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. Forthe 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. Thanks
chi^2= (obs-exp)^2/exp <--- Formula I used
To determine if your calculated chi-square values are correct, we need to go through the steps of calculating the expected values and performing the chi-square test. Here's a step-by-step explanation of how to calculate the chi-square values and determine statistical significance:
1. Chi-Square Test:
The chi-square test is used to determine whether there is a significant difference between observed and expected frequencies in a data set. It is commonly used to analyze categorical variables. In your case, you want to compare the frequencies of leaf discs measured under different light wavelengths.
2. Calculation of Expected Values:
To calculate the expected values, you need to have a null hypothesis (H0) stating that there is no significant difference between the observed frequencies of blue and white light wavelengths.
For the blue light vs. white light comparison, you have 3 leaf discs for blue light and 23 leaf discs for white light. Therefore, the expected value for blue light can be calculated as a ratio of the total number of leaf discs (26) and the proportion of blue light leaf discs. The expected value for blue light is: (3/26) * (3 + 23) = 3.115.
Similarly, for the green light vs. white light comparison, you have 6 leaf discs for green light and 23 leaf discs for white light. The expected value for green light is: (6/29) * (6 + 23) = 5.488.
3. Calculation of Chi-Square Values:
The formula you used, chi^2 = (observed - expected)^2 / expected, is correct. Now you can calculate the chi-square value for each comparison.
For the blue light vs. white light comparison:
chi-square = ((3 - 3.115)^2) / 3.115 = 0.037.
For the green light vs. white light comparison:
chi-square = ((6 - 5.488)^2) / 5.488 = 0.047.
Therefore, your calculated chi-square values are incorrect. The correct values are 0.037 for the blue light vs. white light comparison and 0.047 for the green light vs. white light comparison.
4. Determining Statistical Significance:
To determine statistical significance, you need to compare the calculated chi-square value to a critical chi-square value at a specific significance level (e.g., α = 0.05).
Based on your calculated chi-square values, you can consult a chi-square table or use a statistical software tool to identify the critical chi-square value at the desired significance level and degrees of freedom. The degrees of freedom for this test are (number of categories - 1), which is 1 in your case (blue vs. white) and (green vs. white).
Once you have the critical chi-square value, compare it with your calculated chi-square value. If your calculated chi-square value is greater than the critical value, then there is a statistically significant difference between the observed and expected frequencies. Otherwise, there is no significant difference.
Remember, chi-square tests are subject to assumptions, such as the expected values being greater than 5 for each category. If this assumption is violated, you may need to consider alternative statistical tests.
By following these steps, you can determine the statistical significance of your experiment's results. Repeat the process for other time points using the correct observed and expected values, and then compare the calculated chi-square values with the critical value to assess significance.