(6) Sampling and Detecting Disease

⭐ 1. Q: What is the objective of sampling?

The objective of sampling is to obtain an unbiased estimate of a variable in a population without necessarily testing every animal.

🔎 What this means:

A population is the whole group you care about.

A sample is the smaller group you actually measure.

⭐ 2. Q: What is the basic sequence from a population to a sample and back to a population?

Researchers define the source/target population, create a sampling frame, select a sample, collect observations, and then make inferences back to the population.

🔎 What this means:

The lecture gives this sequence:

population → sampling frame → selected sample → study participants/observations → inference back to population

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A sampling frame is the actual list or set of animals available to be sampled.

• Population = all 500 cows on a farm

• Sampling frame = list of those 500 cows and their ID numbers

• Sample = the 50 cows selected from that list

⭐ 3. Q: What characteristics make a sample useful for making inferences about a population?

Good sampling aims for representativeness, appropriate probability of selection, and independence between selections.

🔎 What this means:

Representativeness means the sample resembles the population you want to learn about.

Probability of selection refers to each animal's chance of being chosen.

Independence means selecting one animal should not automatically determine whether another animal gets selected.

These principles help the sample better reflect the population from which it came.

💡 Think: You want your sample to be a good mini-version of the population.

⭐ 4. Q: How do probability and non-probability sampling differ?

Probability sampling uses a random process to give animals a known chance of selection,

while non-probability sampling does not use random selection.

🔎 What this means:

With probability sampling, chance helps decide who enters the sample.

This is preferred when estimating things like disease prevalence because random selection helps reduce selection bias.

With non-probability sampling, subjects are selected another way. Sometimes that is the only realistic option, but the professor says you should try to approximate probability sampling as closely as possible.

The lecture specifically warns:

Convenience for the researcher is not by itself a valid reason to use non-probability sampling.

⭐ 5. Q: What types of probability and non-probability sampling are taught in this lecture?

You should be able to recognize these names and distinguish how the animals are selected.

Probability sampling includes:

• simple random

• systematic random

• stratified random

• cluster random

• multistage

Non-probability samping includes:

• consecutive

• convenience

• judgmental

⭐ 6. Q: What is simple random sampling, and what are its strengths and limitations?

In simple random sampling, every unit is listed in a sampling frame and a subset is selected randomly.

💡 Think: Put everyone in the hat, then draw names randomly.

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Suppose you have 30 calves and need to sample 12.

You:

1. Make a list of all 30 calves.

2. Assign each calf an ID.

3. Randomly select 12 IDs.

The advantage is that the random process helps avoid deliberately favoring certain animals.

But representativeness still depends on:

• having an accurate sampling frame;

• and successfully finding/enrolling the animals that were randomly chosen.

So random selection cannot help if your starting list itself is incomplete or inaccurate.

⭐ 7. Q: What is systematic random sampling, and what problem can occur with it?

Systematic random sampling randomly selects the first unit and then samples every xth individual, but natural periodic patterns can bias the sample.

🔎 What this means:

Example:

Randomly choose where to start, then sample every 10th cow.

The first animal needs to be randomly selected for this to count as probability sampling.

The danger is periodicity, meaning a repeating pattern in the population.

Imagine every 10th patient happens to be seen by the same clinician. If you sample every 10th patient, your sample may unintentionally contain mostly that clinician's patients.

Then the systematic pattern could make your sample unrepresentative.

💡 Think: Random start + every xth animal.

⭐ 8. Q: What is stratified random sampling, and when is it useful?

Stratified random sampling divides the population into meaningful subgroups called strata and then randomly samples within each subgroup.

• in other words, randomly selecting individuals within an already set up “group”

🔎 What this means:

A stratum is simply a subgroup.

You might divide animals according to:

• age

• sex

• breed

• production stage

• region

Then you randomly sample animals from each group.

For example, suppose a dairy herd contains:

• 20% high producers

• 48% moderate producers

• 10% low producers

• 22% dry cows

If you need 30 cows, the lecture recommends sampling the groups proportionately.

