Some Business Population Database for two periods of time

Description

This data set corresponds to a random sample of BigLucy. It contains some financial variables of 85296 industrial companies of a city in a particular fiscal year.

Usage

BigLucyT0T1

Format

ID

The identifier of the company. It correspond to an alphanumeric sequence (two letters and three digits)

Ubication

The address of the principal office of the company in the city

Level

The industrial companies are discrimitnated according to the Taxes declared. There are small, medium and big companies

Zone

The city is divided by geoghrafical zones. A company is classified in a particular zone according to its address

Income

The total ammount of a company's earnings (or profit) in the previuos fiscal year. It is calculated by taking revenues and adjusting for the cost of doing business

Employees

The total number of persons working for the company in the previuos fiscal year

Taxes

The total ammount of a company's income Tax

SPAM

Indicates if the company uses the Internet and WEBmail options in order to make self-propaganda.

Segments

The cartographic divisions.

Outgoing

Expenses per year.

Years

Age of the company.

ISO

Indicates whether the company is quality-certified.

ISOYears

Indicates the time company has been certified.

CountyP

Indicates wheter the county is participating in the intervention. That is if the county contains companies that have been certified by ISO

Time

Refers to the time of observation.

Author(s)

Hugo Andres Gutierrez Rojas hugogutierrez@usantotomas.edu.co

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.

Examples

data(Lucy)
attach(Lucy)
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
# The population totals
colSums(estima)
# Some parameters of interest
table(SPAM,Level)
xtabs(Income ~ Level+SPAM)
# Correlations among characteristics of interest
cor(estima)
# Some useful histograms
hist(Income)
hist(Taxes)
hist(Employees)
# Some useful plots
boxplot(Income ~ Level)
barplot(table(Level))
pie(table(SPAM))

Estimated sample Effects of Design (DEFF)

Description

This function returns the estimated design effects for a set of inclusion probabilities and the variables of interest.

Usage

DEFF(y, pik)

Arguments

Details

The design effect is somehow defined to be the ratio between the variance of a complex design and the variance of a simple design. When the design is stratified and the allocation is proportional, this measures reduces to

DEFF_{Kish} = 1 + CV(w)

where w is the set of weights (defined as the inverse of the inclusion probabilities) along the sample, and CV refers to the classical coefficient of variation. Although this measure is #' motivated by a stratified sampling design, it is commonly applied to any kind of survey where sampling weight are unequal. On the other hand, the Spencer's DEFF is motivated by the idea that a set of weights may be efficent even when they vary, and is defined by:

DEFF_{Spencer} = (1 - R^2) * DEFF_{Kish} + \frac{\hat{a}^2}{\hat{\sigma}^2_y} * (DEFF_{Kish} - 1)

where

\hat{\sigma}^2_y = \frac{\sum_s w_k (y_k - \bar{y}_w)^2}{\sum_s w_k}

and \hat{a} is the estimation of the intercept in the following model

y_k = a + b * p_k + e_k

with p_k = \pi_k / n is an standardized sampling weight. Finnaly, R^2 is the R-squared of this model.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas. Valliant, R, et. al. (2013), Practical tools for Design and Weighting Survey Samples. Springer

Examples

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

# The sample size
n <- 400
res <- S.piPS(n, Income)
sam <- res[,1]
# The information about the units in the sample is stored in an object called data
data <- BigLucy[sam,]
attach(data)
names(data)
# Pik.s is the inclusion probability of every single unit in the selected sample
pik <- res[,2]
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
E.piPS(estima,pik)
DEFF(estima,pik)

Intraclass Correlation Coefficient

Description

This function computes the intraclass correlation coefficient.

Usage

ICC(y, cl)

Arguments

Details

The intraclass correlation coefficient is defined as:

\rho = 1- \frac{m}{m-1} \frac{WSS}{TSS}

Where m is the average sample sie of units selected inside each sampled cluster.

Value

The total sum of squares (TSS), the between sum of squqres (BSS), the within sum of squares (WSS) and the intraclass correlation coefficient.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

##########################################
# Almost same mean in each cluster       #
#                                        #
# - Heterogeneity within clusters        #
# - Homogeinity between clusters         #
##########################################

# Population size
N <- 100000
# Number of clusters in the population
NI <- 1000
# Number of elements per cluster
N/NI

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- rep(1:NI, length.out=N)

table(cl)
tapply(y, cl, FUN=mean)
boxplot(y~cl)
rho = ICC(y,cl)$ICC
rho


##########################################
# Very different means per cluster       #
#                                        #
# - Heterogeneity between clusters       #
# - Homogeinity within clusters          #
##########################################

# Population size
N <- 100000
# Number of clusters in the population
NI <- 1000
# Number of elements per cluster
N/NI

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- kronecker(c(1:NI),rep(1,N/NI))

table(cl)
tapply(y, cl, FUN=mean)
boxplot(y~cl)
rho = ICC(y,cl)$ICC
rho

############################
# Example 1 with Lucy data #
############################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
y <- Income
cl <- Zone
ICC(y,cl)

############################
# Example 2 with Lucy data #
############################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
y <- as.double(SPAM)
cl <- Zone
ICC(y,cl)

Statistical power for a hyphotesis testing on a single variance

Description

This function computes the power for a (right tail) test of variance

Usage

b4S2(N, n, S2, S20, K = 0, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)

Arguments

Details

We note that the power is defined as:

1-\Phi(Z_{1-\alpha} - \frac{(D-P)}{\sqrt{\frac{DEFF}{n}(1-\frac{n}{N})(P (1-P))}})

Value

The power of the test.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

b4S2(N = 100000, n = 400, S2 = 120, S20 = 100, K = 0, DEFF = 1)
b4S2(N = 100000, n = 400, S2 = 120, S20 = 100, K = 2, DEFF = 1)
b4S2(N = 100000, n = 400, S2 = 120, S20 = 100, K = 2, DEFF = 2.5, plot = TRUE)

Statistical power for a hyphotesis testing on a double difference of means.

Description

This function computes the power for a (right tail) test of double difference of means

Usage

b4ddm(
  N,
  n,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  D,
  DEFF = 1,
  conf = 0.95,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

We note that the power is defined as:

1-\Phi(Z_{1-\alpha} - \frac{(D - [(\mu_1 - \mu_2) - (\mu_3 - \mu_4)])}{\sqrt{\frac{1}{n}(1-\frac{n}{N})S^2}})

where

S^2 = DEFF (\sigma_1^2 + \sigma_2^2 + \sigma_3^2 + \sigma_4^2

Value

The power of the test.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

b4ddm(N = 100000, n = 400, mu1=50, mu2=55, mu3=50, mu4=55, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D = 7)
b4ddm(N = 100000, n = 400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D = 12, plot = TRUE)
b4ddm(N = 100000, n = 4000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D = 11, DEFF = 2, conf = 0.99, plot = TRUE)

Statistical power for a hyphotesis testing on a difference of proportions

Description

This function computes the power for a (right tail) test of difference of proportions.

