Statistical Analysis: Quebec Referendum Vote

[vj9]

Hello All,

I am stuck on this statistical Analysis. I am wondering which statistical method to use, any suggestions and why?

The scenario is as follows

Since the 1960s there has been an ongoing campaign among Quebecois to separate from Canada and form an independent nation. Should Quebec separate, the ramifications for the rest of Canada, American States that border Quebec, the North American Free Trade Agreement and numerous multi-national corporations would be enormous. In the 1993 elections the pro-sovereigntist Bloc Quebecois won 54 of Quebec’s 75 seats in the House of Commons. In 1994 the separatist Parti Quebecois formed the provincial government in Quebec and promised to hold a referendum on separation. As with most political issues, polling plays an important role in trying to influence voters and to predict the outcome of the referendum vote. Shortly after the 1993 federal election, The Financial Magazine, in co-operation with several polling companies, conducted a survey of Quebecois.

A total of 641 adult Quebecois were interviewed. They were asked the following question. (Francophones were asked the question in French). The pollsters also recorded the language (English or French) in which the respondent answered.

If a referendum were held today on Quebec’s sovereignty with the following question, “Do you want Quebec to separate from Canada and become an independent country?” would you vote yes or no?

2 Yes
1 No

The responses were recorded and stored in columns 1 (planned referendum vote for Francophones) and 2(planned referendum vote for Anglophones)

Infer from the data:

a) If the referendum were held on the day of the survey, would Quebec vote to remain in Canada?

b) Estimate with 95% confidence the difference between French and English speaking Quebecers in their support for separation.

 

[EnumaElish]

Recode Yes as 1 and No as 0. If the mean is greater than the referendum threshold percentage (what constitutes a majority under Canadian law) then the answer to a) is "Yes."

For part b), estimate the mean and the variance (http://en.wikipedia.org/wiki/Binomial_distribution) and then apply the independent one-sample t-test (http://en.wikipedia.org/wiki/T_test#Independent_one-sample_t-test).

 

[vj9]

Hi Enuma,

Thanks for you reply i have a sample data of 641 people which include both francophones and anglophones.

..... Yes ... No

Francophones ... 229 ...286

Anglophones ... 10 ... 116

I just want to know which statistical method to calculate in part A and how to represent this data?

Your answer for b was helpful.

 

[statdad]

A t-test isn't appropriate for qualitative data (and it's still qualitative data even if you code it as 0 and 1). You want to look for test and confidence interval procedures for comparing two proportions.

 

[vj9]

Hello Statdad,

Can you suggest me which test is better to use?

Thanks

 

[SW VandeCarr]

Hello Statdad,

Can you suggest me which test is better to use?

Thanks

The policy here is to give guidance, but not to solve the problem for you. Here, you want the test for a single proportion for a) 1-\hat p = \hat q and two proportions for b).

 

[EnumaElish]

A t-test isn't appropriate for qualitative data (and it's still qualitative data even if you code it as 0 and 1). You want to look for test and confidence interval procedures for comparing two proportions.

For the record, t-test can be used as an approximation for testing binomial data, especially for a large sample like the OP's.

Using the frequency table above, I compute a chi-squared of 57.77. With d.f. = 1, it's significant at p = 0.001 or better ("critical" \chi^2\approx 11 given p = 0.001).

Assuming unequal sample sizes and equal [unequal] variances, I compute a t ratio of 216 [338], which is significant at p = 0.0005 or better ("critical" t ---> 3.3 as d.f. ---> infinity, given p = 0.0005).