De Boor's algorithm: Difference between revisions

Revision as of 10:33, 16 January 2014

My name is Winnie and I am studying Anthropology and Sociology and Modern Languages and Classics at Rillieux-La-Pape / France.

Also visit my web site ... hostgator1centcoupon.info An ecological fallacy (or ecological inference fallacy)^[1] is a logical fallacy in the interpretation of statistical data where inferences about the nature of individuals are deduced from inference for the group to which those individuals belong. Ecological fallacy sometimes refers to the fallacy of division which is not a statistical issue. The four common statistical ecological fallacies are: confusion between ecological correlations and individual correlations, confusion between group average and total average, Simpson's paradox, and confusion between higher average and higher likelihood.

Correlation of groups and individuals

Ecological fallacy can refer to the following statistical fallacy: the correlation between individual variables is deduced from the correlation of the variables collected for the group to which those individuals belong.

Examples

Assume that at the individual level, being Protestant impacts negatively one's tendency to commit suicide but the probability that one's neighbor commits suicide increases one's tendency to become Protestant. Then, even if at the individual level there is negative correlation between suicidal tendencies and Protestantism, there can be a positive correlation at the aggregate level.

Similarly, even if at the individual level, wealth is positively correlated to tendency to vote Republican, we observe that wealthier states tend to vote Democrat. For example, in 2004, the Republican candidate, George W. Bush, won the fifteen poorest states, and the Democratic candidate, John Kerry, won 9 of the 11 wealthiest states. Yet 62% of voters with annual incomes over $200,000 voted for Bush, but only 36% of voters with annual incomes of $15,000 or less voted for Bush.^[2]

Formal problem

The correlation of aggregate quantities (or ecological correlation) is not equal to the correlation of individual quantities. Denote $X_{i},Y_{i}$ two quantities at the individual level. The formula for the covariance of the aggregate quantities in groups of size N is

cov\left(\sum _{jN+1}^{(j+1)N}Y_{i},\sum _{1}^{N}X_{i}\right)=\sum _{1}^{N}cov(Y_{jN+i},X_{i})+\sum _{i\neq l}cov(Y_{jN+l},X_{i})

The covariance of two aggregated variables depends not only the covariance of two variables within the same individuals but also of covariances of the variables between different individuals. In other words, correlation of aggregate variables take into account cross sectional effects which are not relevant at the individual level.

The problem for correlations entails naturally a problem for regressions on aggregate variables: the correlation fallacy is therefore an important issue for a researcher who wants to measure causal impacts. Start with a regression model where the outcome $Y_{i}$ is impacted by $X_{i}$

Y_{i}=\alpha +\beta X_{i}+u_{i},

cov[u_{i},X_{i}]=0.

The regression model at the aggregate level is obtained by summing the individual equations:

\sum _{jN+1}^{(j+1)N}Y_{i}=\alpha +\beta \sum _{jN+1}^{(j+1)N}X_{i}+\sum _{jN+1}^{(j+1)N}u_{i},

cov\left[\sum _{jN+1}^{(j+1)N}u_{i},\sum _{k=jN+1}^{(j+1)N}X_{k}\right]\neq 0.

Nothing prevents the regressors and the errors from being correlated at the aggregate level. Therefore, generally, running a regression on aggregate data does not estimate the same model than running a regression with individual data.

The aggregate model is correct if and only if

cov\left[u_{i},\sum _{k=jN+1}^{(j+1)N}X_{k}\right]=0\quad {\text{ for all }}i.

This means that, controlling for $X_{i}$ , $\sum _{jN+1}^{(j+1)N}X_{k}$ does not determine $Y_{i}$ . Going back to the religion example, the aggregate model correctly measures Protestants' tendency to commit suicide if and only, inside each religion, one's tendency to commit suicide is not determined by the number of Protestants in one's state.