Usage

b4ddp(N, n, P1, P2, P3, P4, D, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the power is defined as:

1-\Phi(Z_{1-\alpha} - \frac{(D - [(P_1 - P_2) - (P_3 - P_4)])}{\sqrt{\frac{DEFF}{n}(1-\frac{n}{N})(P_1Q_1+P_2Q_2+P_3Q_3+P_4Q_4)}})

Value

The power of the test.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

b4ddp(N = 10000, n = 400, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D = 0.03)
b4ddp(N = 10000, n = 400, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D = 0.03, plot = TRUE)
b4ddp(N = 10000, n = 4000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, 
D = 0.05, DEFF = 2, conf = 0.99, plot = TRUE)

Statistical power for a hyphotesis testing on a difference of means.

Description

This function computes the power for a (right tail) test of difference of means

Usage

b4dm(N, n, mu1, mu2, sigma1, sigma2, D, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the power is defined as:

1-\Phi(Z_{1-\alpha} - \frac{ (D - (\mu_1 - \mu_2))}{\sqrt{\frac{1}{n}(1-\frac{n}{N})S^2}})

where

S^2 = DEFF (\sigma_1^2 + \sigma_2^2

Value

The power of the test.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

b4dm(N = 100000, n = 400, mu1 = 5, mu2 = 5, sigma1 = 10, sigma2 = 15, D = 5)
b4dm(N = 100000, n = 400, mu1 = 5, mu2 = 5, sigma1 = 10, sigma2 = 15, D = 0.03, plot = TRUE)
b4dm(N = 100000, n = 4000, mu1 = 5, mu2 = 5, sigma1 = 10, sigma2 = 15, 
D = 0.05, DEFF = 2, conf = 0.99, plot = TRUE)

Statistical power for a hyphotesis testing on a difference of proportions

Description

This function computes the power for a (right tail) test of difference of proportions.

Usage

b4dp(N, n, P1, P2, D, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the power is defined as:

1-\Phi(Z_{1-\alpha} - \frac{(D - (P_1 - P_2))}{\sqrt{\frac{DEFF}{n}(1-\frac{n}{N})(P_1Q_1+P_2Q_2)}})

Value

The power of the test.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

b4dp(N = 100000, n = 400, P1 = 0.5, P2 = 0.5, D = 0.03)
b4dp(N = 100000, n = 400, P1 = 0.5, P2 = 0.5, D = 0.03, plot = TRUE)
b4dp(N = 100000, n = 4000, P1 = 0.5, P2 = 0.5, D = 0.05, DEFF = 2, conf = 0.99, plot = TRUE)

Statistical power for a hyphotesis testing on a single mean

Description

This function computes the power for a (right tail) test of means.

Usage

b4m(N, n, mu, sigma, D, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the power is defined as:

1-\Phi(Z_{1-\alpha} - \frac{(D - \mu)}{\sqrt{\frac{1}{n}(1-\frac{n}{N})S^2}})

where

S^2 = DEFF \sigma^2

Value

The power of the test.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

b4m(N = 100000, n = 400, mu = 3, sigma = 1, D = 3.1)
b4m(N = 100000, n = 400, mu = 5, sigma = 10, D = 7, plot = TRUE)
b4m(N = 100000, n = 400, mu = 50, sigma = 100, D = 100, DEFF = 3.4, conf = 0.99, plot = TRUE)

Statistical power for a hyphotesis testing on a single proportion

Description

This function computes the power for a (right tail) test of proportions.

Usage

b4p(N, n, P, D, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the power is defined as:

1-\Phi(Z_{1-\alpha} - \frac{(D-P)}{\sqrt{\frac{DEFF}{n}(1-\frac{n}{N})(P (1-P))}})

Value

The power of the test.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

b4p(N = 100000, n = 400, P = 0.5, D = 0.55)
b4p(N = 100000, n = 400, P = 0.5, D = 0.9, plot = TRUE)
b4p(N = 100000, n = 4000, P = 0.5, D = 0.55, DEFF = 2, conf = 0.99, plot = TRUE)

Statistical errors for the estimation of a single variance

Description

This function computes the cofficient of variation and the margin of error when estimating a single variance under a sample design.

Usage

e4S2(N, n, K = 0, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the coefficient of variation is defined as:

cve = \frac{\sqrt{Var(\hat{S^2})}}{\hat{S^2}}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var(\hat{S^2})}

Value

The coefficient of variation and the margin of error for a predefined sample size.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

e4S2(N=10000, n=400, K = 0)
e4S2(N=10000, n=400, K = 1, DEFF = 2, conf = 0.99)
e4S2(N=10000, n=400, K = 2, DEFF = 2, conf = 0.99, plot=TRUE)

Statistical errors for the estimation of a double difference of means

Description

This function computes the cofficient of variation and the standard error when estimating a double difference of means under a complex sample design.

Usage

e4ddm(
  N,
  n,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  DEFF = 1,
  conf = 0.95,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

We note that the coefficent of variation is defined as:

cve = \frac{\sqrt{Var((\bar{y}_1 - \bar{y}_2)-(\bar{y}_1 - \bar{y}_2))}}{(\bar{y}_1 - \bar{y}_2)-(\bar{y}_3 - \bar{y}_4)}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var((\bar{y}_1 - \bar{y}_2)-(\bar{y}_3 - \bar{y}_4))}

Value

The coefficient of variation and the margin of error for a predefined sample size.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

e4ddm(N=10000, n=400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12)
e4ddm(N=10000, n=400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, plot=TRUE)
e4ddm(N=10000, n=400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, DEFF=3.45, conf=0.99, plot=TRUE)

Statistical errors for the estimation of a double difference of proportions

Description

This function computes the cofficient of variation and the standard error when estimating a double difference of proportions under a complex sample design.

Usage

e4ddp(N, n, P1, P2, P3, P4, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the margin of error is defined as:

cve = \frac{\sqrt{Var((\hat{P}_1 - \hat{P}_2) - (\hat{P}_3 - \hat{P}_4) ) }}{(\hat{P}_1 - \hat{P}_2) - (\hat{P}_3 - \hat{P}_4)}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var((\hat{P}_1 - \hat{P}_2) - (\hat{P}_3 - \hat{P}_4) )}

Value

The coefficient of variation and the margin of error for a predefined sample size.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

e4ddp(N=10000, n=400, P1=0.5, P2=0.6, P3=0.5, P4=0.7)
e4ddp(N=10000, n=400, P1=0.5, P2=0.6, P3=0.5, P4=0.7, plot=TRUE)
e4ddp(N=10000, n=400, P1=0.5, P2=0.6, P3=0.5, P4=0.7, DEFF=3.45, conf=0.99, plot=TRUE)

Statistical errors for the estimation of a difference of means

Description

This function computes the cofficient of variation and the standard error when estimating a difference of means under a complex sample design.

