Jr. Varsity Forward Varsity Guard Jr. Varsity Forward The Coach then sorts the players into separate teams and positions Varsity Guard Varsity Forward Varsity Center Varsity Guard Varsity Forward Varsity Center Varsity Guard Varsity Forward Varsity Forward Varsity Forward Jr. Varsity Center Jr. Varsity Forward Jr. Varsity Forward This data would be easier to view if we created a frequency table. 1 f 1 The table above is a way frequency table that shows the team frequencies by position in the horizontal rows and the position frequencies by team in the vertical rows. The team totals are displayed at the far right of each row and the position totals are displayed at the bottom of each row. We call this Way Frequency Table a Contingency Table Section 4 A Page 1 of 6 01 Eitel
2 Reading and s in a Contingency Table The cells in the bottom row of the table contain the totals for each of the different Variables. The cells in the far right column contain the totals for each of the different Row Variables. Variable 1 Variable Variable Row s Row Variable 1 R1 and C1 R1 and C1 R1 and C of Row 1 Row Variable R and C1 R and C R and C of Row s of 1 of of of all the Row or the of all the The cells in the body of the table contain the frequencies for each cell that have BOTH the Row attribute AND the attribute. Variable 1 Variable Variable Row s Row Variable 1 R1 and C1 R1 and C1 R1 and C of Row 1 Row Variable R and C1 R and C R and C of Row s of 1 of of of all the Row or the of all the Section 4 A Page of 6 01 Eitel
3 Reading the Frequency Table Example 1 1 Reading the Frequency Table s players are V and G V and F V and C number of Varsity Players is JV and G JV and F 1 player who is JV and C number of Jr. Varsity Players is 1 number of is number of is 1 number of is number of all Players is Section 4 A Page of 6 01 Eitel
4 Reading the Frequency Table Data Cells Example 1 1 players are V and G V and F V and C number of Varsity Players is JV and G JV and F 1 player who is JV and C number of Jr. Varsity Players is 1 number of is number of is 1 number of is number of all Players is Section 4 A Page 4 of 6 01 Eitel
5 Extra Lecture Notes Reading in a Two Way Frequency Table The Contingency Tables in this unit requires that each player play on only one team and at only one position. Diagrams where a player plays on more than one team or plays more than one position will be covered in Section 4. Each cell that is at the intersection of a ROW Heading AND column Heading has the attributes of BOTH the Row and headings at the same time. The number found in the single cell that is at the intersection of the a Heading AND a Heading is the frequency or number of people who have attribute of BOTH the Row and headings. Each player has EXACTLY ONE attribute and One Row Attribute 1 1 The intersection of row AND the column contains a There are both a Varsity player AND a Guard The intersection of the row AND the Forward column contains a There are both a Varsity player AND a Forward The intersection of the row AND the column contains a There are both a Varsity player AND a Center The intersection of the row AND the column contains a 6 There are 6 both a Jr. Varsity player AND a Guard The intersection of the row AND the Forward column contains a There are both a Jr. Varsity player AND a Forward The intersection of the row AND the column contains a 1 There is 1 player who is both a Jr. Varsity player AND a Center Section 4 A Page of 6 01 Eitel
6 Reading the Row and Frequency s for a Two Way Frequency Table The cells in the bottom row of the table contain the totals for each of the different Variables. The cells in the far right column contain the totals for each of the different Row Variables. 1 1 There are a total of guards (found at the bottom of the column) A Guard can be a Varsity Guard OR a Jr. Varsity Guard. There are a total of 1 forwards 1 (found at the bottom of the column) A Forward can be a Varsity Forward OR a Jr. Varsity Forward. There are a total of centers (found at the bottom of the column) A Center can be a Varsity Center OR a Jr. Varsity Center There are a total of Varsity players (found at the far right of the Varsity row) A Varsity player can be a Varsity Guard OR a Varsity Forward OR a Varsity Center. There are a total of Jr. Varsity 1 players 1 (found at the far right of the Jr. Varsity row) A Jr. Varsity player can be a Jr. Varsity Guard OR a Jr. Varsity Forward OR a Jr. Varsity Center. There are a total of players (found at the bottom right corner of the table) The of ALL players on any team at any position is Section 4 A Page 6 of 6 01 Eitel
Acknowledgement: Author is indebted to Dr. Jennifer Kaplan, Dr. Parthanil Roy and Dr Ashoke Sinha for allowing him to use/edit many of their slides.
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