| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | C. Expected frequencies should be whole numbers. In a contingency table for a chi-square test for independence, the expected frequencies are calculated based on the marginal totals and the assumption of independence. These expected frequencies are not necessarily whole numbers, as they can be decimal values. The other options are correct: categories are typically not numerical for either variable, observed frequencies should be whole numbers (as they represent counts), and expected frequencies in each cell should ideally be at least 5 to ensure the accuracy of the chi-square approximation, with category combination sometimes used to achieve this. |
C |
| deepseekr1 | The question asks which statement about contingency tables in chi-square tests for independence is not true. Here's the analysis: - **Option A** is true because contingency tables handle categorical variables, which are non-numerical. - **Option B** is true since observed frequencies are actual counts and must be whole numbers. - **Option C** is **false** because expected frequencies are calculated using the formula \(( \text{row total} \times \text{column total} ) / \text{overall total}\), which often results in decimals, not necessarily whole numbers. - **Option D** is true, as a rule of thumb requires expected frequencies ≥5 to ensure test validity, sometimes requiring category merging. The incorrect statement is **C**. Answer: C |
C |
| gpto1 | C | C |
| GPT-4o | C. Expected frequencies should be whole numbers. | C |
| llama3.1-70B-Instruct | C |
C |
| llama3.1-405B-Instruct | C. Expected frequencies should be whole numbers. In a contingency table for a chi-square test for independence, the expected frequencies are calculated based on the marginal totals and the assumption of independence. These expected frequencies are not necessarily whole numbers, as they can be decimal values. The other options are correct: categories are typically not numerical for either variable, observed frequencies should be whole numbers (as they represent counts), and expected frequencies in each cell should ideally be at least 5 to ensure the accuracy of the chi-square approximation, with category combination sometimes used to achieve this. |
C |
| DeepSeek-Coder-V2 | C. Expected frequencies should be whole numbers. | C |
| Qwen2-72B-Instruct | C. Expected frequencies should be whole numbers. | C |
| baichuan4 | C | C |
| doubao | C Expected frequencies do not necessarily have to be whole numbers. |
C |
| minimax | C. Expected frequencies should be whole numbers. | C |
| kimi | C. Expected frequencies should be whole numbers. This statement is not true because expected frequencies in a contingency table are calculated based on the marginal totals and are not necessarily whole numbers. They are theoretical values that represent what we would expect to see in each cell if the variables were independent. |
C |
| wenxinyiyan | C | C |
| zhipu | C Explanation: For chi-square tests for independence using contingency tables: - A is true because the variables are categorical, not numerical. - B is true because observed frequencies are actual counts and must be whole numbers. - C is not true because expected frequencies can be non-whole numbers; they are calculated based on the assumption of independence and do not need to be integers. - D is true because having expected frequencies of at least 5 in each cell is a common guideline to ensure the validity of the chi-square test, and combining categories can help achieve this. |
C |
| gpto1 | C | C |
| deepseekv3 | C. Expected frequencies should be whole numbers. Explanation: Expected frequencies in a chi-square test for independence are calculated based on the row and column totals and are not necessarily whole numbers. They are derived from the formula: \[ \text{Expected frequency} = \frac{(\text{row total}) \times (\text{column total})}{\text{grand total}} \] This often results in decimal values. The other statements (A, B, and D) are true regarding contingency tables for chi-square tests for independence. |
C |