Historical examples of the fallacy

An early example of the ecological fallacy was Émile Durkheim's 1897 study of suicide in France although this has been debated by some.^[3]^[4] Another example is a 1950 paper by William S. Robinson that coined the term.^[5] For each of the 48 states + District of Columbia in the US as of the 1930 census, he computed the illiteracy rate and the proportion of the population born outside the US. He showed that these two figures were associated with a negative correlation of −0.53 — in other words, the greater the proportion of immigrants in a state, the lower its average illiteracy. However, when individuals are considered, the correlation was +0.12 — immigrants were on average more illiterate than native citizens. Robinson showed that the negative correlation at the level of state populations was because immigrants tended to settle in states where the native population was more literate. He cautioned against deducing conclusions about individuals on the basis of population-level, or "ecological" data. In 2011, it was found that Robinson's calculations of the ecological correlations are based on the wrong state level data. The correlation of −0.53 mentioned above is in fact −0.46.^[6] Robinson's paper was seminal, but the term 'ecological fallacy' was not coined until 1958 by Selvin.

Choosing between aggregate and individual inference

There is nothing wrong in running regressions on aggregate data if one is interested in the aggregate model. For instance, as a governor, it is correct to run regressions between police force on crime rate at the state level if one is interested in the policy implication of a rise in police force. However, an ecological fallacy would happen if a city council deduces the impact of an increase in police force in the crime rate at the city level from the correlation at the state level.

Choosing to run aggregate or individual regressions to understand aggregate impacts on some policy depends on the following trade off: aggregate regressions lose individual level data but individual regressions add strong modeling assumptions. Some researchers suggest that the ecological correlation gives a better picture of the outcome of public policy actions, thus they recommend the ecological correlation over the individual level correlation for this purpose (Lubinski & Humphreys, 1996). Other researchers disagree, especially when the relationships among the levels are not clearly modeled. To prevent ecological fallacy, researchers with no individual data can model first what is occurring at the individual level, then model how the individual and group levels are related, and finally examine whether anything occurring at the group level adds to the understanding of the relationship. For instance, in evaluating the impact of state policies, it is helpful to know that policy impacts vary less among the states than do the policies themselves, suggesting that the policy differences are not well translated into results, despite high ecological correlations (Rose, 1973).

Group and total averages

Ecological fallacy can also refer to the following fallacy: the average for a group is approximated by the average in the total population divided by the group size. Suppose one knows the number of Protestants and the suicide rate in the USA, but one does not have data linking religion and suicide at the individual level. If one is interested in the suicide rate of Protestants, it is a mistake to estimate it by the total suicide rate divided by the number of Protestants. Formally, denote $P[{\text{Suicide}}|{\text{Protestant}}]$ the mean of the group, we generally have:

{\begin{aligned}P[{\text{Suicide}}|{\text{Protestant}}]\neq {\frac {P[{\text{Suicide}}]}{P({\text{Protestant}})}}\\\end{aligned}}

However, the law of total expectation gives

{\begin{aligned}P[{\text{Suicide}}]={\color {Blue}P[{\text{Suicide}}|{\text{Protestant}}]}P({\text{Protestant}})+{\color {Blue}P[{\text{Suicide}}|{\text{Not Protestant}}]}(1-P({\text{Protestant}}))\\\end{aligned}}

As we know that $P[{\text{Suicide}}|{\text{Not Protestant}}]$ is between 0 and 1, this equation gives a bound for $P[{\text{Suicide}}|{\text{Protestant}}]$ .

Simpson's paradox

A striking ecological fallacy is Simpson's paradox. Simpson's paradox refers to the fact, when comparing two populations divided in groups of different sizes, the average of some variable in the first population can be higher in every group and yet lower in the total population. Formally, when each value of Z refers to a different group and X refers to some treatment, it can happen that

E[Y|Z=z,X=1]>E[Y|Z=z,X=0]{\text{for all }}z,{\text{ while }}E[Y|X=1]<E[Y|X=0]

When $E[Y|Z=z,X=1]-E[Y|Z=z,X=0]$ does not depend on $Z$ , the Simpson's paradox is exactly the omitted variable bias for the regression of $Y$ on $X$ where the regressor $X$ is a dummy variable and the omitted variable $Z$ is a categorical variable defining groups for each value it takes. The application is striking because the bias is high enough that parameters have opposite signs.

Mean and median

A third example of ecological fallacy is when the average of a population is assumed to have an interpretation in term of likelihood at the individual level.

