Lesson 4 - Sampling Design 2

Question 1

What is sampling for proportions and when is it used?

Answer 1

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

Question 2

what does q hat represent

Answer 2

q hat = 1 - p{hat}

Question 3

what are three approaches for deriving confidence intervals for proportions

Answer 3

1. binomial distribution tables
2. binomial distribution graph
3. if n x p{hat} or n x q{hat} is greater than 5, the normal distribution can be used as an approximation

Question 4

How do you do hypothesis testing for proportions

Answer 4

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

Question 5

When should we use sampling for proportions?

Answer 5

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

Question 6

What is line intersect sampling (LIS)

Answer 6

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

Question 7

What are the uses of LIS?

Answer 7

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

Question 8

What are the steps for using LIS to determine the volume of logging residue

Answer 8

1. determine the volume per ha (y{i}) associated with each line
2. 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

Question 9

What is ratio/regression sampling

Answer 9

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

Question 10

What are the conditions for using ratio/regression sampling

Answer 10

1. 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})
2. a good linear relationship must exist between the variable of interest and the auxiliary variable
3. the remaining depend upon the type of technique being used

Question 11

What are the three ratio/regression sampling techniques? describe them

Answer 11

1. 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
2. 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
3. regression technique
   - uses regression to determine the relationship between x and y

Question 12

steps for ratio of means

Answer 12

??????

Question 13

mean of ratios process

Answer 13

• 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

Question 14

Steps for regression sampling

Answer 14

• 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
  ???

Question 15

Name other sampling methods

Answer 15

cluster sampling , double sampling, sequential sampling, stratification after sampling, two-stage sampling, variable probability sampling