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 waschi^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?
To determine if your calculated chi-square values are correct, let's walk through the process step by step.
First, let's calculate the expected values for each comparison. The expected values for each group can be obtained by taking the average of the observed values in that group.
For example, in the comparison between blue (observed = 3) and white (observed = 23), the expected value would be (3 + 23)/2 = 13.
Similarly, for the comparison between green (observed = 6) and white (observed = 23), the expected value would be (6 + 23)/2 = 14.5.
Next, let's calculate the chi-square value for each comparison using the formula you mentioned:
chi^2 = (observed - expected)^2 / expected
For the blue/white comparison:
chi^2 = (3 - 13)^2 / 13 = 100 / 13 ≈ 7.69
For the green/white comparison:
chi^2 = (6 - 14.5)^2 / 14.5 = 67.25 / 14.5 ≈ 4.64
So, it seems like you made a mistake in your calculations. The correct chi-square value for blue/white is approximately 7.69, not 7.735 as you mentioned. The chi-square value for green/white should be around 4.64, not 24.735.
Now, to address your question about the observed value, in this case, the observed value for each comparison is the number you obtained from your experiment. So, for blue/white, the observed value is 3, and for green/white, the observed value is 6.
Remember that the chi-square test compares the observed values to the expected values, taking into account the sample sizes. It helps determine if there is a significant difference between the observed and expected values.
To calculate chi-square for other time points, you would follow the same steps: calculate the expected values and then use the formula to find the chi-square value.