Estimating the number of fish that return to spawn using capture-recapture methods.
Glossary
Accuracy
The accuracy of an estimator refers to the average error from the true value
over all possible samples. It is a synonym for bias. An accuate estimator
will have small bias.
Case by Variable structure
Many data files are arranged in rectangular arrays with columns representing different
variables and row representing multiple measurements on a single experimental unit.
For example, the selling price ($), the size of the house (square m), and the number of bed rooms in a house could be arranged in a table that looks something like:
| Price | Size | Bedrooms |
|---|
| 75,000 | 200 | 4 |
| 95,000 | 250 | 5 |
.
.
. | .
.
. | .
.
. |
The columns are called variables. The rows are called observations or cases.
In many cases, the distribution of data is approximately symmetrical and mound shaped. In these cases, the empirical rule states that about 68% of values will be within 1 standard deviation of the mean, about 95% of values will be within 2 standard deviations of the mean; and all most all of the values will be within 3 standard deviations of the mean.
Least Squares
Least Squares is a principle often used to find "best fitting" lines to data.
It minimizes the sum of the squared deviations between the predicted values and the
actual data values.
Sampling Distribution
A sampling distribution refers to the fact that everytime a sample is selected, the estimate will change. The entire set of possible estimates when all possible samples from the population are examined, is called the sampling distribution. It should not be confused with the distribution of individual elements in the population or the distribution of individual elements in the sample.
Outliers
Data values that do not seem to fit the relationship found in the remainder of the data are termed outliers. Outliers can be detected using box-plots, dot-plots, or histograms for univariate data and scatterplots for multivariate data.
Precision
The precision of an estimator refers to the variability of the estimator
over all possible samples. A precise estimator will have small variability,
i.e. a small standard error.
Scale of Variables
The scale of a variables refers to the level in the nominal,
ordinal, interval, or ratio hierarchy.
Nominal scaled variables are classifications only, and cannot
be ordered.
Ordinal scaled variables can be ordered, but differences among
the scale points cannot be quantified.
Interval scaled variables can be ordered and differences among
points on the scale are consistent and quantifiable. However
interval scaled variables do not have a natural zero.
Ratio scaled variables can be orderd, differences among scales
points can be quantified, and have a natural zero.
Standard error
The standard error of an estimator is the standard deviation
of the estimator overall all possible samples.
Unbiased
An estimator is unbiased if the average value of the estimator
over all possible samples equals the true population value.