I did a biology experiment where I need to analyze the statistical significance of betweeen a data set. My experiment consisted of measuring the effects in photosynthesis and cellular respiration by exposing solutions with leaf discs to different light wavelength. For the statistical significance, I have to compare data I got with blue and green light to white light. The amount of discs for the time point I chose for blue was: 3, white: 23 and for green: 6 I'm supposed to use the chi square method to compare this values and I got 13 for my expected value between blue and white and 8.5 between green and white and then a chi square of 7.69 for blue/white and of 24.735 for green/white. Are those values right? I have to use this method for many other time points but if I have this one right probably I have the others right, same if I have it wrong, if they are wrong, please explain how to calculate it.
The equation I used was chi^2= (obs-exp)^2/exp I calculated my expected value by taking the average of the ones I have. Will my observed value be any of the two I have, or do I have the add them and that will be my observed value? I don't think I have to add them since I will just get my expected value back but I just want to make sure what my observed values in this case be...
To determine whether the values you calculated are correct, we can go through the steps of calculating a chi-square value for a two-way table using the data you provided.
First, let's create a two-way table with the observed frequencies for each condition (blue, green, and white light):
| Observed Frequencies
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| Blue | Green | White
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Time Point Chosen | 3 | 6 | 23
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Next, calculate the expected frequencies. To do this, you need to calculate the row and column totals, as well as the total sample size:
Row totals:
- Blue: 3
- Green: 6
- White: 23
Column totals:
- Blue: 3 + 6 + 23 = 32
- Green: 3 + 6 + 23 = 32
- White: 3 + 6 + 23 = 32
Total sample size: 3 + 6 + 23 = 32
Now, calculate the expected frequencies by multiplying the row total by the column total and dividing by the total sample size:
Expected frequencies:
- Blue/White: (3*32)/32 = 3
- Green/White: (6*32)/32 = 6
Next, calculate the chi-square value. Use the formula:
chi^2 = Σ((observed - expected)^2 / expected)
For the Blue/White comparison:
chi^2 = [(3-3)^2 / 3] + [(23-3)^2 / 3] = 0 + 200/3 = 66.67
For the Green/White comparison:
chi^2 = [(6-6)^2 / 6] + [(23-6)^2 / 6] = 0 + 289/6 = 48.17
Based on these calculations, the chi-square value for the Blue/White comparison is approximately 66.67, and for the Green/White comparison is approximately 48.17.
Please note that the observed values for each comparison are the individual observed frequencies for blue, green, and white light. You don't need to add them together in this case.
If you need to calculate the chi-square value for other time points, follow the same steps: create a two-way table, calculate the expected frequencies, and then use the chi-square formula to find the chi-square value.
Remember to refer to chi-square distribution tables or statistical software to determine the significance level (p-value) associated with each chi-square value. This will help determine whether the observed differences are statistically significant.