Electronics and Radar Development Establishment: Difference between revisions

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Template:More footnotes In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to the experimenter. An example of a blocking factor might be the sex of a patient; by blocking on sex, this source of variability is controlled for, thus leading to greater accuracy.

Blocking to "remove" the effect of nuisance factors

For randomized block designs, there is one factor or variable that is of primary interest. However, there are also several other nuisance factors.

Nuisance factors are those that may affect the measured result, but are not of primary interest. For example, in applying a treatment, nuisance factors might be the specific operator who prepared the treatment, the time of day the experiment was run, and the room temperature. All experiments have nuisance factors. The experimenter will typically need to spend some time deciding which nuisance factors are important enough to keep track of or control, if possible, during the experiment.

Blocking used for nuisance factors that can be controlled

When we can control nuisance factors, an important technique known as blocking can be used to reduce or eliminate the contribution to experimental error contributed by nuisance factors. The basic concept is to create homogeneous blocks in which the nuisance factors are held constant and the factor of interest is allowed to vary. Within blocks, it is possible to assess the effect of different levels of the factor of interest without having to worry about variations due to changes of the block factors, which are accounted for in the analysis.

Definition of blocking factors

A nuisance factor is used as a blocking factor if every level of the primary factor occurs the same number of times with each level of the nuisance factor. The analysis of the experiment will focus on the effect of varying levels of the primary factor within each block of the experiment.

Block for a few of the most important nuisance factors

The general rule is:

"Block what you can; randomize what you cannot."

Blocking is used to remove the effects of a few of the most important nuisance variables. Randomization is then used to reduce the contaminating effects of the remaining nuisance variables.

Table of randomized block designs

One useful way to look at a randomized block experiment is to consider it as a collection of completely randomized experiments, each run within one of the blocks of the total experiment.

Randomized Block Designs (RBD)
Name of Design	Number of Factors k	Number of Runs n
2-factor RBD	2	L₁ * L₂
3-factor RBD	3	L₁ * L₂ * L₃
4-factor RBD	4	L₁ * L₂ * L₃ * L₄
$\vdots$	$\vdots$	$\vdots$
k-factor RBD	k	L₁ * L₂ * $\cdots$ * L_k

with

L₁ = number of levels (settings) of factor 1

L₂ = number of levels (settings) of factor 2

L₃ = number of levels (settings) of factor 3

L₄ = number of levels (settings) of factor 4

\vdots

L_k = number of levels (settings) of factor k

Example of a Randomized Block Design

Suppose engineers at a semiconductor manufacturing facility want to test whether different wafer implant material dosages have a significant effect on resistivity measurements after a diffusion process taking place in a furnace. They have four different dosages they want to try and enough experimental wafers from the same lot to run three wafers at each of the dosages.

The nuisance factor they are concerned with is "furnace run" since it is known that each furnace run differs from the last and impacts many process parameters.

An ideal way to run this experiment would be to run all the 4x3=12 wafers in the same furnace run. That would eliminate the nuisance furnace factor completely. However, regular production wafers have furnace priority, and only a few experimental wafers are allowed into any furnace run at the same time.

A non-blocked way to run this experiment would be to run each of the twelve experimental wafers, in random order, one per furnace run. That would increase the experimental error of each resistivity measurement by the run-to-run furnace variability and make it more difficult to study the effects of the different dosages. The blocked way to run this experiment, assuming you can convince manufacturing to let you put four experimental wafers in a furnace run, would be to put four wafers with different dosages in each of three furnace runs. The only randomization would be choosing which of the three wafers with dosage 1 would go into furnace run 1, and similarly for the wafers with dosages 2, 3 and 4.

Description of the experiment

HMLet X₁ be dosage "level" and X₂ be the blocking factor furnace run. Then the experiment can be described as follows:

k = 2 factors (1 primary factor X₁ and 1 blocking factor X₂)

L₁ = 4 levels of factor X₁

L₂ = 3 levels of factor X₂

n = 1 replication per cell

N = L₁ * L₂ = 4 * 3 = 12 runs

Before randomization, the design trials look like:

X₁	X₂
1	1
1	2
1	3
2	1
2	2
2	3
3	1
3	2
3	3
4	1
4	2
4	3

Matrix Representation

An alternate way of summarizing the design trials would be to use a 4x3 matrix whose 4 rows are the levels of the treatment X₁ and whose columns are the 3 levels of the blocking variable X₂. The cells in the matrix have indices that match the X₁, X₂ combinations above.

