testing claims “statistics” help please!!?
Question by Snow Y: testing claims “statistics” help please!!?
Proposition 8 originally was worded, “LIMIT ON MARRIAGE. INITIATIVE CONSTITUTIONAL AMENDMENT.” Later, Attorney General Brown changed that wording to, “ELIMINATES RIGHTS OF SAME-SEX COUPLES TO MARRY. INITIATIVE CONSTITUTIONAL AMENDMENT.” Under the original wordking the population proportion p of No voters was 42%. A Field poll the read only the new wording to n=830 randomly selected voters. Of these, 481 voiced a No on Prop. 8 opinion. Is there evidence that the new wording increased the percentage of No on Prop 8 voters?
Null hypothesis:…..
Alternative hypothesis:….
significance level:…..
Assumptions and Conditions verified:…..
Test Used, Statistical Value Obtained: Drawing, Calculation:……
Result:……
Conclusion:….
Best answer:
Answer by justalabelforme
we don’t really have enough data to do a proper test (we’d need to know the sample size on the original wording as well as on the changed wording), but working with what we have, the sample standard deviation (based on the distribution of the second sample) would be roughly 14 votes. that implies that (if the original sample was roughly the same size as the second one, and their was no difference between the populations) you’d expect to see at most a variation of 28 votes. instead, you see something closer to a difference of 130 votes, which (even accounting for the above noted problems) is still an awful lot more variation than one might expect.
additions: (things I forgot to say earlier)
null hypothesis: that the population of responses to the first wording is the same as the population of responses to the second wording (which is what you would expect if both wordings were unbiased, or equally biased)
Alternative hypothesis: (as always) that the null hypothesis is not true. in this case, actually, it would be that the population of responses for the second question is weighted heavier towards ‘no’ than the population of responses for the first question. this is a directional test.
significance level is just the cutoff value for your decision (conventionally, 5%, 1% and .01% are used for social scientific questions).
assumptions are standard binomial/normal distribution assumptions (which are true by default with yes/no type questions, so long as the responses are not too heavily skewed for the sample size. with a mean in the 40-50% range you have almost no skew, so you’re good).
use a standard binomial test. to do it properly, you’d want to get the sample size for the previous set of responses and do a two-sample t-test using binomial data.
results and conclusion I discussed above.
important! my experience with statistics is that getting an answer is rarely sufficient; you need to understand what’s been done, and how it’s been done, otherwise it is *literally* impossible to interpret the results correctly. that’s just an FYI, in case you think I’ve helped you out with homework more than I actually have. 😉
Know better? Leave your own answer in the comments!