Usage

e4dm(N, n, mu1, mu2, sigma1, sigma2, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the coefficent of variation is defined as:

cve = \frac{\sqrt{Var(\bar{y}_1 - \bar{y}_2)}}{\bar{y}_1 - \bar{y}_2}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var(\bar{y}_1 - \bar{y}_2)}

Value

The coefficient of variation and the margin of error for a predefined sample size.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

e4dm(N=10000, n=400, mu1 = 100, mu2 = 12, sigma1 = 10, sigma2=8)
e4dm(N=10000, n=400, mu1 = 100, mu2 = 12, sigma1 = 10, sigma2=8, plot=TRUE)
e4dm(N=10000, n=400, mu1 = 100, mu2 = 12, sigma1 = 10, sigma2=8, DEFF=3.45, conf=0.99, plot=TRUE)

Statistical errors for the estimation of a difference of proportions

Description

This function computes the cofficient of variation and the standard error when estimating a difference of proportions under a complex sample design.

Usage

e4dp(N, n, P1, P2, DEFF = 1, T = 0, R = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the margin of error is defined as:

cve = \frac{\sqrt{Var(\hat{P}_1 - \hat{P}_2) }}{\hat{P}_1 - \hat{P}_2}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var(\hat{P}_1 - \hat{P}_2)}

Value

The coefficient of variation and the margin of error for a predefined sample size.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

e4dp(N=10000, n=400, P1=0.5, P2=0.6)
e4dp(N=10000, n=400, P1=0.5, P2=0.6, plot=TRUE)
e4dp(N=10000, n=400, P1=0.5, P2=0.6, DEFF=3.45, conf=0.99, plot=TRUE)
e4dp(N=10000, n=400, P1=0.5, P2=0.6, T=0.5, R=0.5, DEFF=3.45, conf=0.99, plot=TRUE)

Statistical errors for the estimation of a single mean

Description

This function computes the cofficient of variation and the standard error when estimating a single mean under a complex sample design.

Usage

e4m(N, n, mu, sigma, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the coefficent of variation is defined as:

cve = \frac{\sqrt{Var(\bar{y}_S)}}{\bar{y}_S}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var(\bar{y}_S)}

Value

The coefficient of variation and the margin of error for a predefined sample size.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

e4m(N=10000, n=400, mu = 10, sigma = 10)
e4m(N=10000, n=400, mu = 10, sigma = 10, plot=TRUE)
e4m(N=10000, n=400, mu = 10, sigma = 10, DEFF=3.45, conf=0.99, plot=TRUE)

Statistical errors for the estimation of a single proportion

Description

This function computes the cofficient of variation and the standard error when estimating a single proportion under a sample design.

Usage

e4p(N, n, P, DEFF = 1, conf = 0.95, plot = FALSE)

Arguments

Details

We note that the coefficent of variation is defined as:

cve = \frac{\sqrt{Var(\hat{p})}}{\hat{p}}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var(\hat{p})}

Value

The coefficient of variation, the margin of error and the relative margin of error for a predefined sample size.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

e4p(N=10000, n=400, P=0.5)
e4p(N=10000, n=400, P=0.5, plot=TRUE)
e4p(N=10000, n=400, P=0.01, DEFF=3.45, conf=0.99, plot=TRUE)

Sample Sizes in Two-Stage sampling Designs for Estimating Signle Means

Description

This function computes a grid of possible sample sizes for estimating single means under two-stage sampling designs.

Usage

ss2s4m(N, mu, sigma, conf = 0.95, delta = 0.03, M, to = 20, rho)

Arguments

Details

In two-stage (2S) sampling, the design effect is defined by

DEFF = 1 + (m-1)\rho

Where \rho is defined as the intraclass correlation coefficient, m is the average sample size of units selected inside each cluster. The relationship of the full sample size of the two stage design (2S) with the simple random sample (SI) design is given by

n_{2S} = n_{SI}*DEFF

Value

This function returns a grid of possible sample sizes. The first column represent the design effect, the second column is the number of clusters to be selected, the third column is the number of units to be selected inside the clusters, and finally, the last column indicates the full sample size induced by this particular strategy.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ICC

Examples

ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, rho=0.01)
ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, to=40, rho=0.1)
ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, to=40, rho=0.2)
ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.05, M=50, to=40, rho=0.3)

##########################################
# Almost same mean in each cluster       #
#                                        #
# - Heterogeneity within clusters        #
# - Homogeinity between clusters         #
#                                        #
#  Decision rule:                        #
#    * Select a lot of units per cluster #
#    * Select a few of clusters          #
##########################################

# Population size
N <- 1000000
# Number of clusters in the population
M <- 1000
# Number of elements per cluster
N/M

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- rep(1:M, length.out=N)

rho = ICC(y,cl)$ICC
rho

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)


##########################################
# Very different means per cluster       #
#                                        #
# - Heterogeneity between clusters       #
# - Homogeinity within clusters          #
#                                        #
#  Decision rule:                        #
#    * Select a few of units per cluster #
#    * Select a lot of clusters          #
##########################################

# Population size
N <- 1000000
# Number of clusters in the population
M <- 1000
# Number of elements per cluster
N/M

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- kronecker(c(1:M),rep(1,N/M))

rho = ICC(y,cl)$ICC
rho

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)

##########################
# Example with Lucy data #
##########################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
P <- prop.table(table(SPAM))[1]
y <- Income
cl <- Segments

rho <- ICC(y,cl)$ICC
M <- length(levels(Segments))

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)

##########################
# Example with Lucy data #
##########################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
P <- prop.table(table(SPAM))[1]
y <- Years
cl <- Segments

rho <- ICC(y,cl)$ICC
M <- length(levels(Segments))

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)

Sample Sizes in Two-Stage sampling Designs for Estimating Signle Proportions

Description

This function computes a grid of possible sample sizes for estimating single proportions under two-stage sampling designs.

