R Dataset / Package HistData / YeastD.mat

On this R-data statistics page, you will find information about the YeastD.mat data set which pertains to Student's (1906) Yeast Cell Counts. The YeastD.mat data set is found in the HistData R package. You can load the YeastD.mat data set in R by issuing the following command at the console data("YeastD.mat"). This will load the data into a variable called YeastD.mat. If R says the YeastD.mat data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data with the library() command. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the YeastD.mat R data set. The size of this file is about 991 bytes.

Student's (1906) Yeast Cell Counts

Description

Counts of the number of yeast cells were made each of 400 regions in a 20 x 20 grid on a microscope slide, comprising a 1 sq. mm. area. This experiment was repeated four times, giving samples A, B, C and D.

Student (1906) used these data to investigate the errors in random sampling. He says "there are two sources of error: (a) the drop taken may not be representative of the bulk of the liquid; (b) the distribution of the cells over the area which is examined is never exactly uniform, so that there is an 'error of random sampling.'"

The data in the paper are provided in the form of discrete frequency distributions for the four samples. Each shows the frequency distribution squares containing a count of 0, 1, 2, ... yeast cells. These are combined here in Yeast. In addition, he gives a table (Table I) showing the actual number of yeast cells counted in the 20 x 20 grid for sample D, given here as YeastD.mat.

Usage

data(Yeast)
data(YeastD.mat)

Format

Yeast: A frequency data frame with 36 observations on the following 3 variables, giving the frequencies of

sample: Sample identifier, a factor with levels A B C D
count: The number of yeast cells counted in a square
freq: The number of squares with the given count

YeastD.mat: A 20 x 20 matrix containing the count of yeast cells in each square for sample D.

Details

Student considers the distribution of a total of Nm particles distributed over N unit areas with an average of m particles per unit area. With uniform mixing, for a given particle, the probability of it falling on any one area is p = 1/N, and not falling on that area is q = 1 - 1/N. He derives the probability distribution of 0, 1, 2, 3, ... particles on a single unit area from the binomial expansion of (p + q)^{mN}.

Source

D. J. Hand, F. Daly, D. Lunn, K. McConway and E. Ostrowski (1994). A Handbook of Small Data Sets. London: Chapman \& Hall. The data may be found at: http://www.stat.duke.edu/courses/Spring98/sta113/Data/Hand/yeast.dat

References

"Student" (1906) On the error of counting with a haemocytometer. Biometrika, 5, 351-360. http://www.medicine.mcgill.ca/epidemiology/hanley/c626/Student_counting.pdf

Examples

data(Yeast)require(lattice)
# basic bar charts 
# TODO: frequencies should start at 0, not 1.
barchart(count~freq|sample, data=Yeast, ylab="Number of Cells", xlab="Frequency")
barchart(freq~count|sample, data=Yeast, xlab="Number of Cells", ylab="Frequency",
horizontal=FALSE, origin=0)# same, using xyplot
xyplot(freq~count|sample, data=Yeast, xlab="Number of Cells", ylab="Frequency",
horizontal=FALSE, origin=0, type="h", lwd=10)

Dataset imported from https://www.r-project.org.

Attachments: csv, json

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