(4) EBVM/Epi: Measurement Properties, Summary Statistics

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⭐ 1. Q: What is the difference between a variable and a value?

A variable is a characteristic being measured or recorded, while a value is one possible result for that characteristic.

🔎 What this means:

Think of the variable as the question or column heading.

If the variable is dog breed, the values might be Labrador, Malinois, or Dachshund.

If the variable is weight, the values might be 11 kg, 39 kg, or 53 kg.

💡 Think: Variable = what changes. Value = what you actually observed.

2. Q: How do subjective and objective data differ?

Subjective data depends on observations or judgement without a direct measuring instrument,

while objective data are measurable or countable findings.

🔎 What this means:

Subjective: you assess it without a direct measuring instrument.

• lameness score

• pain score

• body condition score

• attitude

Objective: you actually measure or count it.

• temperature

• weight

• heart rate

• blood glucose

⭐ 3. Q: What is a measurement scale, and why does it matter?

A measurement scale describes the type of data a variable contains and how its values can be compared, which determines appropriate graphs and statistical analyses.

🔎 What this means:

Before doing statistics, ask:

“What kind of data am I working with?”

The three main scales in this course are:

• Nominal

• Ordinal

• Continuous

Once you know the scale, you can decide how the data should be summarized and analyzed.

💡 Think: Measurement scale = the type of your data.
———————————————————————

Example:
Variable = Dog breed
What measurement scale does “dog breed” use? Nominal

Why? Because the values are different categories with no natural order

⭐ 4. Q: How do nominal, ordinal, and continuous data differ?

Nominal: categories with no order

• Categories only

• No natural order.

• Example: breed or color, because you cannont meaningfully put them in order from lowest to highest

Ordinal: categories that have order

• Categories have an order, aka you can meaningfully put the values from low to high

• Gaps between categories are not assumed equal.

• Example: body condition or lameness score, because you can rank BCS from low to high

Continuous: meaningful equal intervals btwn values

• Numerical values are ordered.

• The difference between numbers has a consistent meaning. Numerical differences are uniform across the scale; for example, a 5-year difference from age 10 to 15 means the same amount as a 5-year difference from 50 to 55.

• Example: weight, age

---

💡 Think:
Nominal = names.
Ordinal = ordered categories.
Continuous = measured numbers.

5. Q: How do interval and ratio continuous data differ?

5. Q: What are interval and ratio continuous data and how do they differ?

Interval and ratio data are two types of continuous numerical data with equal, meaningful gaps between values; ratio data have a true zero, while interval data do not.

For example, a difference of 10 units means the same amount anywhere on the scale.

The difference is what zero means:

Interval data

• Zero is just a point on the scale.

• Zero does not mean the thing being measured is completely absent.

• Example: temperature in °F

  • 0°F is still a temperature.

  • You cannot say 80°F is “twice as hot” as 40°F. Because for something to truly be “twice as much” the scale needs a true zero

  • 40°F to 80°F means that the temperature increased by 40°F, not that it became twice as much

Ratio data

• Zero means a true absence of the measured quantity.

• Example: weight

  • 0 kg means no weight.

  • 20 kg really is twice the weight of 10 kg.

Ask: “Does zero actually mean NONE of this thing?”
Yes → ratio
No → interval.

6. Q: What do “all-inclusive” and “mutually exclusive” mean for categorical data?

All-inclusive means every possible observation has a category, while mutually exclusive means each observation can belong to only one category.

🔎 What this means:

All-inclusive: nobody gets left without a category.

Mutually exclusive: nobody can fit into two categories at once.

These rules apply to both nominal and ordinal data

7. Q: What happens when continuous data are converted into categories?

Categorizing continuous data loses information and can reduce statistical power.

🔎 What this means:

Imagine age is recorded exactly.

Ages 1 year and 29 years are very different.

If you turn both into one category called “young,” that difference disappears.

The lecture says this loss of information can decrease statistical power, meaning the ability to detect a real difference when one exists.

⭐ 8. Q: What is a frequency distribution?

A frequency distribution shows how often different values or groups of values occur in a dataset.

🔎 What this means:

For continuous data, values are often placed into bins, meaning ranges such as:

• 5–9.9 kg

• 10–14.9 kg

• 15–19.9 kg

Then you count how many observations fall into each bin and display them in a histogram.

Putting continuous values into bins does not turn the original variable into ordinal data.

⭐ 9. Q: What is central tendency and dispersion and what is the difference between them?

They are summary statistics

Central tendency describes the center or typical value of a dataset, while dispersion describes how spread out the values are.

🔎 What this means:

Central tendency: “Where is the middle?”