By extension, note that the trials for any K-factor randomized block design are simply the cell indices of a k dimensional matrix.

Model for a Randomized Block Design

The model for a randomized block design with one nuisance variable is

Y_{ij}=\mu +T_{i}+B_{j}+\mathrm {random\ error}

where

Y_ij is any observation for which X₁ = i and X₂ = j

X₁ is the primary factor

X₂ is the blocking factor

μ is the general location parameter (i.e., the mean)

T_i is the effect for being in treatment i (of factor X₁)

B_j is the effect for being in block j (of factor X₂)

Estimates for a Randomized Block Design

Estimate for μ :

{\overline {Y}}

= the average of all the data

Estimate for T_i :

{\overline {Y}}_{i}-{\overline {Y}}

with

{\overline {Y}}_{i}

= average of all Y for which X₁ = i.

Estimate for B_j :

{\overline {Y}}_{j}-{\overline {Y}}

with

{\overline {Y}}_{j}

= average of all Y for which X₂ = j.

Generalizations of randomized block designs

Generalized randomized block designs (GRBD) allow tests of block-treatment interaction, and has exactly one blocking factor like the RCBD.
Latin squares (and other row-column designs) have two blocking factors that are believed to have no interaction.
Latin hypercube sampling
Graeco-Latin squares
Hyper-Graeco-Latin square designs

External links

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

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 | mr = 30181

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 Pre-publication chapters are available on-line.

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

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

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
- 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

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
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
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

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

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Electronics and Radar Development Establishment: Difference between revisions