Usage

ss2s4p(N, P, conf = 0.95, delta = 0.03, M, to = 20, rho)

Arguments

Details

In two-stage (2S) sampling, the design effect is defined by

DEFF = 1 + (\bar{m}-1)\rho

Where \rho is defined as the intraclass correlation coefficient, \bar{m} is the average sample size of units selected inside each cluster. The relationship of the full sample size of the two stage design (2S) with the simple random sample (SI) design is given by

n_{2S} = n_{SI}*DEFF

Value

This function returns a grid of possible sample sizes. The first column represent the design effect, the second column is the number of clusters to be selected, the third column is the number of units to be selected inside the clusters, and finally, the last column indicates the full sample size induced by this particular strategy.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ICC

Examples

ss2s4p(N=100000, P=0.5, delta=0.05, M=50, rho=0.01)
ss2s4p(N=100000, P=0.5, delta=0.05, M=500, to=40, rho=0.1)
ss2s4p(N=100000, P=0.5, delta=0.03, M=1000, to=100, rho=0.2) 

############################
# Example 2 with Lucy data #
############################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
P <- prop.table(table(SPAM))[1]
y <- Domains(SPAM)[, 1]
cl <- Segments

rho <- ICC(y,cl)$ICC
M <- length(levels(Segments))
ss2s4p(N, P, conf=0.95, delta = 0.03, M=M, to=30, rho=rho)

Sample Sizes for Household Surveys in Two-Stages for Estimating Single Means

Description

This function computes a grid of possible sample sizes for estimating single means under two-stage sampling designs.

Usage

ss4HHSm(N, M, rho, mu, sigma, delta, conf, m)

Arguments

Details

In two-stage (2S) sampling, the design effect is defined by

DEFF = 1 + (\bar{m}-1)\rho

Where \rho is defined as the intraclass correlation coefficient, \bar{m} is the average sample size of units selected inside each cluster. The relationship of the full sample size of the two stage design (2S) with the simple random sample (SI) design is given by

n_{2S} = n_{SI}*DEFF

Value

This function returns a grid of possible sample sizes. The first column represent the design effect, the second column is the number of clusters to be selected, the third column is the number of units to be selected inside the clusters, and finally, the last column indicates the full sample size induced by this particular strategy.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ICC

Examples

ss4HHSm(N = 50000000, M = 3000, rho = 0.034, 
        mu = 10, sigma = 2, delta = 0.03, conf = 0.95,
        m = c(5:15))

##################################
# Example with BigCity data      #
# Sample size for the estimation #
# of the unemployment rate       #
##################################

library(TeachingSampling)
data(BigCity)

BigCity1 <- BigCity %>% 
            group_by(HHID) %>%
            summarise(IncomeHH = sum(Income),
                      PSU = unique(PSU))
                      
summary(BigCity1$IncomeHH)
mean(BigCity1$IncomeHH)
sd(BigCity1$IncomeHH)

N <- nrow(BigCity)
M <- length(unique(BigCity$PSU))
rho <- ICC(BigCity1$IncomeHH, BigCity1$PSU)$ICC
mu <- mean(BigCity1$IncomeHH)
sigma <- sd(BigCity1$IncomeHH)
delta <- 0.05
conf <- 0.95
m <- c(5:15)
ss4HHSm(N, M, rho, mu, sigma, delta, conf, m)

Sample Sizes for Household Surveys in Two-Stages for Estimating Single Proportions

Description

This function computes a grid of possible sample sizes for estimating single proportions under two-stage sampling designs.

Usage

ss4HHSp(N, M, r, b, rho, P, delta, conf, m)

Arguments

Details

In two-stage (2S) sampling, the design effect is defined by

DEFF = 1 + (\bar{m}-1)\rho

Where \rho is defined as the intraclass correlation coefficient, \bar{m} is the average sample size of units selected inside each cluster. The relationship of the full sample size of the two stage design (2S) with the simple random sample (SI) design is given by

n_{2S} = n_{SI}*DEFF

Value

This function returns a grid of possible sample sizes. The first column represent the design effect, the second column is the number of clusters to be selected, the third column is the number of units to be selected inside the clusters, and finally, the last column indicates the full sample size induced by this particular strategy.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ICC

Examples

ss4HHSp(N = 50000000, M = 3000, r = 1, b = 3.5, 
rho = 0.034, P = 0.05, delta = 0.05, conf = 0.95,
m = c(5:15))

##################################
# Example with BigCity data      #
# Sample size for the estimation #
# of the unemployment rate       #
##################################

library(TeachingSampling)
data(BigCity)

BigCity1 <- BigCity[!is.na(BigCity$Employment), ]
summary(BigCity1$Employment)
BigCity1$Unemp <- Domains(BigCity1$Employment)[, 1]
BigCity1$Active <- Domains(BigCity1$Employment)[, 1] +
Domains(BigCity1$Employment)[, 3]

N <- nrow(BigCity)
M <- length(unique(BigCity$PSU))
r <- sum(BigCity1$Active)/N
b <- N/length(unique(BigCity$HHID))
rho <- ICC(BigCity1$Unemp, BigCity1$PSU)$ICC
P <- sum(BigCity1$Unemp)/sum(BigCity1$Active)
delta <- 0.05
conf <- 0.95
m <- c(5:15)
ss4HHSp(N, M, r, b, rho, P, delta, conf, m)

The required sample size for estimating a single variance

Description

This function returns the minimum sample size required for estimating a single variance subjecto to predefined errors.

Usage

ss4S2(N, K = 0, DEFF = 1, conf = 0.95, cve = 0.05, me = 0.03, plot = FALSE)

Arguments

Details

Note that the minimun sample size to achieve a particular relative margin of error \varepsilon is defined by:

n = \frac{n_0}{\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{\alpha}{2}}*DEFF}{\varepsilon^2}

Also note that the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{N^2(N*K+2N+2)*DEFF}{cve^2*(N-1)^3+N(N*K+2N+2)*DEFF}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4S2(N = 10000, K = 0, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.05, DEFF = 2)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03, plot = TRUE)

#############################
# Example with BigLucy data #
#############################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
K <- kurtosis(BigLucy$Income)
# The minimum sample size for simple random sampling
ss4S2(N, K, DEFF=1, conf=0.99, cve=0.03, me=0.1, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4S2(N, K, DEFF=3.45, conf=0.99, cve=0.03, me=0.1, plot=TRUE)

The required sample size for testing a null hyphotesis for a single variance

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a single variance

Usage

ss4S2H(N, S2, S20, K = 0, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)

Arguments

Details

We assume that it is of interest to test the following set of hyphotesis:

H_0: P - P_0 = 0 \ \ \ \ vs. \ \ \ \ H_a: P - P_0 = D > 0

Note that the minimun sample size, restricted to the predefined power \beta and confidence 1-\alpha, is defined by:

n = \frac{S2^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{S2^2}{N}}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 0)
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 2, DEFF = 2, power = 0.9)
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 2, DEFF = 2, power = 0.8, plot = TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
S2 <- var(BigLucy$Income)

# The minimum sample size for testing 
# H_0: S2 - S2_0 = 0   vs.   H_a: S2 - S2_0 = D = 8000
D = 8000 
S20 = S2 - D 
K <- kurtosis(BigLucy$Income)
ss4S2H(N, S2, S20, K, DEFF=1, conf = 0.99, power = 0.8, plot=TRUE)

The required sample size for estimating a double difference of means

Description

This function returns the minimum sample size required for estimating a double difference of means subjecto to predefined errors.