For instance, if the average score of group A is larger than zero, it does not mean that a random individual of group A is more likely to have a positive score. Similarly, if a particular group of people is measured to have a lower average IQ than the general population, it is an error to conclude that a randomly selected member of the group is more likely to have a lower IQ than the average general population. Mathematically, this comes from the fact that a distribution can have a positive mean but a negative median. This property is linked to the skewness of the distribution.

Consider the following numerical example:

Group A: 80% of people got 40 points and 20% of them got 95 points. The average score is 51 points.
Group B: 50% of people got 45 points and 50% got 55 points. The average score is 50 points.
If we pick two people at random from A and B, there are 4 possible outcomes:
- A - 40, B - 45 (B wins, 40% probability)
- A - 40, B - 55 (B wins, 40% probability)
- A - 95, B - 45 (A wins, 10% probability)
- A - 95, B - 55 (A wins, 10% probability)
Although Group A has a higher average score, 80% of the time a random individual of A will score lower than a random individual of B.

Legal applications

The ecological fallacy was discussed in a court challenge to the Washington gubernatorial election, 2004 in which a number of illegal voters were identified, after the election; their votes were unknown, because the vote was by secret ballot. The challengers argued that illegal votes cast in the election would have followed the voting patterns of the precincts in which they had been cast, and thus adjustments should be made accordingly.^[7] An expert witness said this approach was like trying to figure out Ichiro Suzuki's batting average by looking at the batting average of the entire Seattle Mariners team, since the illegal votes were cast by an unrepresentative sample of each precinct's voters, and might be as different from the average voter in the precinct as Ichiro was from the rest of his team.^[8] The judge determined that the challengers' argument was an ecological fallacy, and rejected it.^[9]

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ Freedman, David A. 2002. The Ecological Fallacy. University of California. [1]
↑ H. C. Selvin. 1965. "Durkheim's Suicide:Further Thoughts on a Methodological Classic", in R. A. Nisbet (ed.) Émile Durkheim pp. 113-136
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ The research note on this curious data glitch is published in the International Journal for Epidemiology (http://ije.oxfordjournals.org/content/early/2011/05/24/ije.dyr081.full%20). The data Robinson used and the corrections are available at http://www.ru.nl/mt/rob/downloads/
↑ Template:Cite news
↑ Christopher Adolph (May 12, 2005). "Report on the 2004 Washington Gubernatorial Election". Expert witness report to the Chelan County Superior Court in Borders et al v. King County et al.
↑ Borders et al. v. King County et al., transcript of the decision by Chelan County Superior Court Judge John Bridges, June 6, 2005, published: June 8, 2005

[1] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[2] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[3] Freedman, David A. 2002. The Ecological Fallacy. University of California. [1]

[4] H. C. Selvin. 1965. "Durkheim's Suicide:Further Thoughts on a Methodological Classic", in R. A. Nisbet (ed.) Émile Durkheim pp. 113-136

[5] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[6] The research note on this curious data glitch is published in the International Journal for Epidemiology (http://ije.oxfordjournals.org/content/early/2011/05/24/ije.dyr081.full%20). The data Robinson used and the corrections are available at http://www.ru.nl/mt/rob/downloads/

[7] Template:Cite news

[8] Christopher Adolph (May 12, 2005). "Report on the 2004 Washington Gubernatorial Election". Expert witness report to the Chelan County Superior Court in Borders et al v. King County et al.

[9] Borders et al. v. King County et al., transcript of the decision by Chelan County Superior Court Judge John Bridges, June 6, 2005, published: June 8, 2005