For high producers:

20% of 30 = 6 cows

Then randomly select those 6 from the high-producing group.

This prevents a major subgroup from accidentally being ignored or disproportionately represented.

💡 Think: Split into meaningful groups → randomly sample from every group.

⭐ 9. Q: How do cluster sampling and multistage sampling differ?

Cluster sampling randomly chooses whole natural groups and studies everyone within them,

• choose randomly once

while multistage sampling randomly chooses groups and then randomly samples individuals within those groups.

• choose randomly twice

🔎 What this means:

A cluster is a naturally occurring group, such as:

• a farm

• a pen

• a room

Suppose there are 100 farms.

Cluster sampling:

Randomly choose 10 farms → study all animals on those farms.

Multistage sampling:

Randomly choose 10 farms → then randomly choose some animals from each selected farm.

💡 Think:
Cluster = choose groups, take everybody.
Multistage = choose groups, then choose animals inside them.

⭐ 10. Q: What is consecutive sampling?

Consecutive sampling includes every accessible patient who meets the selection criteria during a defined sampling period.

🔎 What this means:

Suppose your hospital wants dogs with a particular disease.

Instead of randomly choosing dogs, you enroll:

every qualifying dog that presents during the study period.

One concern is time.

If disease occurrence changes by season or another temporal pattern, the sampling period needs to be long enough to account for that variation.

💡 Think: Every eligible patient, one after another.

This is a form on non-probability sampling

⭐ 11. Q: What is convenience sampling, and what is its main weakness?

Convenience sampling selects subjects that are easiest to access, which can produce a sample that does not represent the source or target population.

🔎 What this means:

Examples might include:

• animals easiest to catch;

• owners willing to participate;

• subjects physically easiest to access.

The problem is that easy to sample does not mean representative.

Imagine trying to estimate the average weight of pigs in a pen but only catching the calmest pigs near the gate. Those pigs may differ from the rest of the pen.

So convenience sampling can introduce selection bias.

⭐ 12. Q: What is judgmental sampling, and what is its main weakness?

Judgmental sampling intentionally selects subjects considered most appropriate for the study, but it can have the same representativeness problems as convenience sampling.

🔎 What this means:

Instead of selecting whoever is easiest, the researcher deliberately says:

“These subjects seem like the best ones to study.”

Examples from lecture include:

• farms with excellent records;

• owners willing to participate;

• animals with the most severe disease.

A farm with excellent records may give you very accurate information about that farm, but such farms might be systematically different from ordinary farms.

So the resulting sample may still not represent the larger population.

⭐ 13. Q: How can you distinguish consecutive, convenience, and judgmental sampling?

Consecutive sampling takes every eligible accessible subject,

convenience sampling takes subjects easiest to access, and

judgmental sampling takes subjects deliberately considered most appropriate.

⭐ 14. Q: What sampling approach should generally be used when estimating disease prevalence?

A probability sampling scheme should generally be used when estimating prevalence so the sample can provide an unbiased estimate of the population

15. Q: What are the two main sample-size questions taught in this Sampling lecture?

Question 1:

“What is the prevalence?”

You need enough animals to estimate the actual percentage with acceptable precision.

Question 2:

“Can I be reasonably confident the disease is below a certain prevalence?”

You choose enough animals that you would be likely to detect at least one positive if disease were present at or above your chosen minimum prevalence.

Sample-size calculations are used either to estimate disease prevalence or to determine whether disease is present or below a chosen prevalence threshold.

16. Q: What information determines sample size when estimating prevalence?

Estimating sample size requires expected prevalence, desired confidence, acceptable margin of error, and consideration of test sensitivity and specificity.

• These factors determine how many animals must be sampled to estimate population prevalence with the desired amount of confidence and precision.

Sample size = how many animals you need to test so that your prevalence estimate is trustworthy enough for the amount of certainty and precision you want.

🔎 What this means:

The lecture identifies:

• p = expected true prevalence

• Z = reliability/confidence coefficient

• L = maximum tolerable error

• Se = sensitivity

• Sp = specificity

Smaller allowed error → generally need a larger sample.