Usage

ss4ddm(
  N,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  DEFF = 1,
  conf = 0.95,
  cve = 0.05,
  rme = 0.03,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

Note that the minimun sample size to achieve a relative margin of error \varepsilon is defined by:

n = \frac{n_0}{1+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{alpha}{2}}S^2}{\varepsilon^2 \mu^2}

and S^2=(\sigma_1^2 + \sigma_2^2 + \sigma_3^2 + \sigma_4^2) * (1 - (T * R)) * DEFF Also note that the minimun sample size to achieve a coefficient of variation cve is defined by:

n = \frac{S^2}{|(\bar{y}_1-\bar{y}_2) - (\bar{y}_3-\bar{y}_4) |^2 cve^2 + \frac{S^2}{N}}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4ddm(N=100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, cve=0.05, rme=0.03)
ss4ddm(N=100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, cve=0.05, rme=0.03, plot=TRUE)
ss4ddm(N=100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, DEFF=3.45, conf=0.99, cve=0.03, 
     rme=0.03, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucyT0T1)
attach(BigLucyT0T1)

BigLucyT0 <- BigLucyT0T1[Time == 0,]
BigLucyT1 <- BigLucyT0T1[Time == 1,]
N1 <- table(BigLucyT0$ISO)[1]
N2 <- table(BigLucyT0$ISO)[2]
N <- max(N1,N2)

BigLucyT0.yes <- subset(BigLucyT0, ISO == "yes")
BigLucyT0.no <- subset(BigLucyT0, ISO == "no")
BigLucyT1.yes <- subset(BigLucyT1, ISO == "yes")
BigLucyT1.no <- subset(BigLucyT1, ISO == "no")
mu1 <- mean(BigLucyT0.yes$Income)
mu2 <- mean(BigLucyT0.no$Income)
mu3 <- mean(BigLucyT1.yes$Income)
mu4 <- mean(BigLucyT1.no$Income)
sigma1 <- sd(BigLucyT0.yes$Income)
sigma2 <- sd(BigLucyT0.no$Income)
sigma3 <- sd(BigLucyT1.yes$Income)
sigma4 <- sd(BigLucyT1.no$Income)

# The minimum sample size for simple random sampling
ss4ddm(N, mu1, mu2, mu3, mu4, sigma1, sigma2, sigma3, sigma4, 
DEFF=1, conf=0.95, cve=0.001, rme=0.001, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4ddm(N, mu1, mu2, mu3, mu4, sigma1, sigma2, sigma3, sigma4, 
DEFF=3.45, conf=0.99, cve=0.03, rme=0.03, plot=TRUE)

The required sample size for testing a null hyphotesis for a double difference of proportions

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a double difference of proportions.

Usage

ss4ddmH(
  N,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  D,
  DEFF = 1,
  conf = 0.95,
  power = 0.8,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

We assume that it is of interest to test the following set of hyphotesis:

H_0: (mu_1 - mu_2) - (mu_3 - mu_4) = 0 \ \ \ \ vs. \ \ \ \ H_a: (mu_1 - mu_2) - (mu_3 - mu_4) = D \neq 0

Note that the minimun sample size, restricted to the predefined power \beta and confidence 1-\alpha, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}

where S^2=(\sigma_1^2 + \sigma_2^2 + \sigma_3^2 + \sigma_4^2) * (1 - (T * R)) * DEFF

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4pH

Examples

ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=3)
ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=1, plot=TRUE)
ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=0.5, DEFF = 2, plot=TRUE)
ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=0.5, DEFF = 2, conf = 0.99, 
       power = 0.9, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucyT0T1)
attach(BigLucyT0T1)

BigLucyT0 <- BigLucyT0T1[Time == 0,]
BigLucyT1 <- BigLucyT0T1[Time == 1,]
N1 <- table(BigLucyT0$ISO)[1]
N2 <- table(BigLucyT0$ISO)[2]
N <- max(N1,N2)

BigLucyT0.yes <- subset(BigLucyT0, ISO == 'yes')
BigLucyT0.no <- subset(BigLucyT0, ISO == 'no')
BigLucyT1.yes <- subset(BigLucyT1, ISO == 'yes')
BigLucyT1.no <- subset(BigLucyT1, ISO == 'no')
mu1 <- mean(BigLucyT0.yes$Income)
mu2 <- mean(BigLucyT0.no$Income)
mu3 <- mean(BigLucyT1.yes$Income)
mu4 <- mean(BigLucyT1.no$Income)
sigma1 <- sd(BigLucyT0.yes$Income)
sigma2 <- sd(BigLucyT0.no$Income)
sigma3 <- sd(BigLucyT1.yes$Income)
sigma4 <- sd(BigLucyT1.no$Income)

# The minimum sample size for testing 
# H_0: (mu_1 - mu_2) - (mu_3 - mu_4) = 0   vs.   
# H_a: (mu_1 - mu_2) - (mu_3 - mu_4) = D = 3

ss4ddmH(N, mu1, mu2, mu3, mu4, sigma1, sigma2, sigma3, sigma4,
 D = 3, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)

The required sample size for estimating a double difference of proportions

Description

This function returns the minimum sample size required for estimating a double difference of proportion subjecto to predefined errors.

