(Hypothetical.) A study is carried out to determine the...

(Hypothetical.) A study is carried out to determine the effect of party affili-ation on voting behavior in a certain city. The city is divided up into wards. In each ward, the percentage of registered Democrats who vote is higher than the percentage of registered Republicans who vote. True or false: for the city as a whole, the percentage of registered Democrats who vote must be higher than the percentage of registered Republicans who vote. If true, why? If false, give an example.

(Hypothetical.) A study is carried out to determine the effect of party affili-ation on voting behavior in a certain city. The city is divided up into wards. In each ward, the percentage of registered Democrats who vote is higher than the percentage of registered Republicans who vote. True or false: for the city
as a whole, the percentage of registered Democrats who vote must be higher
than the percentage of registered Republicans who vote. If true, why? If false, give an example.

Key Concepts

Simpson's Paradox

Simpson's Paradox occurs when a trend present within multiple groups disappears or reverses when the groups are combined. In this context, even though in every ward the percentage of registered Democrats who vote is higher than that of Republicans, aggregating the data without considering the different sizes or proportions of registrants in each ward can potentially lead to the overall percentage for Democrats being lower than that for Republicans. This counterintuitive result is a central aspect of Simpson's Paradox.

Weighted Averages

Weighted averages are used when combining data from different groups where each group may have a different number of observations. In the context of voting behavior, if wards vary in the number of registered voters, each ward's voting percentage contributes differently to the citywide average. This concept is crucial because larger wards can have a disproportionate impact on the overall aggregated percentage, potentially reversing the trend observed within smaller wards.

Aggregation Bias

Aggregation bias refers to the mistake of assuming that relationships observed in aggregated data will hold true for the individual components or vice versa. In political studies, it means that ward-level findings (such as higher voting percentages for Democrats) might not directly translate to citywide results due to different ward sizes and distributions. Understanding aggregation bias is key to correctly interpreting combined data from varied subgroups.

Transcript

00:01 Over here, i would say that the question that they have asked, based on the given information, i would say the answer for this is false.

00:09 So why false? because i'm going to give an example here.

00:12 So we say that in simpson's paradox, relationship between, say, percentages in subgroups can be reversed when the subgroups are combined, right? so now suppose i talk about an example that the city is divided into two words as follows.

00:46 So if i make it like this, we have party and under the party we will have the democrats.

00:53 And the next we have is the republicans.

00:58 All right, and we are talking about their data now.

01:00 So this we are talking about the participants, then the next is going to the votes and the percentage of them.

01:06 So the democrats, you see, suppose there are three participants and we have 100 republicans here.

01:10 And the number of votes is also 3 but over here it is 99 so in this case the person you can see is complete 100 % but over here this is exactly 99 % so now if i talk about ward 1 so this we have taken for two words so if i talk about ward 1 from the above table we can observe that the democrat party voting percentage is higher in ward 1 if you see this part over here this percentage is higher in ward 1 so i would actually consider so suppose now in terms of this was like for ward 1 we say i will just write it here that the democrat party voting percentage is higher in ward 1 right now the next table i'm going to talk is for ward 2 so again we are going to consider suppose this is the party then under party we have the democrats then the republicans and again the party then the votes and the percentage that we'll calculate so suppose now i have democrats which are 100 and republicans are two and suppose we've got 51 votes out here and only one vote here so here the percentage is 51 and over here it is 50 so now ward 2 what we're going to talk about it over here is that the democratic percentage of voting is again higher...

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