According to Newspapers, Poe Is Leading According to Mathematics, Duterte Is Leading

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According to Newspapers, Poe Is Leading According to Mathematics, Duterte Is Leading

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The Pulse Asia Poll Survey for March 15-20 was published in the newspapers.  The newspapers said that for president of the Philippines Grace Poe = 28%, Rody Duterte = 24%, Jojo Binay = 23%, Santiago = 2%.  Even though it is said that there is a “statistical tie”, still there is an insinuation that Senator Poe is still leading.

However, if we will apply the proper mathematics in a Poll Survey, the result is different. It is Mayor Duterte that is leading.

Sample Evaluation

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The mathematical evaluation of a sampling survey will depend upon the sampling procedure being used.

If you want to make a direct percentage of the samples you must make a pure random sampling for the whole Philippines.  You must travel to different places throughout the Philippines and ask 1,200 people.  It is expensive and time consuming.

What is done by Pulse Asia and SWS (Social Weather Station) is to divide the whole Philippines into four (4) geographical areas as NCR (National Capital Region), Luzon, Visayas, and Mindanao.  They will then ask local pollsters to make a proper poll survey in their area by taking 300 samples in their area.

In this procedure, if the area populations are not equal, you cannot directly add the area results and say that it represents the Philippines.  You can only add the results if the area populations taken are also equal.

Example Survey

You are asked who between Sen. Poe and Mayor Duterte will win in Cogon, Tagbilaran and Cabawan, Tagbilaran.  Cogon has a voting population of 9,000 while Cabawan has 900 voters or total of 9,900 voters.

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One thousand (1,000) samples were taken.  The sample results were directly added and gave a result of 700 or 70% for Sen. Poe and 300 or 30% for Mayor Duterte.  If you will not be careful, you might say that the 70% of the samples indicate that Sen. Poe will win.

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Upon investigation it was found out that the samples were equally divided as 500 for Cogon and 500 for Cabawan.

It was also found out that in the 500 samples for Cogon, 275 or 55% were for Duterte and 225 or 45% were for Sen. Poe.  In Cabawan, 25 or 5% were for Duterte and 475 or 95% were for Sen. Poe.

Since there are two separate samplings, we must compute separately.  In Cogon, Duterte will obtain 0.55 x 9,000 = 4,950 votes and Sen. Poe will obtain 0.45 x 9,000 = 4,040 votes.  In Cabawan, Duterte will get 0.05 x 900 = 45 votes and Sen. Poe will get 0.95 x 900 = 855 votes.

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The next step is to add the votes in Cogon and Cabawan.  Duterte = 4,950 + 45 = 4,995 votes.  Sen. Poe = 4,050 + 855 = 4,905 votes.  Therefore, Duterte with 4,995 votes will win against Poe’s 4,905.

The direct percentage computation of 30% and 70% was not valid because the voting populations were not the same.

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Pulse Asia Results

The newspapers carried the direct percentage computation.  It will be valid only if the voting populations considered per regional area are equal.

Fortunately it can be done in the Philippines.  Let us assume that of the 54,363,329 registered voters in the Philippines only 44 million will vote.  This can be divided into four as NCR (Manila and environs) = 11 million.  Luzon, Visayas, and Mindanao will also have 11 million each.

The result of the 300 samples per region will now be valid if you add directly because the populations are equal.

Here are the results:

Computing the poll survey results using equal samples representing and equally divided area population will give us, 1st = Duterte, 2nd = Poe, 3rd = Binay, and 4th Roxax.

In terms of the 44 million voters, the percentages will be Duterte = (11.88 ÷ 44) x 100 = 27%, Poe = 26.75%, Binay = 22.5%, and Roxas = 17.75%.

Therefore it is already Duterte who is leading in the poll surveys.  However, the difference is still within the margin of error of the survey and a statistical tie is declared.

In the March 5, 2016 Pulse Asia Survey the results using equal population for equal samples, the results were, 1st = Binay; 2nd = Duterte; 3rd = Poe; 4th = Roxas; 5th = Santiago. (By Jes B. Tirol)

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