Revision as of 12:29, 4 June 2013

Contents

Blocking to "remove" the effect of nuisance factors

Blocking used for nuisance factors that can be controlled

Definition of blocking factors

Block for a few of the most important nuisance factors

Table of randomized block designs

Example of a Randomized Block Design

Description of the experiment

Matrix Representation

Model for a Randomized Block Design

Estimates for a Randomized Block Design

Generalizations of randomized block designs

See also

External links

References

Navigation menu

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+{{more footnotes|date=January 2013}}
+In the [[statistical]] theory of the [[design of experiments]], [[blocking (statistics)|blocking]] is the arranging of [[experimental unit]]s in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of [[statistical dispersion|variability]] that is not of primary interest to the experimenter. An example of a blocking factor might be the sex of a patient; by blocking on sex, this source of variability is controlled for, thus leading to greater accuracy.
+==Blocking to "remove" the effect of nuisance factors==
+For randomized block designs, there is one factor or variable that is of primary interest. However, there are also several other [[nuisance variable|nuisance factors]].
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+Nuisance factors are those that may affect the measured result, but are not of primary interest. For example, in applying a treatment, nuisance factors might be the specific operator who prepared the treatment, the time of day the experiment was run, and the room temperature. All experiments have nuisance factors. The experimenter will typically need to spend some time deciding which nuisance factors are important enough to keep track of or control, if possible, during the experiment.
+==Blocking used for nuisance factors that can be controlled==
+When we can control nuisance factors, an important technique known as blocking can be used to reduce or eliminate the contribution to experimental error contributed by nuisance factors. The basic concept is to create homogeneous blocks in which the nuisance factors are held constant and the factor of interest is allowed to vary. Within blocks, it is possible to assess the effect of different levels of the factor of interest without having to worry about variations due to changes of the block factors, which are accounted for in the analysis.
+==Definition of blocking factors==
+A nuisance factor is used as a blocking factor if every level of the primary factor occurs the same number of times with each level of the nuisance factor. The analysis of the experiment will focus on the effect of varying levels of the primary factor within each block of the experiment.
+==Block for a few of the most important nuisance factors==
+The general rule is:
+:"Block what you can; randomize what you cannot."
+Blocking is used to remove the effects of a few of the most important nuisance variables. Randomization is then used to reduce the contaminating effects of the remaining nuisance variables.
+==Table of randomized block designs==
+One useful way to look at a randomized block experiment is to consider it as a collection of [[completely randomized design|completely randomized]] experiments, each run within one of the blocks of the total experiment.
+{| class="wikitable"
+|+ Randomized Block Designs (RBD)
+|-
+! Name of Design
+! Number of Factors ''k''
+! Number of Runs ''n''
+|-
+| 2-factor RBD
+| 2
+| ''L''<sub>1</sub> * ''L''<sub>2</sub>
+|-
+| 3-factor RBD
+| 3
+| ''L''<sub>1</sub> * ''L''<sub>2</sub> * ''L''<sub>3</sub>
+|-
+| 4-factor RBD
+| 4
+| ''L''<sub>1</sub> * ''L''<sub>2</sub> * ''L''<sub>3</sub> * ''L''<sub>4</sub>
+|-
+| <math>\vdots</math>
+| <math>\vdots</math>
+| <math>\vdots</math>
+|-
+| ''k''-factor RBD
+| ''k''
+| ''L''<sub>1</sub> * ''L''<sub>2</sub> * <math>\cdots</math> * ''L<sub>k</sub>''
+|}
+with
+:''L''<sub>1</sub> = number of levels (settings) of factor 1
+:''L''<sub>2</sub> = number of levels (settings) of factor 2
+:''L''<sub>3</sub> = number of levels (settings) of factor 3
+:''L''<sub>4</sub> = number of levels (settings) of factor 4
+::<math>\vdots</math>
+:''L<sub>k</sub>'' = number of levels (settings) of factor ''k''
+==Example of a Randomized Block Design==
+Suppose engineers at a semiconductor manufacturing facility want to test whether different wafer implant material dosages have a significant effect on resistivity measurements after a diffusion process taking place in a furnace. They have four different dosages they want to try and enough experimental wafers from the same lot to run three wafers at each of the dosages.