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

@@ Line 1: / Line 1: @@
+{{technical|date=October 2013}}
+An '''ecological fallacy''' (or '''ecological ''inference'' fallacy''')<ref>{{cite book |isbn=978-0-7914-5015-4 |title=Culture, technology, communication: towards an intercultural global village |author=Charles Ess |author2=Fay Sudweeks |publisher=SUNY Press |year=2001 |page=90 |quote=The problem lies with the 'ecological fallacy' (or fallacy of division)—the impulse to apply group or societal level characteristics onto individuals within that group.}}</ref> is a [[Informal fallacy|logical fallacy]] in the interpretation of [[statistic]]al data where [[inference]]s about the nature of individuals are deduced from inference for the group to which those individuals belong.  Ecological fallacy  sometimes refers to the [[fallacy of division]] which is not a statistical issue. The four common statistical ecological fallacies are:  confusion between ecological correlations and individual correlations, confusion between group average and total average, [[Simpson's paradox]], and confusion between higher average and higher likelihood.
+== Correlation of groups and individuals ==
+Ecological fallacy can refer to the following statistical fallacy: the correlation between individual variables is deduced from the correlation of the variables collected for the group to which those individuals belong.
-Prior to invest loads of money things like controls actually memory cards, appear on-line for a secondhand deviation. Occasionally a store will probably be out of used-game hardware, which could be very economical. Make sure you look which has a web-based seller's feedback prior to making the purchase so you know whether you are procuring what you covered.<br><br>Video games are fun to practice with your kids. Aid you learn much more info on your kid's interests. Sharing interests with your kids like this can will also create great conversations. It also gives an opportunity to monitor growth and development of their skills.<br><br>Nevertheless, if you want to stop at the top of one's competitors, there are several simple points you want to keep in mind.  If you have any type of concerns pertaining to where and the best ways to make use of clash of clans hack cydia ([http://circuspartypanama.com read what he said]), you can contact us at our own internet site. Realize your foe, grasp the game and the win will be yours. It is possible try the aid of clash of clans hack tools and second rights if you similar your course. So that for your convenience, here i list the general details in this particular sport that you must have to remember of. As a result of all of them precisely!<br><br>Principally clash of clans identify tool no survey plots believe in among a new people. Society is almost certainly definitely powered by professional pressure, one of the most powerful forces about the planet. As long as peer blood pressure utilizes its power for good, clash of clans hack tool no stare at will have its place in community.<br><br>Unquestionably the aboriginal phase, Alertness Moment is back your [http://www.romantic.com romantic] relationship prepares their own defenses, gathers admonition about your family enemy, and starts delivering extramarital liasons of episode. During this appearance there isnrrrt any attacking. Instead, there are three big activities during alertness wedding day time: rearranging your battle starting, altruistic accretion defense force in your association mates, and aloof adversary warfare bases.<br><br>It is difficult to select the required xbox game gaming multilevel. In the beginning, you should consider your standard requirements being a video game player, following check out the extras made available from together unit you are considering. Consider investigating on-line. Check testimonials to ascertain if more gamers have discovered problems with the unit. For you to buying a game process, you should know nearly everything you are able to actually regarding it.<br><br>Think about to restrain your heavy gaming to only one kind of machine. Buying all the key consoles plus a gaming-worthy personal computer can [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=charges&Submit=Go charges] up to thousands, undoubtedly in hardware. Yet, most big titles definitely will be available on almost all of them. Choose one platform in which to stick with for economic.
+=== Examples ===
+Assume that at the individual level,  being Protestant impacts negatively one's tendency to commit suicide but the probability that one's neighbor commits suicide increases one's tendency to become Protestant. Then, even if at the individual level there is negative correlation between suicidal tendencies and Protestantism, there can be a positive correlation at the aggregate level.
