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Observed Number (7th generation) Allele Expected Number (0 generation) O-E (O-E)? (O-E)?/E R r x2 =

Observed Number (7th generation) Allele Expected Number (0 generation) O-E (O-E)? (O-E)?/E R r x2 =

Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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x2=______

### Chi Square Test of Alleles A Chi Square test is a statistical method used to determine if there is a significant difference between the expected and observed frequencies in one or more categories. In this example, the Chi Square test is used to analyze the distribution of two alleles, R and r, across generations. #### Table Explanation | Allele | Observed Number (7th generation) | Expected Number (0 generation) | O-E | (O-E)² | (O-E)²/E | |-------|----------------------------------|-------------------------------|------|----------|------------| | R | 124 | 196 | -72 | 5184 | 26.45 | | r | 276 | 204 | 72 | 5184 | 25.41 | - **Observed Number (7th generation)**: The count of each allele observed in the 7th generation. - **Expected Number (0 generation)**: The count of each allele expected based on the initial generation. - **O-E**: The difference between the observed and expected numbers (Observed - Expected). - **(O-E)²**: The square of the difference (O-E)². - **(O-E)²/E**: The square of the difference divided by the expected number (((O-E)²)/E). #### Calculation Summary - For allele R: - Observed: 124 - Expected: 196 - (O-E): -72 - (O-E)²: 5184 - (O-E)²/E: 26.45 - For allele r: - Observed: 276 - Expected: 204 - (O-E): 72 - (O-E)²: 5184 - (O-E)²/E: 25.41 #### Chi Square Value Calculation - The Chi Square value is the sum of (O-E)²/E for all alleles. - Chi Square = 26.45 + 25.41 = 51.86 #### Degrees of Freedom - Degrees of Freedom (Df) = Number of categories - 1 = 2 - 1 = 1 #### P Value - The P value range is less than 0.005 (<0.005). This indicates that there is
Transcribed Image Text:### Chi Square Test of Alleles A Chi Square test is a statistical method used to determine if there is a significant difference between the expected and observed frequencies in one or more categories. In this example, the Chi Square test is used to analyze the distribution of two alleles, R and r, across generations. #### Table Explanation | Allele | Observed Number (7th generation) | Expected Number (0 generation) | O-E | (O-E)² | (O-E)²/E | |-------|----------------------------------|-------------------------------|------|----------|------------| | R | 124 | 196 | -72 | 5184 | 26.45 | | r | 276 | 204 | 72 | 5184 | 25.41 | - **Observed Number (7th generation)**: The count of each allele observed in the 7th generation. - **Expected Number (0 generation)**: The count of each allele expected based on the initial generation. - **O-E**: The difference between the observed and expected numbers (Observed - Expected). - **(O-E)²**: The square of the difference (O-E)². - **(O-E)²/E**: The square of the difference divided by the expected number (((O-E)²)/E). #### Calculation Summary - For allele R: - Observed: 124 - Expected: 196 - (O-E): -72 - (O-E)²: 5184 - (O-E)²/E: 26.45 - For allele r: - Observed: 276 - Expected: 204 - (O-E): 72 - (O-E)²: 5184 - (O-E)²/E: 25.41 #### Chi Square Value Calculation - The Chi Square value is the sum of (O-E)²/E for all alleles. - Chi Square = 26.45 + 25.41 = 51.86 #### Degrees of Freedom - Degrees of Freedom (Df) = Number of categories - 1 = 2 - 1 = 1 #### P Value - The P value range is less than 0.005 (<0.005). This indicates that there is
The table and formula presented are used to perform a Chi-Square (χ²) test, which is a statistical method used to determine if there is a significant difference between expected and observed data. ### Chi-Square (χ²) Calculation Table #### Table Breakdown: - **Allele**: The allele column lists the different alleles being studied. - **R**: One type of allele. - **r**: Another type of allele. - **Observed Number (7th generation)**: This column is used to record the number of each allele observed in the 7th generation of the study. - **Expected Number (0 generation)**: This column contains the expected number of each allele based on the initial conditions or previous data from the 0 generation. - **O-E**: The difference between the Observed number and Expected number for each allele. - **(O-E)²**: The square of the difference between the Observed number and Expected number. - **(O-E)²/E**: The squared difference divided by the Expected number. - The final section **χ² = ______** indicates the location where the calculated Chi-Square value will be recorded. This value is obtained by summing the values in the (O-E)²/E column for all alleles. ### Detailed Steps for Chi-Square Calculation: 1. **Calculate O-E**: Subtract the Expected Number (E) from the Observed Number (O) for each allele. 2. **Calculate (O-E)²**: Square the result from step 1 for each allele. 3. **Calculate (O-E)²/E**: Divide the result from step 2 by the Expected Number (E) for each allele. 4. **Sum (O-E)²/E**: Add up all the values obtained in step 3 to get the chi-square value (χ²). This chi-square value is then compared to a critical value from the chi-square distribution table to determine if the difference between observed and expected frequencies is statistically significant.
Transcribed Image Text:The table and formula presented are used to perform a Chi-Square (χ²) test, which is a statistical method used to determine if there is a significant difference between expected and observed data. ### Chi-Square (χ²) Calculation Table #### Table Breakdown: - **Allele**: The allele column lists the different alleles being studied. - **R**: One type of allele. - **r**: Another type of allele. - **Observed Number (7th generation)**: This column is used to record the number of each allele observed in the 7th generation of the study. - **Expected Number (0 generation)**: This column contains the expected number of each allele based on the initial conditions or previous data from the 0 generation. - **O-E**: The difference between the Observed number and Expected number for each allele. - **(O-E)²**: The square of the difference between the Observed number and Expected number. - **(O-E)²/E**: The squared difference divided by the Expected number. - The final section **χ² = ______** indicates the location where the calculated Chi-Square value will be recorded. This value is obtained by summing the values in the (O-E)²/E column for all alleles. ### Detailed Steps for Chi-Square Calculation: 1. **Calculate O-E**: Subtract the Expected Number (E) from the Observed Number (O) for each allele. 2. **Calculate (O-E)²**: Square the result from step 1 for each allele. 3. **Calculate (O-E)²/E**: Divide the result from step 2 by the Expected Number (E) for each allele. 4. **Sum (O-E)²/E**: Add up all the values obtained in step 3 to get the chi-square value (χ²). This chi-square value is then compared to a critical value from the chi-square distribution table to determine if the difference between observed and expected frequencies is statistically significant.
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