+The nuisance factor they are concerned with is "furnace run" since it is known that each furnace run differs from the last and impacts many process parameters.
+An ideal way to run this experiment would be to run all the 4x3=12 wafers in the same furnace run. That would eliminate the nuisance furnace factor completely. However, regular production wafers have furnace priority, and only a few experimental wafers are allowed into any furnace run at the same time.
+A non-blocked way to run this experiment would be to run each of the twelve experimental wafers, in random order, one per furnace run. That would increase the experimental error of each resistivity measurement by the run-to-run furnace variability and make it more difficult to study the effects of the different dosages. The blocked way to run this experiment, assuming you can convince manufacturing to let you put four experimental wafers in a furnace run, would be to put four wafers with different dosages in each of three furnace runs. The only randomization would be choosing which of the three wafers with dosage 1 would go into furnace run 1, and similarly for the wafers with dosages 2, 3 and 4.
+===Description of the experiment===
+HMLet ''X''<sub>1</sub> be dosage "level" and ''X''<sub>2</sub> be the blocking factor furnace run. Then the experiment can be described as follows:
+:''k'' = 2 factors (1 primary factor ''X''<sub>1</sub> and 1 blocking factor ''X''<sub>2</sub>)
+:''L''<sub>1</sub> = 4 levels of factor ''X''<sub>1</sub>
+:''L''<sub>2</sub> = 3 levels of factor ''X''<sub>2</sub>
+:''n'' = 1 replication per cell
+:''N'' = ''L''<sub>1</sub> * ''L''<sub>2</sub> = 4 * 3 = 12 runs
+Before randomization, the design trials look like:
+{| class="wikitable"
+|-
+! ''X''<sub>1</sub>
+! ''X''<sub>2</sub>
+|-
+| 1
+| 1
+|-
+| 1
+| 2
+|-
+| 1
+| 3
+|-
+| 2
+| 1
+|-
+| 2
+| 2
+|-
+| 2
+| 3
+|-
+| 3
+| 1
+|-
+| 3
+| 2
+|-
+| 3
+| 3
+|-
+| 4
+| 1
+|-
+| 4
+| 2
+|-
+| 4
+| 3
+|}
+===Matrix Representation===
+An alternate way of summarizing the design trials would be to use a 4x3 matrix whose 4 rows are the levels of the treatment ''X''<sub>1</sub> and whose columns are the 3 levels of the blocking variable ''X''<sub>2</sub>. The cells in the matrix have indices that match the ''X''<sub>1</sub>, ''X''<sub>2</sub> combinations above.
+By extension, note that the trials for any K-factor randomized block design are simply the cell indices of a ''k'' dimensional matrix.
+==Model for a Randomized Block Design==
+The model for a randomized block design with one nuisance variable is
+:<math>
+Y_{ij} = \mu + T_i + B_j + \mathrm{random\ error}
+</math>
+where
+:''Y''<sub>ij</sub> is any observation for which ''X''<sub>1</sub> = ''i'' and ''X''<sub>2</sub> = ''j''
+:''X''<sub>1</sub> is the primary factor
+:''X''<sub>2</sub> is the blocking factor
+:&mu; is the general location parameter (i.e., the mean)
+:''T''<sub>i</sub> is the effect for being in treatment ''i'' (of factor ''X''<sub>1</sub>)
+:''B''<sub>j</sub> is the effect for being in block ''j'' (of factor ''X''<sub>2</sub>)
+==Estimates for a Randomized Block Design==
+:Estimate for &mu; : <math>\overline{Y}</math> = the average of all the data
+:Estimate for ''T''<sub>i</sub> : <math>\overline{Y}_i - \overline{Y}</math> with <math>\overline{Y}_i</math> = average of all ''Y'' for which ''X''<sub>1</sub> = ''i''.
+:Estimate for ''B''<sub>j</sub> : <math>\overline{Y}_j - \overline{Y}</math> with <math>\overline{Y}_j</math> = average of all ''Y'' for which ''X''<sub>2</sub> = ''j''.
+==Generalizations of randomized block designs==
+* [[Generalized randomized block design]]s (GRBD) allow tests of block-treatment interaction, and has exactly one blocking factor like the RCBD.
+* [[Latin square]]s (and other row-column designs) have two blocking factors that are believed to have no interaction.
+* [[Latin hypercube sampling]]
+* [[Graeco-Latin square]]s
+* [[Hyper-Graeco-Latin square design]]s
+==See also==
+* [[Algebraic statistics]]
+* [[Combinatorial design]]
+* [[Generalized randomized block design]]
+* [[Glossary of experimental design]]
+* [[Optimal design]]
+==External links==
+* [http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm  Examples of all ANOVA and ANCOVA models with up to three treatment factors, including randomized block, split plot, repeated measures, and Latin squares, and their analysis in R]
+*[http://www.itl.nist.gov/div898/handbook/pri/section3/pri332.htm Randomized Block Designs]
+==References==
+* {{cite journal
+|doi=10.2307/2681737
+|title=The Generalized Randomized Block Design <!-- |authorlink=Sidney Addelman -->
+|first=Sidney
+|last=Addelman
+|journal=The American Statistician
+|volume=23
+|issue=4
+|date=Oct 1969
+|pages=35–36
+|jstor=2681737
+}}
+* {{cite journal
+|doi=10.2307/2284277
+|title=Variability of Treatments and Experimental Units in the Design and Analysis of Experiments