+Similarly, even if at the individual level, wealth is positively correlated to tendency to vote Republican, we observe that wealthier states tend to vote Democrat. For example, in 2004, the Republican candidate, [[George W. Bush]], won the fifteen poorest states, and the Democratic candidate, [[John Kerry]], won 9 of the 11 wealthiest states. Yet 62% of voters with annual incomes over $200,000 voted for Bush, but only 36% of voters with annual incomes of $15,000 or less voted for Bush.<ref>{{cite book | last1=Gelman | first1=Andrew | last2=Park | first2=David | last3=Shor | first3=Boris | last4=Bafumi | first4=Joseph | last5=Cortina | first5=Jeronimo | title=Red State, Blue State, Rich State, Poor State | publisher=Princeton University Press | year=2008| isbn=978-0-691-13927-2 | authorlink1=Andrew Gelman}}</ref>
+=== Formal problem ===
+The correlation of aggregate quantities (or [[Ecological Correlation|ecological correlation]]) is not equal to the correlation of individual quantities.
+Denote  <math>X_i,Y_i  </math> two quantities at the individual level. The formula for the covariance of the aggregate quantities in groups of size N is
+:<math>cov\left( \sum_{jN+1}^{(j+1)N} Y_i, \sum_1^N X_i\right)= \sum_{1}^{N} cov(Y_{jN+i},X_i)+ \sum_{i\neq l} cov(Y_{jN+l},X_i)</math>
+The covariance of  two aggregated variables depends not only the covariance of two variables within the same individuals but also of covariances of the variables between different individuals. In other words, correlation of aggregate variables take into account cross sectional effects which are not relevant at the individual level.
+The problem for correlations entails naturally a problem for regressions on aggregate variables: the correlation fallacy is therefore an important issue for a researcher who wants to measure causal impacts. Start with a regression model where the  outcome  <math>Y_i </math> is impacted by  <math>X_i </math>
+:<math> Y_i=\alpha+\beta X_i+u_i , </math>
+:<math> cov[u_i,X_i]=0  .</math>
+The regression model at the aggregate level is obtained by summing the individual equations:
+:<math> \sum_{jN+1}^{(j+1)N} Y_i=\alpha+ \beta \sum_{jN+1}^{(j+1)N} X_i+ \sum_{jN+1}^{(j+1)N} u_i ,</math>
+:<math> cov\left[\sum_{jN+1}^{(j+1)N}  u_i,\sum_{k=jN+1}^{(j+1)N} X_k\right]\neq 0 .</math>
+Nothing prevents the regressors and the errors from being correlated at the aggregate level. Therefore, generally, running a regression on aggregate data does not estimate the same model  than running a regression with individual data.
+The aggregate model is correct if and only if
+:<math>  cov\left[u_i,\sum_{k=jN+1}^{(j+1)N} X_k\right]= 0 \quad \text{ for all } i. </math>
+This means that, controlling for <math>X_i </math>, <math>\sum_{jN+1}^{(j+1)N} X_k</math> does not determine <math>Y_i</math>. Going back to the religion example, the aggregate model correctly measures Protestants' tendency to commit suicide if and only, inside each religion, one's tendency to commit suicide is not determined by the number of Protestants  in one's state.
+=== Historical examples of the fallacy ===
+An early example of the ecological fallacy was [[Émile Durkheim#Suicide|Émile Durkheim]]'s 1897 [[Suicide (book)|study of suicide]] in France although this has been debated by some.<ref>Freedman, David A. 2002. ''The Ecological Fallacy''. University of California. [http://www.stat.berkeley.edu/~census/ecofall.txt]</ref><ref>H. C. Selvin. 1965. "Durkheim's Suicide:Further Thoughts on a Methodological Classic", in R. A. Nisbet (ed.) ''Émile Durkheim'' pp. 113-136</ref>
+Another example is a 1950 paper by William S. Robinson that coined the term.<ref>{{cite journal|author=Robinson, W.S.|year=1950|title=Ecological Correlations and the Behavior of Individuals|journal=American Sociological Review|volume=15|pages=351–357|doi=10.2307/2087176|jstor=2087176|issue=3|publisher=American Sociological Review, Vol. 15, No. 3}}</ref> For each of the 48 states + District of Columbia in the US as of the [[U.S. Census|1930 census]], he computed the illiteracy rate and the proportion of the population born outside the US. He showed that these two figures were associated with a negative correlation of −0.53&nbsp;— in other words, the greater the proportion of immigrants in a state, the lower its average illiteracy. However, when individuals are considered, the correlation was +0.12 — immigrants were on average more illiterate than native citizens. Robinson showed that the negative correlation at the level of state populations was because immigrants tended to settle in states where the native population was more literate. He cautioned against deducing conclusions about individuals on the basis of population-level, or "ecological" data. In 2011, it was found that Robinson's calculations of the ecological correlations are based on the wrong state level data. The correlation of −0.53 mentioned above is in fact −0.46.<ref>The research note on this curious data glitch is published in the International Journal for Epidemiology (http://ije.oxfordjournals.org/content/early/2011/05/24/ije.dyr081.full%20). The data Robinson used and the corrections are available at
