contingency table using chi-square test

8/13/2019 Contingency Table Using Chi-Square Test

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Contingency Table Using

Chi-Square test (2 - Test)

Test of Independence



Chi-Square Test (2 - Test)

• Chi-Square (2) Test is used to test claims about

categorical data consisting of frequency countsfor different categories (attributes).

• Common applications of a 2 – Test.

–Goodness-of-fit Test : used to test the hypothesis thatan observed frequency distribution fits (or conforms

to) some claimed distribution.

– Contingency Tables: Independence and Homogeneity :

A contingency table (two-way frequency table) is a

table in which frequencies correspond to two

variables. (one variable is used to categorize rows,

and a second variable is used to categorize columns)



Contingency Tables

• Test of Independence: Test the null hypothesis thatthe row variable and the column variable in acontingency table are not related (the nullhypothesis is the statement that the row and columnvariables are independent/not related/not

associated).

Null Hypothesis:

Ho: Variable A is independent from variable B

Variable A and variable B are independent

Variable A is not related to variable B

Variable A and variable B are not related



Contingency Tables

An r c contingency table shows the observed

frequencies for two variables and arranged in r rows and c columns. The intersection of a row and

column is called a cell.

2 x 5 contingency table

Row 1

Row 2

Col 1 Col 2 Col 3 Col 4 Col 5



Contingency Tables

GenderFavorite way to eat ice cream

Cup Cone Sundae Sandwich Other

Male 600 288 204 24 84

Female 410 340 180 20 50

The observed frequencies in the interior of a

contingency table are called joint frequencies.



Contingency Tables

Gender

Favorite way to eat ice cream

Row TotalCup Cone Sundae Sandwich Other

Male 600 288 204 24 84 1200

Female 410 340 180 20 50 1000

ColumnTotal

1010 628 384 44 134 n = 2200

The sum of each row and column in acontingency table are called marginal frequencies.



Finding Expected Frequencies (fe)



Contingency Tables


Row Total

Cup Cone Sundae Sandwich OtherMale 600 288 204 24 84 1200

Female 410 340 180 20 50 1000

Column

Total

1010 628 384 44 134 n = 2200

Male – Cup: (1200 1010) ÷ 2200 = 550.91 = 551

Male – Cone: (1200 628) ÷ 2200 = 342.55 = 343

Male –

Sundae: (1200 384) ÷ 2200 = 209.45 = 209Male – Sandwich : (1200 44) ÷ 2200 = 24

Male – Other: (1200 134) ÷ 2200 = 73.09 = 73



Contingency Tables


Row Total

Cup Cone Sundae Sandwich OtherMale 600 288 204 24 84 1200

Female 410 340 180 20 50 1000

Column

Total

1010 628 384 44 134 n = 2200

Female – Cup: (1000 1010) ÷ 2200 = 459.09 = 459

Female – Cone: (1000 628) ÷ 2200 = 285.45 = 285

Female –

Sundae: (1000 384) ÷ 2200 = 174.55 = 175Female – Sandwich: (1000 44) ÷ 2200 = 20

Female – Other: (1000 134) ÷ 2200 = 60.91 = 61



Contingency Tables Gender – Favorite Observed

Frequency (fo)

Expected

Frequency (fe)

Male – Cup 600 551

Male – Cone 288 343

Male – Sundae 204 209

Male – Sandwich 24 24

Male – Other 84 73

Female – Cup 410 459

Female –

Cone 340 285

Female – Sundae 180 175

Female – Sandwich 20 20

Female –

Other 50 61



Gender – Favorite (fo) (fe) (fo – fe) (fo – fe)2 ÷ fe

Male – Cup 600 551 49 (49)2÷ 551 = 4.2575

Male –

Cone 288 343 –

55 (-55)2

÷ 343 = 8.8192Male – Sundae 204 209 – 5 (-5)2÷ 209 = 0.1196

Male – Sandwich 24 24 0 (0)2÷ 24 = 0.0000

Male – Other

84 73 11 (11)2

÷ 73 = 1.6575Female – Cup 410 459 – 49 (-49)2÷ 459 = 5.2309

Female – Cone 340 285 55 (55)2÷ 285 = 10.6140

Female – Sundae

180 175 5 (5)

2

÷ 175 = 0.1429Female – Sandwich 20 20 0 (0)2÷ 20 = 0.0000

Female – Other 50 61 – 11 (-11)2÷ 61 = 1.9836

2 = 32.8252



Critical Region = 5% = 0.05

df = (row –

1)(column –

1)df = (2 – 1)(5 – 1) = (1)(4) = 4



Critical Region

9.488 2

= 32.8252

CRITICAL REGION

REJECT HO

DO NOT REJECT HO

DECISION: REJECT HO



Ho: Favorite way to eat ice cream and gender,

are independent.

H1: Favorite way to eat ice cream and gender,are dependent.

Conclusion: Favorite way to eat ice cream andgender are dependent.

Interpretation:

This indicates that males prefer cup and other as theirfavorite way to eat ice cream than females as expectedwhile females prefer cone as their favorite way to eatice cream than males as expected.

contingency table using chi-square test

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