Usage

ss4ddp(
  N,
  P1,
  P2,
  P3,
  P4,
  DEFF = 1,
  conf = 0.95,
  cve = 0.05,
  me = 0.03,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

Note that the minimun sample size (for each group at each wave) to achieve a particular margin of error \varepsilon is defined by:

n = \frac{n_0}{1+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{\alpha}{2}}S^2}{\varepsilon^2}

and

S^2 = (P1 * Q1 + P2 * Q2 + P3 * Q3 + P4 * Q4) * (1 - (T * R)) * DEFF

Also note that the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{S^2}{(ddp)^2cve^2+\frac{S^2}{N}}

And ddp is the expected estimate of the double difference of proportions.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4dp

Examples

ss4ddp(N=100000, P1=0.05, P2=0.55, P3= 0.5, P4= 0.6, cve=0.05, me=0.03)
ss4ddp(N=100000, P1=0.05, P2=0.55, P3= 0.5, P4= 0.6, cve=0.05, me=0.03, plot=TRUE)
ss4ddp(N=100000, P1=0.05, P2=0.55, P3= 0.5, P4= 0.6, DEFF=3.45, conf=0.99, 
cve=0.03, me=0.03, plot=TRUE)
ss4ddp(N=100000, P1=0.05, P2=0.55, P3= 0.5, P4= 0.6, DEFF=3.45, conf=0.99,
 cve=0.03, me=0.03, T = 0.5, R = 0.9, plot=TRUE)

#################################
# Example with BigLucyT0T1 data #
#################################
data(BigLucyT0T1)
attach(BigLucyT0T1)

BigLucyT0 <- BigLucyT0T1[Time == 0,]
BigLucyT1 <- BigLucyT0T1[Time == 1,]
N1 <- table(BigLucyT0$SPAM)[1]
N2 <- table(BigLucyT1$SPAM)[1]
N <- max(N1,N2)
P1 <- prop.table(table(BigLucyT0$ISO))[1]
P2 <- prop.table(table(BigLucyT1$ISO))[1]
P3 <- prop.table(table(BigLucyT0$ISO))[2]
P4 <- prop.table(table(BigLucyT1$ISO))[2]
# The minimum sample size for simple random sampling
ss4ddp(N, P1, P2, P3, P4, conf=0.95, cve=0.05, me=0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4ddp(N, P1, P2, P3, P4, T = 0.5, R = 0.5, conf=0.95, cve=0.05, me=0.03, plot=TRUE)

The required sample size for testing a null hyphotesis for a double difference of proportions

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a double difference of proportion.

Usage

ss4ddpH(
  N,
  P1,
  P2,
  P3,
  P4,
  D,
  DEFF = 1,
  conf = 0.95,
  power = 0.8,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

We assume that it is of interest to test the following set of hyphotesis:

H_0: (P_1 - P_2) - (P_3 - P_4) = 0 \ \ \ \ vs. \ \ \ \ H_a: (P_1 - P_2) - (P_3 - P_4) = D \neq 0

Note that the minimun sample size, restricted to the predefined power \beta and confidence 1-\alpha, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}

Where S^2 = (P1 * Q1 + P2 * Q2 + P3 * Q3 + P4 * Q4) * (1 - (T * R)) * DEFF and Q_i=1-P_i for i=1,2, 3, 4.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4pH

Examples

ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D=0.03)
ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D=0.03, plot=TRUE)
ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D=0.03, DEFF = 2, plot=TRUE)
ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, 
D=0.03, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

#################################
# Example with BigLucyT0T1 data #
#################################
data(BigLucyT0T1)
attach(BigLucyT0T1)

BigLucyT0 <- BigLucyT0T1[Time == 0,]
BigLucyT1 <- BigLucyT0T1[Time == 1,]
N1 <- table(BigLucyT0$SPAM)[1]
N2 <- table(BigLucyT1$SPAM)[1]
N <- max(N1,N2)
P1 <- prop.table(table(BigLucyT0$ISO))[1]
P2 <- prop.table(table(BigLucyT1$ISO))[1]
P3 <- prop.table(table(BigLucyT0$ISO))[2]
P4 <- prop.table(table(BigLucyT1$ISO))[2]
# The minimum sample size for simple random sampling
ss4ddpH(N, P1, P2, P3, P4, D = 0.05, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4ddpH(N, P1, P2, P3, P4, D = 0.05, DEFF = 2, T = 0.5, R = 0.5, conf=0.95, plot=TRUE)

The required sample size for estimating a single difference of proportions

Description

This function returns the minimum sample size required for estimating a single proportion subjecto to predefined errors.

Usage

ss4dm(
  N,
  mu1,
  mu2,
  sigma1,
  sigma2,
  DEFF = 1,
  conf = 0.95,
  cve = 0.05,
  rme = 0.03,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

Note that the minimun sample size to achieve a relative margin of error \varepsilon is defined by:

n = \frac{n_0}{1+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{alpha}{2}}S^2}{\varepsilon^2 (\mu_1 - \mu_2)^2}

and S^2=(\sigma_1^2 + \sigma_2^2) * (1 - (T * R)) * DEFF Also note that the minimun sample size to achieve a coefficient of variation cve is defined by:

n = \frac{S^2}{|\bar{y}_1-\bar{y}_2|^2 cve^2 + \frac{S^2}{N}}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4dm(N=100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, cve=0.05, rme=0.03)
ss4dm(N=100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, cve=0.05, rme=0.03, plot=TRUE)
ss4dm(N=100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, DEFF=3.45, conf=0.99, cve=0.03, 
     rme=0.03, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N1 <- table(SPAM)[1]
N2 <- table(SPAM)[2]
N <- max(N1,N2)

BigLucy.yes <- subset(BigLucy, SPAM == 'yes')
BigLucy.no <- subset(BigLucy, SPAM == 'no')
mu1 <- mean(BigLucy.yes$Income)
mu2 <- mean(BigLucy.no$Income)
sigma1 <- sd(BigLucy.yes$Income)
sigma2 <- sd(BigLucy.no$Income)

# The minimum sample size for simple random sampling
ss4dm(N, mu1, mu2, sigma1, sigma2, DEFF=1, conf=0.99, cve=0.03, rme=0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4dm(N, mu1, mu2, sigma1, sigma2, DEFF=3.45, conf=0.99, cve=0.03, rme=0.03, plot=TRUE)

The required sample size for testing a null hyphotesis for a single difference of proportions

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a single difference of proportions.

Usage

ss4dmH(
  N,
  mu1,
  mu2,
  sigma1,
  sigma2,
  D,
  DEFF = 1,
  conf = 0.95,
  power = 0.8,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

We assume that it is of interest to test the following set of hyphotesis:

H_0: mu_1 - mu_2 = 0 \ \ \ \ vs. \ \ \ \ H_a: mu_1 - mu_2 = D \neq 0

Note that the minimun sample size, restricted to the predefined power \beta and confidence 1-\alpha, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}

where S^2=(\sigma_1^2 + \sigma_2^2) * (1 - (T * R)) * DEFF

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4pH

Examples

ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=3)
ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=1, plot=TRUE)
ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=0.5, DEFF = 2, plot=TRUE)
ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=0.5, DEFF = 2, conf = 0.99, 
       power = 0.9, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N1 <- table(SPAM)[1]
N2 <- table(SPAM)[2]
N <- max(N1,N2)

BigLucy.yes <- subset(BigLucy, SPAM == 'yes')
BigLucy.no <- subset(BigLucy, SPAM == 'no')
mu1 <- mean(BigLucy.yes$Income)
mu2 <- mean(BigLucy.no$Income)
sigma1 <- sd(BigLucy.yes$Income)
sigma2 <- sd(BigLucy.no$Income)

# The minimum sample size for testing 
# H_0: mu_1 - mu_2 = 0   vs.   H_a: mu_1 - mu_2 = D = 3
D = 3
ss4dmH(N, mu1, mu2, sigma1, sigma2, D, DEFF = 2, plot=TRUE)

# The minimum sample size for testing 
# H_0: mu_1 - mu_2 = 0   vs.   H_a: mu_1 - mu_2 = D = 3
D = 3
ss4dmH(N, mu1, mu2, sigma1, sigma2, D, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)

The required sample size for estimating a single difference of proportions

Description

This function returns the minimum sample size required for estimating a single proportion subjecto to predefined errors.

