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Published bySofia O'Connell Modified over 2 years ago

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1 2 Test for Independence 2 Test for Independence

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2 Data Types

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3 Hypothesis Tests Qualitative Data

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4 2 Test of Independence 2 Test of Independence 1.Shows If a Relationship Exists Between 2 Qualitative Variables, but does Not Show Causality 2.Assumptions Multinomial Experiment All Expected Counts 5 3.Uses Two-Way Contingency Table

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5 2 Test of Independence Contingency Table 2 Test of Independence Contingency Table 1.Shows # Observations From 1 Sample Jointly in 2 Qualitative Variables 1.Shows # Observations From 1 Sample Jointly in 2 Qualitative Variables

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6 2 Test of Independence Contingency Table 2 Test of Independence Contingency Table 1.Shows # Observations From 1 Sample Jointly in 2 Qualitative Variables Levels of variable 2 Levels of variable 1

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7 2 Test of Independence Hypotheses & Statistic 2 Test of Independence Hypotheses & Statistic 1.Hypotheses H 0 : Variables Are Independent H 0 : Variables Are Independent H a : Variables Are Related (Dependent) H a : Variables Are Related (Dependent)

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8 2 Test of Independence Hypotheses & Statistic 2 Test of Independence Hypotheses & Statistic 1.Hypotheses H 0 : Variables Are Independent H a : Variables Are Related (Dependent) 2.Test Statistic Observed count Expected count

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9 2 Test of Independence Hypotheses & Statistic 2 Test of Independence Hypotheses & Statistic 1.Hypotheses H 0 : Variables Are Independent H a : Variables Are Related (Dependent) 2.Test Statistic Degrees of Freedom: (r - 1)(c - 1) Rows Columns Observed count Expected count

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10 Expected Count Example

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11 Expected Count Example Marginal probability =

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12 Expected Count Example Marginal probability =

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13 Expected Count Example Marginal probability = Joint probability =

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14 Expected Count Example Marginal probability = Joint probability = Expected count = 160· = 54.6

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15 Expected Count Calculation

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16 Expected Count Calculation

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17 Expected Count Calculation 112x x x x78 160

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