Surveys - Sample Designs

Question 1

what is a controlled experiment?

Answer 1

1. Comparitive (2+ things, groups, ideas etc.)
2. Manipulative (manipulate one variable or more (ie treatment), to study relationships)
   - cause and effect
   - before and after

Question 2

What is an observational study?

Answer 2

1. Absolute (no baseline comparison)
2. Mensurative (measure natural variation between variables, with no manipulation)
   - survey
   - monitoring

Question 3

What is the difference between a survey and monitoring?

Answer 3

Survey - (estimate a statistic, no temporal change in period or survey)

Monitoring - (estimate a change in statistic, temporal changes during period of observations)

Question 4

What are the 2 types of survey sampling?

Answer 4

1. sampling with replacement (SIR)

2. sampling without replacement (SI)

Question 5

Mean for random sampling

Answer 5

Sum of all values divided by the number of samples

Question 6

Variance of mean for simple random sampling

Answer 6

SD squared of all samples, divided by # of samples

Question 7

What is a confidence interval?

Answer 7

The interval in which we are x% confident that the true pop mean u lies.

Question 8

What do confidence intervals consist of?

Answer 8

• un upper and lower limit

- a degree of confidence

Question 9

What is the solution to bad random sampling pick?

Answer 9

• divide population into sub-groups (strata)
• don’t overlap
• randomisation within strata

Question 10

What are the 2 types of stratified random sampling?

Answer 10

1. Stratification - elements in pop divided into strata based on their variables
   * must be non-overlapping and together constitute the whole pop*
2. Sampling within strata - samples selected randomly and independently from each stratum

Question 11

Why do we stratify?

Answer 11

1. Precision - more homogenous strata then more precise estimates.
2. Captures individual strata characteristics - characteristics of each sample weighed proportional to entire pop - similar to weighted average.
3. Practical - already know info may differ between groups/ strata is occuring (e.g suburbs)

Question 12

How is the mean for stratified random sampling (StR) calculated?

Answer 12

First calculate the mean of each strata, then multiply each mean by its weighting (usually a proportion)
Then add up weighted means

Question 13

How do we calculate the variance of the mean for stratified random sampling?

Answer 13

First calculate varience for mean of each strata, multiply each varience value by square of weighting
Then add up weighted variences

Question 14

Worked example: Stratified sampling

Answer 14

# definitions
A = c(90, 78, 86, 71) # define stratum A (4 samples)
B = c(48, 56, 42)     # defime stratum B (3 samples)
n = 7                 # total number of samples
tcrit = qt(.975, df = n-2) # t critical value for 95% CI
wt = c(A = .62, B = .38)   # define weights
# calculations:
wmean = sum(mean(A) * wt[1], mean(B) * wt[2]) # weighted mean
# weighted^2 variance of mean:
wvar = sum(var(A)/4 * wt[1]^2, var(B)/3 * wt[2]^2) 
L95t = wmean - tcrit * se # lower 95% CI
U95t = wmean + tcrit * se # upper 95% CI
c(lower95 = L95t, upper95 = U95t)
##  lower95  upper95 
## 61.04864 76.68803

Question 15

Worked example: Simple Random Sampling

Answer 15

# definitions
A = c(90, 78, 86, 71) # define stratum A (4 samples)
B = c(48, 56, 42)     # defime stratum B (3 samples)
n = 7                 # total number of samples
tcrit = qt(.975, df = n-1) # t critical value for 95% CI
# calculations:
mean_ab = mean(c(A, B))   # mean
var_ab = var(c(A, B))/n   # variance of the mean
L95s = mean_ab - tcrit * sqrt(var_ab) # lower 95% CI 
U95s = mean_ab + tcrit * sqrt(var_ab) # upper 95% CI
c(lower95 = L95s, upper95 = U95s)
##  lower95  upper95 
## 49.84627 84.72516

Question 16

What does monitoring study?

Answer 16

the change in the mean overtime