+http://www.ru.nl/mt/rob/downloads/</ref> Robinson's paper was seminal, but the term 'ecological fallacy' was not coined until 1958 by Selvin.
+=== Choosing between aggregate and individual inference ===
+There is nothing wrong in running regressions on aggregate data if one is interested in the aggregate model. For instance, as a governor, it is correct to run regressions between police force on crime rate at the state level if one is interested in the policy implication of a rise in police force. However, an ecological fallacy would happen if a city council deduces the impact of an increase in police force in the crime rate at the city level from the correlation at the state level.
+Choosing to run aggregate or individual regressions to understand aggregate impacts on some policy depends on the following trade off: aggregate regressions lose individual level data but individual regressions add strong modeling assumptions.   Some researchers suggest that the ecological correlation gives a better picture of the outcome of public policy actions, thus they recommend the ecological correlation over the individual level correlation for this purpose (Lubinski & Humphreys, 1996).  Other researchers disagree, especially when the relationships among the levels are not clearly modeled. To prevent ecological fallacy, researchers with no individual data can model first what is occurring at the individual level, then model how the individual and group levels are related, and finally examine whether anything occurring at the group level adds to the understanding of the relationship.  For instance, in evaluating the impact of state policies, it is helpful to know that policy impacts vary less among the states than do the policies themselves, suggesting that the policy differences are not well translated into results, despite high ecological correlations (Rose, 1973).
+== Group and total averages ==
+Ecological fallacy can also refer to the following fallacy: the average for a group is approximated by the average in the total population divided by the group size.  Suppose one knows the number of Protestants and the suicide rate in the USA, but one does not have data linking religion and suicide at the individual level. If one is interested in the suicide rate of Protestants, it is a mistake to estimate it by the total suicide rate divided by the number of Protestants.
+Formally, denote <math> P[\text{Suicide}|\text{Protestant}]</math> the mean of the group, we generally have:
+:<math>
+\begin{align}
+P[\text{Suicide}|\text{Protestant}] \neq \frac{P[\text{Suicide}]}{P(\text{Protestant})}\\
+\end{align}
+</math>
+However, the [[law of total expectation]] gives
+:<math>
+\begin{align}
+P[\text{Suicide}]= {\color{Blue}P[\text{Suicide}|\text{Protestant}]} P(\text{Protestant})+ {\color{Blue}P[\text{Suicide}|\text{Not Protestant}]}(1-P(\text{Protestant}))\\
+\end{align}
+</math>
+As we know that <math> P[\text{Suicide}|\text{Not Protestant}]</math> is between 0 and 1, this equation gives a bound for <math> P[\text{Suicide}|\text{Protestant}]</math>.
+== Simpson's paradox ==
+A striking ecological fallacy is [[Simpson's paradox]]. Simpson's paradox refers to the fact, when comparing two populations divided in groups of different sizes, the average of some variable in the first population can be higher in every group and yet lower in the total population.  Formally,  when each value of Z refers to a different group and X refers to some treatment, it can happen that
+:<math>
+ 	E[Y|Z=z, X=1]> E[Y|Z=z,X=0] \text{for all } z, \text{ while } 	E[Y|X=1]< E[Y|X=0]
+</math>
+When <math>E[Y|Z=z, X=1]-E[Y|Z=z,X=0]</math>  does not depend on <math> Z</math>, the Simpson's paradox is exactly the [[Omitted-variable bias|omitted variable bias]] for the regression of <math> Y</math> on <math> X</math> where the regressor <math> X</math> is a [[Dummy variable (statistics)|dummy variable]] and the omitted variable <math> Z</math> is a [[categorical variable]]  defining groups for each value it takes. The application is striking because the bias is high enough that parameters have opposite signs.
+== Mean and median ==
+A third example of ecological fallacy is when the average of a population is assumed to have an interpretation in term of likelihood at the individual level.