+|first=Sidney
+|last=Addelman
+|journal=Journal of the American Statistical Association
+|volume=65
+|issue=331
+|date=Sep 1970
+|pages=1095–1108
+|jstor = 2284277
+}}
+* {{cite journal|doi=10.2307/2984159|title=The Validity of Comparative Experiments|authorlink=Francis J. Anscombe|first=F. J.|last=Anscombe|journal=[[Journal of the Royal Statistical Society]]. Series A (General)|volume=111|issue=3|year=1948|pages=181–211|jstor=2984159}} | mr = 30181
+* {{cite book |author=[http://www.maths.qmw.ac.uk/~rab/ Bailey, R. A]|title=Design of Comparative Experiments|url=http://www.maths.qmul.ac.uk/~rab/DOEbook/|publisher=[http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579 Cambridge University Press]|year=2008 |isbn=978-0-521-68357-9}} Pre-publication chapters are available on-line.
+* {{cite book |author=[http://www.isid.ac.in/~rbb/ Bapat, R. B.]|title=Linear Algebra and Linear Models|url=http://books.google.se/books?id=T5dsExIP3aAC|edition=Second|publisher=[http://www.springer.com/math/algebra/book/978-0-387-98871-9?cm_mmc=Google-_-Book%20Search-_-Springer-_-0 Springer] |year=2000 |isbn=978-0-387-98871-9}}
+* {{cite book
+|author=Caliński, Tadeusz and Kageyama, Sanpei
+|title=Block designs: A Randomization approach, Volume '''I''': Analysis
+|series=Lecture Notes in Statistics
+|volume=150
+|publisher=Springer-Verlag
+|location=New York
+|year=2000
+|isbn=0-387-98578-6
+}}
+* {{cite book
+|author=Caliński, Tadeusz and Kageyama, Sanpei
+|title=Block designs: A Randomization approach, Volume '''II''': Design
+|series=Lecture Notes in Statistics
+|volume=170
+|publisher=Springer-Verlag
+|location=New York
+|year=2003
+|isbn=0-387-95470-8|mr=1994124
+}}
+* {{cite journal
+|doi=10.2307/2684574
+|title=What Really Is Experimental Error in Block Designs?
+|first=Charles E.
+|last=Gates
+|journal=The American Statistician
+|volume=49
+|issue=4
+|date=Nov 1995
+|pages = 362–363
+|jstor = 2684574
+}}
+*{{cite book
+|author=[[Oscar Kempthorne|Kempthorne, Oscar]]
+|year=1979
+|title=The Design and Analysis of Experiments
+|edition=Corrected reprint of (1952) Wiley
+|publisher=Robert E. Krieger
+|isbn=0-88275-105-0
+}}
+*{{cite book
+|author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
+|year=2008
+|title=Design and Analysis of Experiments
+|volume=I and II
+|edition=Second
+|publisher=Wiley
+|isbn=978-0-470-38551-7}}
+**{{cite book
+|author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
+|year=2008
+|title=Design and Analysis of Experiments, Volume I: Introduction to Experimental Design
+|edition=Second
+|publisher=Wiley
+|isbn=978-0-471-72756-9
+}}
+**{{cite book
+|author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
+|year=2005
+|title=Design and Analysis of Experiments, Volume 2: Advanced Experimental Design
+|edition=First
+|publisher=Wiley
+|isbn=978-0-471-55177-5
+}}
+* {{cite book
+|first=Marvin
+|last=Lentner
+|coauthor=Thomas Bishop
+|chapter=The Generalized RCB Design (Chapter 6.13)
+|pages=225–226
+|title=Experimental design and analysis
+|edition=Second
+|publisher=Valley Book Company
+|location=P.O. Box 884, Blacksburg, VA 24063
+|year=1993
+|isbn=0-9616255-2-X
+}}
+* {{cite book
+|title=Constructions and Combinatorial Problems in Design of Experiments
+|author=[[Damaraju Raghavarao|Raghavarao, Damaraju]]
+|location=New York
+|year=1988
+|edition=corrected reprint of the 1971 Wiley
+|publisher=Dover
+|isbn=0-486-65685-3
+}}
+* {{cite book
+|title=Block Designs: Analysis, Combinatorics and Applications
+|author=[[Damaraju Raghavarao|Raghavarao, Damaraju]] and Padgett, L.V.
+|year=2005
+|edition=
+|publisher=World Scientific
+|isbn=981-256-360-1
+}}
+*{{cite book |author=Shah, Kirti R. and Sinha, Bikas K. |title=Theory of [[Optimal design|Optimal Designs]] |series=[http://www.springer.com/series/694 Lecture Notes in Statistics]| volume=54 | publisher=Springer-Verlag | year=1989 | pages=171+viii |isbn=0-387-96991-8 |doi=}}
+*{{cite book
+|author=Street, Anne Penfold and Street, Deborah J.
+|title=Combinatorics of Experimental Design
+|publisher=Oxford U. P. [Clarendon]
+|year=1987
+|pages=400+xiv
+|isbn=0-19-853256-3
+}}
+* {{cite journal
+|title=The Randomization Analysis of a Generalized Randomized Block Design
+|first=M. B.
+|last=Wilk
+|journal=Biometrika
+|volume=42
+|issue=1–2
+|date=June 1955
+|pages=70–79
+| jstor = 2333423
+}}
+* {{cite journal
+|title=Some Consequences of randomization in a Generalization of the Balanced Incomplete Block Design
+|first=George
+|last=Zyskind
+|journal=The Annals of Mathematical Statistics
+|volume=34
+|issue=4
+|date=Dec 1963
+|pages=1569–1581
+|jstor = 2238364
+|doi = 10.1214/aoms/1177703889
+}}
+{{Experimental design|state=expanded}}
+{{Statistics|state=collapsed}}
+{{NIST-PD|state=collapsed}}
+[[Category:Design of experiments]]