What is sampling for proportions and when is it used?
a sampling technique that estimates a parameter, p, the proportion of the population with a particular attribute, the estimator of p is designated as p hat
we use sampling for proportions for regeneration surveys, survival studies and insect/disease surveys
what does q hat represent
q hat = 1 - p{hat}
what are three approaches for deriving confidence intervals for proportions
- binomial distribution tables
- binomial distribution graph
- if n x p{hat} or n x q{hat} is greater than 5, the normal distribution can be used as an approximation
How do you do hypothesis testing for proportions
similar to SRS
- if a constant value is given (c) (ex. p might be the true proportion of seeding survival, c could be the hypothesized survival rate), if c is within the confidence intervals we can reject the null hypothesis
- compare calculated z statistic to critical values from z distribution table
When should we use sampling for proportions?
whenever the variable of interest can be expressed as a proportion
- formulas and example apply to SRS, but modifications can be made to use proportions with STRS, or any sampling method
What is line intersect sampling (LIS)
lines are randomly located in the area you are sampling, each line is considered to be a cluster of the elements that intersect that line
- equation can be used to estimate the value for any line providing the variable of interest can be measured and the probability of the item intersecting the line can be determined
What are the uses of LIS?
determine the volume of woody material lying on the ground following a logging operation (residue)
- residue volumes are needed for cut control purposes, determining avoidable waste, determining fuel loading
- in the equation y{ij} can become the volume of the individual log that is intersected
What are the steps for using LIS to determine the volume of logging residue
- determine the volume per ha (y{i}) associated with each line
- once you have a list of values for each variable of interest the steps become identical to SRS
- summary stats
- estimate of the mean volume per hectare
- variance of the observation
- standard deviation of our estimate of the mean volume per hectare
- estimate of the total volume and its associated standard deviation
- 90% confidence interval for the mean residue volume per hectare
- 90% confidence interval for the total residue volume
What is ratio/regression sampling
class of techniques that uses the relationship between a variable that is known for all elements in the population (the auxiliary variable) and variable of interest to predict the parameters of interest
What are the conditions for using ratio/regression sampling
- the value for the auxiliary variable must be known for every element in the population
(aka we know the population total and population mean for the aux variable (x{i}) - a good linear relationship must exist between the variable of interest and the auxiliary variable
- the remaining depend upon the type of technique being used
What are the three ratio/regression sampling techniques? describe them
- ratio of means
- uses the ratio of the sample means for x and y to produce estimates of population total and population mean
- more weight is given to larger observations
- appropriate for estimating average volume per truck load, and total volume from an area - mean of ratios
- uses the average of all of the ratios of the x and y values in the sample to produce estimates of population total and population mean
- equal weight is given to every observation - regression technique
- uses regression to determine the relationship between x and y
steps for ratio of means
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mean of ratios process
- estimate of the mean ratio (r bar)
- estimate of the total
- data summary (sum of y, sum of y2, sum of r (y/x), sum of r2
- standard deviation of the statistics (r bar)
- first do variance of r
- then plug that into standard deviation - standard deviation of our estimate
- 95% confidence interval for ty
Steps for regression sampling
- data summary (sum of y, sum of y2, sum of xy, sum of x, sum of x2, SSY, SSX, SPXY)
- calculate regression coefficients
- put coefficients into regression equation
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Name other sampling methods
cluster sampling , double sampling, sequential sampling, stratification after sampling, two-stage sampling, variable probability sampling