Usage

ss4dp(
  N,
  P1,
  P2,
  DEFF = 1,
  conf = 0.95,
  cve = 0.05,
  me = 0.03,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

Note that the minimun sample size to achieve a particular margin of error \varepsilon is defined by:

n = \frac{n_0}{1+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{\alpha}{2}}S^2}{\varepsilon^2}

and

S^2 = (P1 * Q1 + P2 * Q2) * (1 - (T * R)) * DEFF

Also note that the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{S^2}{p^2cve^2+\frac{S^2}{N}}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4dp(N=100000, P1=0.5, P2=0.55, cve=0.05, me=0.03)
ss4dp(N=100000, P1=0.5, P2=0.55, cve=0.05, me=0.03, plot=TRUE)
ss4dp(N=100000, P1=0.5, P2=0.55, DEFF=3.45, conf=0.99, cve=0.03, me=0.03, plot=TRUE)
ss4dp(N=100000, P1=0.5, P2=0.55, DEFF=3.45, T=0.5, R=0.5, conf=0.99, cve=0.03, me=0.03, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N1 <- table(SPAM)[1]
N2 <- table(SPAM)[2]
N <- max(N1,N2)
P1 <- prop.table(table(SPAM))[1]
P2 <- prop.table(table(SPAM))[2]
# The minimum sample size for simple random sampling
ss4dp(N, P1, P2, DEFF=1, conf=0.99, cve=0.03, me=0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4dp(N, P1, P2, DEFF=3.45, conf=0.99, cve=0.03, me=0.03, plot=TRUE)

The required sample size for testing a null hyphotesis for a single difference of proportions

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a single proportion.

Usage

ss4dpH(
  N,
  P1,
  P2,
  D,
  DEFF = 1,
  conf = 0.95,
  power = 0.8,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

Details

We assume that it is of interest to test the following set of hyphotesis:

H_0: P_1 - P_2 = 0 \ \ \ \ vs. \ \ \ \ H_a: P_1 - P_2 = D \neq 0

Note that the minimun sample size, restricted to the predefined power \beta and confidence 1-\alpha, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}

Where S^2 = (P1 * Q1 + P2 * Q2) * (1 - (T * R)) * DEFF and Q_i=1-P_i for i=1,2.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4pH

Examples

ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03)
ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03, plot=TRUE)
ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03, DEFF = 2, plot=TRUE)
ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N1 <- table(SPAM)[1]
N2 <- table(SPAM)[2]
N <- max(N1,N2)
P1 <- prop.table(table(SPAM))[1]
P2 <- prop.table(table(SPAM))[2]

# The minimum sample size for testing 
# H_0: P_1 - P_2 = 0   vs.   H_a: P_1 - P_2 = D = 0.05
D = 0.05  
ss4dpH(N, P1, P2, D, DEFF = 2, plot=TRUE)

# The minimum sample size for testing 
# H_0: P - P_0 = 0   vs.   H_a: P - P_0 = D = 0.02
D = 0.01
ss4dpH(N, P1, P2, D, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)

The required sample size for estimating a single mean

Description

This function returns the minimum sample size required for estimating a single mean subjec to predefined errors.

Usage

ss4m(
  N,
  mu,
  sigma,
  DEFF = 1,
  conf = 0.95,
  error = "cve",
  delta = 0.03,
  plot = FALSE
)

Arguments

Details

Note that the minimun sample size to achieve a relative margin of error \varepsilon is defined by:

n = \frac{n_0}{1+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{alpha}{2}}S^2}{\varepsilon^2 \mu^2}

and

S^2=\sigma^2 DEFF

Also note that the minimun sample size to achieve a coefficient of variation cve is defined by:

n = \frac{S^2}{\bar{y}_U^2 cve^2 + \frac{S^2}{N}}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4m(N=10000, mu=10, sigma=2, DEFF = 2, error = "cve", delta = 0.03, plot=TRUE)
ss4m(N=10000, mu=10, sigma=2, DEFF = 2, error = "me", delta = 1, plot=TRUE)
ss4m(N=10000, mu=10, sigma=2, DEFF = 2, error = "rme", delta = 0.03, plot=TRUE)

##########################
# Example with Lucy data #
##########################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
mu <- mean(Income)
sigma <- sd(Income)
# The minimum sample size for simple random sampling
ss4m(N, mu, sigma, DEFF=1, conf=0.95, error = "rme", delta = 0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4m(N, mu, sigma, DEFF=1, conf=0.95, error = "me", delta = 5, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4m(N, mu, sigma, DEFF=3.45, conf=0.95, error = "rme", delta = 0.03, plot=TRUE)

The required sample size for testing a null hyphotesis for a single mean

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a single mean

Usage

ss4mH(N, mu, mu0, sigma, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)

Arguments

Details

We assume that it is of interest to test the following set of hyphotesis:

H_0: mu - mu_0 = 0 \ \ \ \ vs. \ \ \ \ H_a: mu - mu_0 = D \neq 0

Note that the minimun sample size, restricted to the predefined power \beta and confidence 1-\alpha, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}

Where S^2=\sigma^2 * DEFF and \sigma^2 is the population variance of the varible of interest.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100)
ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100, plot=TRUE)
ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100, DEFF = 2, plot=TRUE)
ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N <- nrow(BigLucy)
mu <- mean(Income)
sigma <- sd(Income)

# The minimum sample size for testing 
# H_0: mu - mu_0 = 0   vs.   H_a: mu - mu_0 = D = 15
D = 15 
mu0 = mu - D 
ss4mH(N, mu, mu0, sigma, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

# The minimum sample size for testing 
# H_0: mu - mu_0 = 0   vs.   H_a: mu - mu_0 = D = 32
D = 32
mu0 = mu - D 
ss4mH(N, mu, mu0, sigma, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)

The required sample size for estimating a single proportion

Description

This function returns the minimum sample size required for estimating a single proportion subjecto to predefined errors.

