MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
Based on your χ² calculations, is the deviation seen between your observed and expected results significant or nonsignificant? _______ Explain your results. In your explanation include the probability of getting these data and whether the deviation is significant or not. Also include whether the data supports the hypothesis.
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Transcribed Image Text:Based on your χ² calculations, is the deviation seen between your observed and expected results significant or nonsignificant? _______ Explain your results. In your explanation include the probability of getting these data and whether the deviation is significant or not. Also include whether the data supports the hypothesis.
Title: Chi-Square Test for Independence: Analyzing Class Data In this table, we analyze class data using a chi-square (χ²) test to determine whether or not there is a significant difference between observed and expected frequencies in each category or event. This test helps assess the association between categorical variables. ### Table Explanation | Category/Event | Observed (O) | Expected (E) | Deviation (O-E) | (O-E)² | (O-E)²/E | |----------------|-------------|-------------|----------------|-------|---------| | AO Present | 75 | 108 | 33 | 1089 | 10.083 | | AO Absent | 69 | 36 | 33 | 1089 | 30.25 | | Totals | 144 | 144 | 66 | 2178 | | ### Detailed Steps: 1. **Observed Frequencies (O):** - AO Present: 75 - AO Absent: 69 2. **Expected Frequencies (E):** - AO Present: 108 - AO Absent: 36 3. **Deviation (O-E):** - For both AO Present and AO Absent: 33 4. **Squared Deviation (O-E)²:** - For both AO Present and AO Absent: 1089 5. **Chi-Square Contribution (O-E)²/E:** - AO Present: 10.083 - AO Absent: 30.25 6. **Total Squared Deviation:** - Sum of (O-E)²: 2178 ### Summary This table displays the calculated values used in a chi-square test of independence. By comparing observed frequencies with expected frequencies, and calculating the deviations and their squares, we assess the difference between what is observed and what is expected under the null hypothesis. The chi-square statistic (χ²) is ultimately derived from summing the (O-E)²/E values across all categories.
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Transcribed Image Text:Title: Chi-Square Test for Independence: Analyzing Class Data In this table, we analyze class data using a chi-square (χ²) test to determine whether or not there is a significant difference between observed and expected frequencies in each category or event. This test helps assess the association between categorical variables. ### Table Explanation | Category/Event | Observed (O) | Expected (E) | Deviation (O-E) | (O-E)² | (O-E)²/E | |----------------|-------------|-------------|----------------|-------|---------| | AO Present | 75 | 108 | 33 | 1089 | 10.083 | | AO Absent | 69 | 36 | 33 | 1089 | 30.25 | | Totals | 144 | 144 | 66 | 2178 | | ### Detailed Steps: 1. **Observed Frequencies (O):** - AO Present: 75 - AO Absent: 69 2. **Expected Frequencies (E):** - AO Present: 108 - AO Absent: 36 3. **Deviation (O-E):** - For both AO Present and AO Absent: 33 4. **Squared Deviation (O-E)²:** - For both AO Present and AO Absent: 1089 5. **Chi-Square Contribution (O-E)²/E:** - AO Present: 10.083 - AO Absent: 30.25 6. **Total Squared Deviation:** - Sum of (O-E)²: 2178 ### Summary This table displays the calculated values used in a chi-square test of independence. By comparing observed frequencies with expected frequencies, and calculating the deviations and their squares, we assess the difference between what is observed and what is expected under the null hypothesis. The chi-square statistic (χ²) is ultimately derived from summing the (O-E)²/E values across all categories.
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