Chi – Square

The graph below shows a few samples of chi – square graphs. Notice when the d.f. increase, the graph will flatten out and the high point ( mode ) shifts right and begins to look more bell shaped.

Chi – Square

The value we will be looking for is the area in the tail to the RIGHT of the critical value

Chi – Square Here is a table of chi square values…

Chi – Square Here is a table of chi square values… The left side is degrees of freedom

Chi – Square Here is a table of chi square values… The left side is degrees of freedom The top row is area of the right tail

Chi – Square Here is a table of chi square values… The left side is degrees of freedom The top row is area of the right tail These values are the probabilities

Chi – Square Let’s dive right into an example to learn this… A computer keyboard company has developed two new letter arrangement keyboards. The company wants to see is there any relationship between the arrangement of letters on the keyboard and the number of hours it takes for a new user to be able to type at 20 words per minute.

Chi – Square

Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total A B Standard Column Total Sample size This table is called a contingency table. The pink shaded boxes are called cells. These contain the observed frequencies. The size of the contingency table is determined by the number of rows and columns that contain data. This table is a 3 X 3 ( read three by three ) table and contains 9 cells. The row and column totals are not included in the cell count.

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total A O = 25 E = ___ O = 30 E = ___ O = 25 E = ___ 80 B O = 30 E = ___ O = 71 E = ___ O = 19 E = ___ 120 Standard O = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total Sample size To use this table correctly, we need to modify it just a bit to show what are called observed and expected frequencies for each cell. The observed frequencies we already knew, it was the sample data.

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = ___ O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = ___ O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = ___ O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = ___ O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = ___ O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = ___ O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = BO = 30 E = 36 O = 71 E = 60 O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = BO = 30 E = 36 O = 71 E = 60 O = 19 E = StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = ___ 100 Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = BO = 30 E = 36 O = 71 E = 60 O = 19 E = StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = BO = 30 E = 36 O = 71 E = 60 O = 19 E = StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = Column Total Sample size

Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = BO = 30 E = 36 O = 71 E = 60 O = 19 E = StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = Column Total Sample size

Chi – Square Cell So I just transferred the data from my contingency table into this table…

Chi – Square Cell

Chi – Square Cell

Chi – Square Cell

Chi – Square Cell ∑ = 13.31

Chi – Square Cell ∑ = 13.31

Chi – Square Cell ∑ = 13.31

Chi – Square Cell ∑ = 13.31

Chi – Square Cell ∑ = 13.31

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size 1. State the null and alternate hypotheses

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = Mountain Mist O = 30 E = 20 O = 20 E = Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = Mountain Mist O = 30 E = 20 O = 20 E = Jungle Grape O = 5 E = 16 O = 35 E = Diet Pop O = 12 E = O = 8 E =20 Column Total Sample size

Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = Mountain Mist O = 30 E = 20 O = 20 E = Jungle Grape O = 5 E = 16 O = 35 E = Diet Pop O = 12 E = 8 O = 8 E = 1220 Column Total Sample size

Chi – Square Cell ∑ =

Chi – Square Cell ∑ =

Chi – Square Cell ∑ = 24.68

Chi – Square Cell ∑ = 24.68

Chi – Square Cell ∑ = 24.68

Chi – Square Cell ∑ = 24.68

Chi – Square Cell ∑ = 24.68