More confidence → generally need a larger sample.

For example, estimating a prevalence of 20% with an allowed error of ±5% means you want an estimate roughly within 15–25%.

In general:

• wanting a smaller margin of error requires more animals

• wanting greater confidence requires more animals

The exact formula is not something you need to memorize.

💡 Think: The more certain and precise you want your answer to be, the more animals you generally need to sample.

⭐ 17. Q: Why can sampling usually not prove that a disease is completely absent?

To be completely certain disease is absent, every animal would have to be tested with a perfect diagnostic test, which the lecture says is not realistically achievable.

⭐ 18. Q: What information is needed to determine a sample size for detecting disease?

Disease-detection sampling uses a minimum expected prevalence, desired confidence level, population size, and diagnostic-test accuracy.

🔎 What this means:

The question is:

“If disease really exists at or above this minimum prevalence, how many animals must I test to have a good chance of detecting at least one positive?”

The lecture lists:

• p = minimum true prevalence

• confidence level

• N = population size

• Se and Sp = sensitivity and specificity

⭐ 19. Q: What does the disease-detection sample-size equation calculate, and do you need to memorize it?

The disease-detection equation calculates how many animals must be sampled to detect at least one truly positive animal at a chosen prevalence and confidence level, but the professor explicitly says the formula does not need to be memorized.

🔎 What this means:

You should understand the ingredients rather than memorize the whole equation.

Important symbols in the lecture are:

• n = required sample size

• N = population size

• D = estimated number of diseased animals

• C = desired confidence

First:

D = population size × minimum expected prevalence

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Example:

A veterinarian wants to know whether a disease is present in a herd of 200 animals.

The veterinarian decides:

• If the disease is present, they expect at least 10% prevalence

• They want to be 95% confident

• Assume the diagnostic test is perfect

200 animals × 10% expected prevalence:

D = 200 × 0.10 = 20 diseased animals expected

• N = 200

• D = 20

• C = 0.95

• The result is:

  n = 26.5 ≈ 27 animals

  So you need to test approximately:

  27 animals

💡 Think: Know what goes into the equation and what the answer means, not the ugly equation itself.

⭐ 21. Q: How should you interpret an all-negative sample in disease-detection sampling?

If all sampled animals test negative, you can be confident that disease prevalence is below the predetermined cutoff, but you cannot conclude that disease is completely absent.

🔎 What this means:

The sample size is chosen so that if disease prevalence were at or above the cutoff, you would have a high chance of finding at least one positive animal.

For example, with a 10% cutoff and 95% confidence:

• 0 positives → 95% confident prevalence is <10%

• this does not mean prevalence is 0%

💡 Think:
No positives = “probably below my cutoff,” not “definitely disease-free.”

22. Q: What happens to disease-detection sample-size calculations when diagnostic tests are imperfect?

Imperfect sensitivity and specificity make disease-detection calculations more complicated, so the lecture uses specialized software for those situations.

🔎 What this means:

If the test can produce:

• false negatives, or

• false positives,

then “all negative” or “one positive” becomes harder to interpret.

The lecture uses perfect tests for the basic calculations and mentions FreeCalc for calculations involving imperfect sensitivity and specificity.

The takeaway is the logic of confidence and prevalence thresholds, not memorizing the complicated imperfect-test calculations.

23. Q: Which statement correctly describes judgmental sampling?

A. A random subset of the population is selected.
B. Every xth subject is selected.
C. Subjects are randomly sampled within subgroups.
D. The accessible population considered most appropriate is selected.
E. Every eligible patient is taken over a time period.

D. Judgmental sampling selects subjects considered most appropriate for the study.

24. Q: Which statement correctly describes systematic random sampling?

A. A random subset is selected.
B. Subjects are selected periodically, such as every xth individual.
C. Subjects are randomly selected within subgroups.
D. Natural groups are randomly selected.
E. Every eligible patient is taken during a period.

B. Systematic random sampling selects subjects through a periodic process such as every xth individual.