Testing proportions

[Ilovestats!!]

Hi,

I have survey results were I have asked respondents if they are familiar with certain foods, so they are to check all that apply. There are three options. I would like to determine if there is a significant difference between the three options based on the percent answered. Can I do this even though the same person could be present in each option?

Thanks!

[Rich Ulrich]

On Mon, 18 Dec 2017 07:34:29 -0800 (PST), "Ilovestats!!"

Post by Ilovestats!!
Hi,
I have survey results were I have asked respondents if they are familiar with certain foods, so they are to check all that apply. There are three options. I would like to determine if there is a significant difference between the three options based on the percent answered. Can I do this even though the same person could be present in each option?

Consider them in pairs. A vs. B, A vs. C, B vs. C.

As a 2x2 table, this is Kendall's Test for "Changes"...
the 0,0 and 1,1 (for No, Yes) cells are irrelevant when
you compare the 0,1 count to the 1,0 count.

The comparison is between Number of A-not-B and
Number of B-not-A. If you just look at those two
counts, you can figure out that Kendall's Test is an
approximation for the Sign Test with compares the
equality of two conditions that have equal Expectations.

There is a multi-variable extension of Kendall's whcih I
have never bothered with. If there is a difference, you
then want to look back at the separate comparisons.

If you need to relate to an overall test size of 5%, use
the Bonferroni correction, that is, 3 tests at 1.67%.

[Ilovestats!!]

Post by Rich Ulrich
On Mon, 18 Dec 2017 07:34:29 -0800 (PST), "Ilovestats!!"

Post by Ilovestats!!
Hi,
I have survey results were I have asked respondents if they are familiar with certain foods, so they are to check all that apply. There are three options. I would like to determine if there is a significant difference between the three options based on the percent answered. Can I do this even though the same person could be present in each option?

Consider them in pairs. A vs. B, A vs. C, B vs. C.
As a 2x2 table, this is Kendall's Test for "Changes"...
the 0,0 and 1,1 (for No, Yes) cells are irrelevant when
you compare the 0,1 count to the 1,0 count.
The comparison is between Number of A-not-B and
Number of B-not-A. If you just look at those two
counts, you can figure out that Kendall's Test is an
approximation for the Sign Test with compares the
equality of two conditions that have equal Expectations.
There is a multi-variable extension of Kendall's whcih I
have never bothered with. If there is a difference, you
then want to look back at the separate comparisons.
If you need to relate to an overall test size of 5%, use
the Bonferroni correction, that is, 3 tests at 1.67%.
--
Rich Ulrich

Hi Rich,

Thanks! This got me thinking, could I use the Cochran's Q?

[Rich Ulrich]

On Mon, 18 Dec 2017 11:29:12 -0800 (PST), "Ilovestats!!"

Post by Ilovestats!!

Post by Rich Ulrich
On Mon, 18 Dec 2017 07:34:29 -0800 (PST), "Ilovestats!!"

Post by Ilovestats!!
Hi,
I have survey results were I have asked respondents if they are familiar with certain foods, so they are to check all that apply. There are three options. I would like to determine if there is a significant difference between the three options based on the percent answered. Can I do this even though the same person could be present in each option?

Consider them in pairs. A vs. B, A vs. C, B vs. C.
As a 2x2 table, this is Kendall's Test for "Changes"...
the 0,0 and 1,1 (for No, Yes) cells are irrelevant when
you compare the 0,1 count to the 1,0 count.
The comparison is between Number of A-not-B and
Number of B-not-A. If you just look at those two
counts, you can figure out that Kendall's Test is an
approximation for the Sign Test with compares the
equality of two conditions that have equal Expectations.
There is a multi-variable extension of Kendall's whcih I
have never bothered with. If there is a difference, you
then want to look back at the separate comparisons.
If you need to relate to an overall test size of 5%, use
the Bonferroni correction, that is, 3 tests at 1.67%.
--
Rich Ulrich

Hi Rich,
Thanks! This got me thinking, could I use the Cochran's Q?

Yes, but why? You will want to describe the separate results,
I assume, if p(Q) < 0.05. If p(Q) > 0.05, you will want the separate
results to show that the failure-to-reject is not wholly a matter
of insufficient power.

There is a Wikipedia page on Cochran's Q. At the end, it mentions
that the 2x2 instance is the same as Kendall's and the same as a
two-tailed sign test.