7
$\begingroup$

I'm looking for a suitable statistical test for my situation. The best way to describe it is a "Chi-Squared test for continuous data". Please tell me otherwise.

Here is a made-up scenario: Say we spend a few days observing whales and sharks in the Atlantic and Indian oceans. Here are the counts in a contingency table:

|          |Atlantic |Indian |Total |
|----------|---------|-------|------|
| whales   | 8       | 2     | 10   |
| sharks   | 1       | 5     | 6    |
|----------|---------|-------|------|
| Total:   | 9       | 7     | 16   |

Here I use the Chi-squared test to determine if the observations of whales/sharks are independent of ocean location.

Let's consider another metric: the average weight of the animals. Here again, is the table:

|          |Atlantic |Indian |Avg.  |
|----------|---------|-------|------|
| whales   | 6.9     | 7.2   | 7.1  |
| sharks   | 2.3     | 2.9   | 2.5  |
|----------|---------|-------|------|
| Avg.:    | 4.3     | 5.4   | 4.9  |

Instead of total counts, I now have averages for the total of the populations along the side and last row. Here is my question: is the average weight of an animal independent of the ocean? Which test do I use now?

Just as a side note, the population sizes of each category might be very uneven such as a ratio of 1:999.

I appreciate your help in advance.

$\endgroup$

2 Answers 2

5
$\begingroup$

The question you are asking could be answered by performing what is very often called a 2-way ANOVA (also called two factor analysis of variance in Zar's Biostatistical Analysis).

Side comment: What I find very interesting in the way you ask your question is that indeed there are striking similarities between a 2-way ANOVA and a $\chi^2$ test.

In order to use the method, we need more information that what is available in the "mean" table: in order to calculate the statistic of the test, we also need to be able to compute the variability within each cell, and the total variability.

$\endgroup$
4
  • $\begingroup$ I would be very greatful if you could show how I could apply the example to the test $\endgroup$
    – joshlk
    Feb 29, 2016 at 11:02
  • $\begingroup$ If I had the averages and variability pre-calculated, do you how could I perform the test using R or Python? $\endgroup$
    – joshlk
    Mar 1, 2016 at 11:10
  • $\begingroup$ Do you have all the values, then? $\endgroup$ Mar 1, 2016 at 13:23
  • $\begingroup$ Yes. But it may be easier if I can just input the mean and variability (thanks for you help) $\endgroup$
    – joshlk
    Mar 1, 2016 at 13:54
0
$\begingroup$

On the first part at least, I think it's wrong to say you can use the Chi2 test "to determine if the NUMBER of whales/sharks are independent to ocean location". One can use the Chi2 test to determine "whether observations of a big animal is whale or shark are independent to ocean location". And for this hypothesis, you use the "count of whale/shark observations" to construct a contingency table.

$\endgroup$
1
  • $\begingroup$ I know its a bit late but thanks - I have edited the original question $\endgroup$
    – joshlk
    Jul 31, 2023 at 15:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.