I'm having some trouble with a stats portion of an animal behavior lab. We have to do chi-sqaure tests to test 3 hypothesis, which are 1) percent prey captured will decline as prey group size increases 2) percent successful hunts will decline as prey group size increases 3) orange balls will constitute significantly more than 25% of the prey captured.

Question

I'm having some trouble with a stats portion of an animal behavior lab. We have to do chi-sqaure tests to test 3 hypothesis, which are 1) percent prey captured will decline as prey group size increases 2) percent successful hunts will decline as prey group size increases 3) orange balls will constitute significantly more than 25% of the prey captured.

The data has four columns (singles, doubles, triples, quads are the headings). The # of prey expected to be caught for each is 12 (total=48). The # of prey caught is 12, 11, 10, 7, (total=40).
Number of hunts expected to be successful are 12, 6, 4, 3. Number of successful hunts is 12, 6, 4, 2. Number of orange balls expected to be caught is 3 for each column. The actual is 2, 2, 1, 1.

So, I assume I don't have to calculate any expected values. But do I plug directly in such as for hypothesis 1:
((7-12)^2)/12 ???

Answer 1

To perform chi-square tests for your hypotheses, you will need to calculate the expected values for each category before plugging them into the chi-square formula.

Let's go through each hypothesis and the corresponding calculations:

Hypothesis 1: Percent prey captured will decline as prey group size increases.

1. Calculate the expected values:
Start by calculating the total number of prey captured: 12 + 11 + 10 + 7 = 40.
Next, calculate the proportions for each category based on the total captured prey:
- Singles: 12/40 = 0.3 (30%)
- Doubles: 11/40 = 0.275 (27.5%)
- Triples: 10/40 = 0.25 (25%)
- Quads: 7/40 = 0.175 (17.5%)

Now, multiply each proportion by the total expected prey captured (48) to get the expected values for each category:
- Singles: 0.3 * 48 = 14.4
- Doubles: 0.275 * 48 = 13.2
- Triples: 0.25 * 48 = 12
- Quads: 0.175 * 48 = 8.4

2. Calculate the chi-square value:
For each category, calculate (observed - expected)^2 divided by expected.

For the "Quads" category:
((7 - 8.4)^2) / 8.4 = 0.391

Do the same calculation for each category and sum up the results:
((12 - 14.4)^2) / 14.4 + ((11 - 13.2)^2) / 13.2 + ((10 - 12)^2) / 12 + ((7 - 8.4)^2) / 8.4 = Chi-square value

Hypotheses 2 and 3 would require similar calculations using the expected values.

Note: If using a statistical software or calculator for chi-square test, it usually automatically calculates the expected values and performs the chi-square test for you.