We are using Chi Squares to understand if descrepancies in aniaml populations are random or significant. On the developed land, 20 traps were set. 7 Road runners were caught, and two were marked. On the Undeveloepd land, 20 traps were also set, but 11 Road Runners were caught and 1 was marked. I know the formula for the chi square, x^2=sigma (observed-expected)^2/expected. But which values are observed, and which are expected? And how do the marked values fit into this?
In the context of the Chi-Square test, the observed values refer to the actual data that you have collected during your experiment. These values are the quantities you directly observed or counted. In your case, the observed values are:
- On developed land: 7 road runners caught, 2 marked
- On undeveloped land: 11 road runners caught, 1 marked
On the other hand, the expected values are the values that you would expect to obtain under the assumption of randomness or no significant difference. In this case, since you want to determine if the discrepancies in animal populations are random or significant, the expected values can be calculated based on a null hypothesis, which assumes no significant difference between the populations on developed and undeveloped land.
To calculate the expected values, you need the total number of animals in each category (caught and marked) and the total number of traps in each land type. Here's how you can calculate the expected values:
1. Calculate the proportion of marked road runners in each land type:
- Developed land: 2 marked / 7 caught = 2/7 = 0.286
- Undeveloped land: 1 marked / 11 caught = 1/11 ≈ 0.091
2. Multiply the proportions from step 1 by the total number of caught road runners in each land type to get the expected marked values:
- Expected marked on developed land: 0.286 * 7 ≈ 2.00
- Expected marked on undeveloped land: 0.091 * 11 ≈ 1.00
3. Subtract the expected marked values from the observed marked values to calculate the observed - expected values:
- On developed land: 2 marked - 2.00 expected marked = 0 (observed - expected)
- On undeveloped land: 1 marked - 1.00 expected marked = 0 (observed - expected)
Finally, you can plug these observed - expected values into your Chi-Square formula to calculate the chi-square statistic.