based on the results below, how would you decribe the relationship between heart attack patients being treated with aspirin and whether or not they live? males who lived and treated with aspirin = 15, males who did not live, and treated with aspirin = 2, and males who lived and not treated with aspirin = 4, and males who did not live and not treated with aspirin = 8. , chi square = 8.34, df = 1, p is less than and equal to 0.01
P is less than OR equal (≤) .01, which leads me to believe that taking aspirin reduces mortality.
To describe the relationship between heart attack patients being treated with aspirin and whether or not they live, we can use a chi-square test.
1. Create a contingency table:
| | Treated with Aspirin | Not Treated with Aspirin |
|----------------------|----------------------|--------------------------|
| Lived | 15 | 4 |
| Did not live | 2 | 8 |
2. Calculate the expected frequencies for each cell in the contingency table. This can be done using the formula: Expected Frequency = (Row Total * Column Total) / Grand Total. The grand total is the sum of all cells in the table.
| | Treated with Aspirin | Not Treated with Aspirin | Row Total |
|---------------------|----------------------|--------------------------|-----------|
| Lived | 13.6 | 5.4 | 19 |
| Did not live | 3.4 | 6.6 | 10 |
| Column Total | 17 | 12 | 29 |
| Grand Total | 29 | |
3. Calculate the chi-square statistic using the formula:
chi-square = Σ[(Observed Frequency - Expected Frequency)² / Expected Frequency]
Calculation for each cell:
- (15 - 13.6)² / 13.6 = 0.122
- (2 - 3.4)² / 3.4 = 0.552
- (4 - 5.4)² / 5.4 = 0.518
- (8 - 6.6)² / 6.6 = 0.242
Add up the calculated values:
0.122 + 0.552 + 0.518 + 0.242 = 1.434
4. Determine the degrees of freedom (df) for the chi-square test. It is calculated as:
df = (Number of rows - 1) * (Number of columns - 1)
In this case, df = (2 - 1) * (2 - 1) = 1
5. Look up the critical chi-square value for the given df and desired level of significance (p-value), which is 0.01.
From the chi-square distribution table, the critical chi-square value is approximately 6.635.
6. Compare the calculated chi-square statistic with the critical chi-square value. If the calculated chi-square value is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
In this case, chi-square = 1.434 and the critical chi-square value = 6.635. Since the calculated chi-square value (1.434) is less than the critical value (6.635), we fail to reject the null hypothesis.
7. Interpretation: Based on the results, there is no significant relationship between heart attack patients being treated with aspirin and whether or not they live.
To describe the relationship between heart attack patients being treated with aspirin and whether or not they live, we can analyze the results using the Chi-Square test. The Chi-Square test helps determine if there is a statistically significant association between two categorical variables.
In this case, we have two categorical variables: treatment with aspirin (Yes or No) and survival (Lived or Did not live).
From the given data:
- Males who lived and were treated with aspirin = 15
- Males who did not live and were treated with aspirin = 2
- Males who lived and were not treated with aspirin = 4
- Males who did not live and were not treated with aspirin = 8
To calculate the Chi-Square statistic, we compare the observed frequencies (the given data) with the expected frequencies (which are based on the assumption that there is no association between the variables).
First, we need to calculate the expected frequencies. To do this, we assume that the probability of survival is the same regardless of treatment with aspirin. We can find the probabilities by comparing the observed totals for each category with the total sample size.
The total number of males who lived = 15 + 4 = 19
The total number of males who did not live = 2 + 8 = 10
Total number of males treated with aspirin = 15 + 2 = 17
Total number of males not treated with aspirin = 4 + 8 = 12
Probability of survival = (males who lived / total sample) = 19 / (19 + 10) = 0.655
Probability of not survival = (males who did not live / total sample) = 10 / (19 + 10) = 0.345
Probability of treatment with aspirin = (males treated with aspirin / total sample) = 17 / (17 + 12) = 0.586
Probability of not treatment with aspirin = (males not treated with aspirin / total sample) = 12 / (17 + 12) = 0.414
To calculate the expected frequencies, we multiply the probabilities for each category:
Expected frequency for males who lived and were treated with aspirin = Probability of survival * Probability of treatment with aspirin * Total sample size = 0.655 * 0.586 * (19 + 10) ≈ 7.21
Expected frequency for males who did not live and were treated with aspirin = Probability of not survival * Probability of treatment with aspirin * Total sample size = 0.345 * 0.586 * (19 + 10) ≈ 3.79
Expected frequency for males who lived and were not treated with aspirin = Probability of survival * Probability of not treatment with aspirin * Total sample size = 0.655 * 0.414 * (19 + 10) ≈ 4.79
Expected frequency for males who did not live and were not treated with aspirin = Probability of not survival * Probability of not treatment with aspirin * Total sample size = 0.345 * 0.414 * (19 + 10) ≈ 3.11
Now we have both the observed and expected frequencies for each category. To calculate the Chi-Square statistic, we compare the squared difference between observed and expected frequencies, divided by the expected frequency:
Chi-Square = ∑[(Observed - Expected)^2 / Expected]
Plugging in the values:
Chi-Square = [(15 - 7.21)^2 / 7.21] + [(2 - 3.79)^2 / 3.79] + [(4 - 4.79)^2 / 4.79] + [(8 - 3.11)^2 / 3.11]
= 6.297 + 0.811 + 0.629 + 13.880
≈ 21.617
Next, we need to determine the degrees of freedom (df) for the Chi-Square test. In this case, df = (number of categories - 1) * (number of groups - 1) = (2 - 1) * (2 - 1) = 1.
Finally, we compare the calculated Chi-Square value to the critical value of the Chi-Square distribution with df = 1 and the desired level of significance (alpha), in this case, p ≤ 0.01.
The critical value for Chi-Square at p ≤ 0.01 with df = 1 is approximately 6.63 (from statistical tables or using a statistical software).
Since our calculated Chi-Square value (21.617) is greater than the critical value (6.63), we reject the null hypothesis of independence between treatment with aspirin and survival.
Therefore, based on the given results and the Chi-Square test, there is evidence to suggest that there is a statistically significant relationship between treatment with aspirin and the survival rate of male heart attack patients.