In a plant trial, the number of plants that had diseases and rotten leaves were 4 and those without disease but had rotten leaves was 6. The number of plants observed to have the disease without rotten leaves was 2 and those with healthy leaves was and no disease was 8. The chi square value was?
Chi-square value = (4-2)^2/2 + (6-2)^2/2 + (2-2)^2/2 + (8-2)^2/2 = 8
Why did the leaf go to the doctor? Because it wasn't feeling well... it needed a "chir"-opractor!
But seriously, in order to calculate the chi-square value, we'll need the observed frequencies for each category. From the information given, we can deduce the following:
- Number of plants with disease and rotten leaves = 4
- Number of plants without disease but with rotten leaves = 6
- Number of plants with disease and without rotten leaves = 2
- Number of plants with healthy leaves and no disease = 8
Now, let's calculate the expected frequencies assuming independence:
- Expected frequency for plants with disease and rotten leaves = (Total number of plants with disease) * (Total number of plants with rotten leaves) / Total number of plants = (4+2) * (4+6) / (4+6+2+8) = 6
- Expected frequency for plants without disease but with rotten leaves = (Total number of plants without disease) * (Total number of plants with rotten leaves) / Total number of plants = (8+2) * (4+6) / (4+6+2+8) = 6
- Expected frequency for plants with disease and without rotten leaves = (Total number of plants with disease) * (Total number of plants without rotten leaves) / Total number of plants = (4+2) * (2+8) / (4+6+2+8) = 3
- Expected frequency for plants with healthy leaves and no disease = (Total number of plants without disease) * (Total number of plants without rotten leaves) / Total number of plants = (8+2) * (2+8) / (4+6+2+8) = 9
Now, we can use the formula for the chi-square test statistic:
chi-square = sum((observed - expected)^2 / expected) for all categories
Plugging in the values, we get:
chi-square = ((4-6)^2 / 6) + ((6-6)^2 / 6) + ((2-3)^2 / 3) + ((8-9)^2 / 9) = 0.67
So, the chi-square value is approximately 0.67.
To calculate the chi-square value, we need to create a contingency table with the given information:
| Disease | No Disease | Total
-------------------------------------------
Rotten Leaves | 4 | 6 | 10
Healthy Leaves| | 8 | 8
-------------------------------------------
Total | 6 | 14 | 18
Next, we calculate the expected frequencies for each cell:
| Disease | No Disease | Total
-------------------------------------------
Rotten Leaves | 2.67 | 7.33 | 10
Healthy Leaves| 3.33 | 4.67 | 8
-------------------------------------------
Total | 6 | 14 | 18
The formula to calculate the chi-square value is:
χ² = ∑ (O - E)² / E
Where:
O = Observed frequency
E = Expected frequency
Calculating the chi-square value for each cell:
χ² = (4 - 2.67)² / 2.67 + (6 - 7.33)² / 7.33 + (2 - 3.33)² / 3.33 + (8 - 4.67)² / 4.67
Now, we calculate each squared difference and divide it by the expected frequency:
χ² = (1.333² / 2.67) + (1.33² / 7.33) + (1.333² / 3.33) + (3.333³ / 4.67)
Finally, we sum up these values to get the chi-square value:
χ² = 0.177 + 0.24 + 0.537 + 2.11
χ² ≈ 3.064
Therefore, the chi-square value is approximately 3.064.
To calculate the chi-square value, you need to set up a contingency table based on the given information and then follow a step-by-step process. Here's how you can calculate the chi-square value:
Step 1: Set up the contingency table:
| Disease | No Disease | Total
----------|----------------------|--------------------|--------
Rotten | 4 | 6 | 10
Leaves |----------------------|--------------------|--------
Healthy | 2 | 8 | 10
----------|----------------------|--------------------|--------
Total | 6 | 14 | 20
Step 2: Calculate the expected frequencies for each cell in the contingency table. The expected frequency for each cell is determined by multiplying the row total by the column total and then dividing by the grand total.
| Disease | No Disease | Total
----------|----------------------|--------------------|--------
Rotten | (6*10)/20 = 3 | (14*10)/20 = 7 | 10
Leaves |----------------------|--------------------|--------
Healthy | (6*10)/20 = 3 | (14*10)/20 = 7 | 10
----------|----------------------|--------------------|--------
Total | 6 | 14 | 20
Step 3: Calculate the chi-square value for each cell. The chi-square value for each cell is determined by subtracting the expected frequency from the observed frequency, squaring the result, and then dividing by the expected frequency.
| Disease | No Disease | Total
----------|----------------------|--------------------|--------
Rotten | (4-3)^2/3 = 0.33 | (6-7)^2/7 = 0.14 | 10
Leaves |----------------------|--------------------|--------
Healthy | (2-3)^2/3 = 0.33 | (8-7)^2/7 = 0.14 | 10
----------|----------------------|--------------------|--------
Total | 6 | 14 | 20
Step 4: Sum up the chi-square values for each cell to obtain the chi-square statistic:
Chi-square = 0.33 + 0.14 + 0.33 + 0.14 = 0.94
Therefore, the chi-square value for the given data is 0.94.