Usage

ss4p(N, P, DEFF = 1, conf = 0.95, error = "cve", delta = 0.03, plot = FALSE)

Arguments

Details

Note that the minimun sample size to achieve a particular margin of error \varepsilon is defined by:

n = \frac{n_0}{1+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{\alpha}{2}}S^2}{\varepsilon^2}

and

S^2=P(1-P)DEFF

Also note that the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{S^2}{P^2cve^2+\frac{S^2}{N}}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4p(N=10000, P=0.05, error = "cve", delta=0.05, DEFF = 1, conf = 0.95, plot=TRUE)
ss4p(N=10000, P=0.05, error = "me", delta=0.05, DEFF = 1, conf = 0.95, plot=TRUE)
ss4p(N=10000, P=0.5, error = "rme", delta=0.05, DEFF = 1, conf = 0.95, plot=TRUE)

##########################
# Example with Lucy data #
##########################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
P <- prop.table(table(SPAM))[1]
# The minimum sample size for simple random sampling
ss4p(N, P, DEFF=3.45, conf=0.95, error = "cve", delta = 0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4p(N, P, DEFF=3.45, conf=0.95, error = "rme", delta = 0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4p(N, P, DEFF=3.45, conf=0.95, error = "me", delta = 0.03, plot=TRUE)

The required sample size for testing a null hyphotesis for a single proportion

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a single proportion.

Usage

ss4pH(N, p, p0, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)

Arguments

Details

We assume that it is of interest to test the following set of hyphotesis:

H_0: P - P_0 = 0 \ \ \ \ vs. \ \ \ \ H_a: P - P_0 = D \neq 0

Note that the minimun sample size, restricted to the predefined power \beta and confidence 1-\alpha, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}

Where

S^2=p(1-p)DEFF

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4pH(N = 10000, p = 0.5, p0 = 0.55)
ss4pH(N = 10000, p = 0.5, p0 = 0.55, plot=TRUE)
ss4pH(N = 10000, p = 0.5, p0 = 0.55, DEFF = 2, plot=TRUE)
ss4pH(N = 10000, p = 0.5, p0 = 0.55, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N <- nrow(BigLucy)
p <- prop.table(table(SPAM))[1]

# The minimum sample size for testing 
# H_0: P - P_0 = 0   vs.   H_a: P - P_0 = D = 0.1
D = 0.1 
p0 = p - D 
ss4pH(N, p, p0, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

# The minimum sample size for testing 
# H_0: P - P_0 = 0   vs.   H_a: P - P_0 = D = 0.02
D = 0.02
p0 = p - D 
ss4pH(N, p, p0, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)

The required sample size for estimating a single proportion based on a logaritmic transformation of the estimated proportion

Description

This function returns the minimum sample size required for estimating a single proportion subjecto to predefined errors.

Usage

ss4pLN(N, P, DEFF = 1, cve = 0.05, plot = FALSE)

Arguments

Details

As for low proportions, the coefficient of variation tends to infinity, it is customary to use a simmetrycal transformation of this measure (based on the relative standard error RSE) to report the uncertainity of the estimation. This way, if p \leq 0.5, the transformed CV will be:

RSE(-ln(p))= \frac{SE(p)}{-ln(p)*p}

Otherwise, when p > 0.5, the transformed CV will be:

RSE(-ln(1-p))= \frac{SE(p)}{-ln(1-p)*(1-p)}

Note that, when p \leq 0.5 the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{S^2}{P^2cve^2+\frac{S^2}{N}}

When p > 0.5 the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{S^2}{P^2cve^2+\frac{S^2}{N}}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

ss4pLN(N=10000, P=0.8, cve=0.10)
ss4pLN(N=10000, P=0.2, cve=0.10)
ss4pLN(N=10000, P=0.7, cve=0.05, plot=TRUE)
ss4pLN(N=10000, P=0.3, cve=0.05, plot=TRUE)
ss4pLN(N=10000, P=0.05, DEFF=3.45, cve=0.03, plot=TRUE)
ss4pLN(N=10000, P=0.95, DEFF=3.45, cve=0.03, plot=TRUE)

##########################
# Example with Lucy data #
##########################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
P <- prop.table(table(SPAM))[1]
# The minimum sample size for simple random sampling
ss4pLN(N, P, DEFF=1, cve=0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4pLN(N, P, DEFF=3.45, cve=0.03, plot=TRUE)

Sample Size for Estimation of Means in Stratified Sampling

Description

This function computes the minimum sample size required for estimating a single mean, in a stratified sampling, subject to predefined errors.

Usage

ss4stm(Nh, muh, sigmah, DEFFh = 1, conf = 0.95, rme = 0.03)

Arguments

Details

Let assume that the population U is partitioned in H strate. Under a stratified sampling, the neccesary sample size to achieve a relative margin of error \varepsilon is defined by:

n = \frac{(\sum_{h=1}^H w_h S_h)^2}{\frac{\varepsilon^2}{z^2_{1-\frac{\alpha}{2}}}+\frac{\sum_{h=1}^H w_h S^2_h}{N}}

Where

S^2_h = DEFF_h \sigma^2_h

Then, the required sample size in each stratum is given by:

n_h = n \frac{w_h S_h}{\sum_{h=1}^H w_h S_h}

Value

The required sample size for the sample and the required sample size per stratum.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4m

Examples

Nh <- c(15000, 10000, 5000)
muh <- c(300, 200, 100)
sigmah <- c(200, 100, 20)
DEFFh <- c(1, 1.2, 1.5)

ss4stm(Nh, muh, sigmah, rme=0.03)
ss4stm(Nh, muh, sigmah, conf = 0.99, rme=0.03)
ss4stm(Nh, muh, sigmah, DEFFh, conf= 0.99, rme=0.03)

##########################
# Example with Lucy data #
##########################
data(Lucy)
attach(Lucy)

Strata <- as.factor(paste(Zone, Level))
levels(Strata)

Nh <- summary(Strata)
muh <- tapply(Income, Strata, mean)
sigmah <- tapply(Income, Strata, sd)

ss4stm(Nh, muh, sigmah, DEFFh=1, conf = 0.95, rme = 0.03)
ss4stm(Nh, muh, sigmah, DEFFh=1.5, conf = 0.95, rme = 0.03)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

Nh <- summary(Zone)
muh <- tapply(Income, Zone, mean)
sigmah <- tapply(Income, Zone, sd)

ss4stm(Nh, muh, sigmah, DEFFh=1, conf = 0.95, rme = 0.03)
ss4stm(Nh, muh, sigmah, DEFFh=1.5, conf = 0.95, rme = 0.03)