+For instance, if the average score of group A is larger than zero, it does not mean that a random individual of group A is more likely to have a positive score. Similarly, if a particular group of people is measured to have a lower average IQ than the general population, it is an error to conclude that a randomly selected member of the group is more likely to have a lower IQ than the average general population. Mathematically, this comes from the fact that a distribution can have a positive mean but a negative median. This property is linked to the [[skewness]] of the distribution.
+Consider the following numerical example:
+* Group A: 80% of people got 40 points and 20% of them got 95 points. The average score is 51 points.
+* Group B: 50% of people got 45 points and 50% got 55 points. The average score is 50 points.
+* If we pick two people at random from A and B, there are 4 possible outcomes:
+** A - 40, B - 45 (B wins, 40% probability)
+** A - 40, B - 55 (B wins, 40% probability)
+** A - 95, B - 45 (A wins, 10% probability)
+** A - 95, B - 55 (A wins, 10% probability)
+* Although Group A has a higher average score, 80% of the time a random individual of A will score lower than a random individual of B.
+== Legal applications ==
+The ecological fallacy was discussed in a court challenge to the [[Washington gubernatorial election, 2004]] in which a number of illegal voters were identified, after the election; their votes were unknown, because the vote was by [[secret ballot]]. The challengers argued that illegal votes cast in the election would have followed the voting patterns of the precincts in which they had been cast, and thus adjustments should be made accordingly.<ref>{{cite news |title=The Monkey Wrench Trial: Dino Rossi's challenge of the 2004 election is on shaky legal ground. But if he prevails, watch litigation become an option in close races everywhere |author=George Howland Jr. |date= May 18, 2005 |work=Seattle Weekly |url=http://www.seattleweekly.com/features/0520/050518_news_election.php }}</ref> An expert witness said this approach was like trying to figure out [[Ichiro Suzuki]]'s batting average by looking at the batting average of the entire [[Seattle Mariners]] team, since the illegal votes were cast by an unrepresentative sample of each precinct's voters, and might be as different from the average voter in the precinct as Ichiro was from the rest of his team.<ref>Christopher Adolph (May 12, 2005). [http://faculty.washington.edu/cadolph/papers/AdolphWAreport.pdf "Report on the 2004 Washington Gubernatorial Election"].  Expert witness report to the Chelan County Superior Court in Borders et al v. King County et al.</ref> The judge determined that the challengers' argument was an ecological fallacy, and rejected it.<ref>[http://www.seattleweekly.com/content/printVersion/165891 Borders et al. v. King County et al.], transcript of the decision by [[Chelan County, Washington|Chelan County]] Superior Court Judge John Bridges, June 6, 2005, published: June 8, 2005</ref>
+== See also ==
+{{Div col|2}}
+;Correlation Fallacy
+* [[Complete spatial randomness]]
+* [[Ecological regression]]
+* [[Modifiable areal unit problem]]
+* [[Spatial autocorrelation]]
+* [[Spatial epidemiology]]
+* [[Spatial econometrics]]
+; Simpson's paradox
+*[[Simpson's paradox]]
+*[[Statistical discrimination]]
+{{Div col end}}
+== Notes ==
+{{Reflist|colwidth=40em}}
+== References ==
+*{{cite journal |last=Lubinski |first=D. |last2=Humphreys |first2=L. G. |year=1996 |title=Seeing the forest from the trees: When predicting the behavior or status of groups, correlate means |journal=Psychology, Public Policy, and Law |volume=2 |issue=2 |pages=363–376 |doi=10.1037/1076-8971.2.2.363 }}
+*{{cite journal |last=Rose |first=D. D. |year=1973 |title=National and local forces in state politics: The implications of multi-level policy analysis |journal=[[American Political Science Review]] |volume=67 |issue=4 |pages=1162–1173 |jstor=1956538 }}
+[[Category:Misuse of statistics]]
+[[Category:Logical fallacies]]

De Boor's algorithm: Difference between revisions

Revision as of 10:33, 16 January 2014

Contents

Correlation of groups and individuals

Examples

Formal problem

Historical examples of the fallacy

Choosing between aggregate and individual inference

Group and total averages

Simpson's paradox

Mean and median

Legal applications

See also

Notes

References

Navigation menu

De Boor's algorithm: Difference between revisions

Revision as of 10:33, 16 January 2014

Correlation of groups and individuals

Examples

Formal problem

Historical examples of the fallacy

Choosing between aggregate and individual inference

Group and total averages

Simpson's paradox

Mean and median

Legal applications

See also

Notes

References

Navigation menu

Search