money: Money Data Frame

In samplingbook: Survey Sampling Procedures

Description

Data provides guesses and true values for students wallet money.

Usage

data(money)

Format

A data frame with 13 observations (corresponding to the students) on the following 3 variables.

id

a numeric vector of identification number

X

a numeric vector of secondary information, guesses of money in the wallet

y

a numeric vector of primary information, counted money in the wallet. NA means subject was not included into the sample.

Details

In a lesson an experiment was made, in which the students were asked to guess the current amount of money in their wallet. A simple sample of these students was drawn, who counted the money in their wallet exactly. Using this secondary information, model based estimation of the population mean is possible.

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

data(money)
print(money)

# Usage of mbes()
mu.X <-  mean(money$X)
x <- money$X[which(!is.na(money$y))]
y <- na.omit(money$y)
# estimation
mbes(y~x, aux=mu.X, N=13, method='all')

Example output

Loading required package: pps
Loading required package: sampling
Loading required package: survey
Loading required package: grid
Loading required package: Matrix
Loading required package: survival

Attaching package: ‘survival’

The following objects are masked from ‘package:sampling’:

    cluster, strata


Attaching package: ‘survey’

The following object is masked from ‘package:graphics’:

    dotchart

   id   X     y
1   1  30 45.04
2   2  18    NA
3   3  29 30.66
4   4 100    NA
5   5  25 28.28
6   6  35 45.50
7   7  30 53.61
8   8   9    NA
9   9   7  8.68
10 10  18 19.77
11 11  40    NA
12 12  15    NA
13 13   6    NA

mbes object: Model Based Estimation of Population Mean
Population size N = 13, sample size n = 7

Values for auxiliary variable: 
X.mean.1 = 27.8462, x.mean.1 = 24.8571
----------------------------------------------------------------
Simple Estimate

Mean estimate:  33.0771 
Standard error:  4.0872 

95% confidence interval [25.0663,41.088]

----------------------------------------------------------------
Difference Estimate

Mean estimate:  36.0662 
Standard error:  2.1998 

95% confidence interval [31.7546,40.3778]

----------------------------------------------------------------
Ratio Estimate

Mean estimate:  37.0546 
Standard error:  1.8764 

95% confidence interval [33.3768,40.7323]

----------------------------------------------------------------
Linear Regression Estimate

Mean estimate:  37.5665 
Standard error:  2.0042 

95% confidence interval [33.6383,41.4946]

----------------------------------------------------------------
Linear Regression Model:
Call:
lm(formula = formula, data = data)

Residuals:
     1      2      3      4      5      6      7 
 4.239 -8.640 -5.012 -2.811 12.809  2.423 -3.008 
attr(,"na.action")
[1]  2  4  8 11 12 13
attr(,"class")
[1] "omit"

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  -4.2571     8.8633  -0.480   0.6513   
x             1.5020     0.3362   4.467   0.0066 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.805 on 5 degrees of freedom
Multiple R-squared:  0.7996,	Adjusted R-squared:  0.7596 
F-statistic: 19.95 on 1 and 5 DF,  p-value: 0.006598

samplingbook documentation built on April 3, 2021, 1:06 a.m.