• mean

• median

Dispersion: “How spread out are the observations?”

• standard deviation

• range

• interquartile range IQR

yes memorize this

⭐ 10. Q: How do the mean and median differ?

The mean is the sum of all observations divided by the number of observations, while the median is the middle value after the data are ordered.

🔎 What this means:

Mean: ordinary mathematical average.

Median: value sitting in the middle.

The median is especially helpful when extreme values pull the mean away from the center.

11. Q: What does standard deviation describe, and what is variance?

Standard deviation describes how much observations tend to vary around the center, while variance is the standard deviation squared.

🔎 What this means:

A small standard deviation means observations are relatively tightly clustered.

A large standard deviation means they are more spread out.

The lecture uses standard deviation primarily for normally distributed continuous data

⭐ 12. Q: Which summary statistics should be used for normal continuous, skewed continuous, ordinal, and nominal data?

Normal continuous data use mean and standard deviation; skewed continuous and ordinal data use median with IQR or range; nominal data use frequencies.

🔎 What this means:

Normal continuous: bell shape

• Mean

• Standard deviation

• Confidence intervals

Skewed continuous: values are not distributed symmetrically.

• Median, because the skewed values can skew the mean

• IQR, percentile range, or range

Ordinal: ordered categories, like BCS

• Median

• IQR or range

• Because we can’t tell the exact biological difference between the numbers, so calculating a mean would be misleading

Nominal: categories with no order

• Frequencies

13. Q: How do the mean and median behave in right- and left-skewed distributions?

In a right-skewed distribution the mean is greater than the median (right tail pulls mean to the right), while in a left-skewed distribution the mean is less than the median (left tail pulls mean to the left)

🔎 What this means:

The long tail pulls the mean toward it.

Therefore:

• long tail to the right → mean pulled right

• long tail to the left → mean pulled left

For skewed data, the professor recommends using the median rather than the mean

⭐ 14. Q: What are the range, interquartile range, and percentile range?

The range spans the minimum to maximum, the IQR spans Q1 to Q3, and a percentile range spans two selected percentiles.

🔎 What this means:

Range: maximum minus minimum.

Interquartile range (IQR):

• from the first quartile, Q1

• to the third quartile, Q3

• contains the middle 50% of observations

Percentile range: the observations between chosen percentiles, such as the 5th and 95th percentile.

⭐ 15. Q: What is a confidence interval, and what does its width tell you?

A confidence interval is a range around an estimate that expresses uncertainty about the true population value; narrower intervals indicate greater precision.

🔎 What this means:

The lecture's formal interpretation of a 95% CI is:

If the sampling procedure were repeated many times, about 95% of the calculated intervals would contain the true population mean.

Higher confidence requires a wider interval:

99% CI is wider than 95%, which is wider than 90%.

💡 Think: Narrow CI = more precise estimate.

⭐ 16. Q: How do a ratio and a proportion differ?

A ratio compares one count with another, while a proportion compares a part with the entire group.

🔎 What this means:

If:

• 5 pigs cough

• 45 do not cough

A ratio compares coughing pigs with non-coughing pigs.

• 5 coughing pigs : 45 non-coughing pigs

• so 1:9

• coughing : non-coughing

A proportion asks:

“What fraction of all 50 pigs cough?”

• 5 coughing / 50 total pigs

• Proportion is 10%

Ratio = part compared to another part
Proportion = part compared to the whole

17. Q: What is a dangling numerator?

A dangling numerator is a count reported without the total population or denominator needed to interpret it.

• A numerator is just the top number in a fraction

• A dangling numerator is when someone gives you only the numerator but not the demoninator

  • ex: There were 5 coughing pigs

  • but 5 of how many??😭

• Therefore the “dangling” term

🔎 What this means:

“5 coughing pigs” means very little by itself.

• 5 out of 50 = 10%

• 5 out of 100 = 5%

Same numerator, very different frequency.

⭐ 18. Q: How do prevalence and incidence risk differ?

Prevalence measures all current cases at a particular time, while incidence risk measures new cases developing over a period of time among initially disease-free animals.

🔎 What this means:

Prevalence = who has it now?

It includes both old and newly present cases.

Incidence risk = who develops it?

Everyone must start without the condition, and you follow them through a specified period.

💡 Think:

Prevalence = snapshot.

Incidence = new cases over time.

⭐ 19. Q: How does this course use the terms accuracy and validity?

For this course, accuracy and validity can essentially be treated as synonyms describing how truthful or correct a study's result is.

🔎 What this means:

Validity asks:

“Can I trust this study's answer to be close to the truth?”

💡 Think: Validity/accuracy = the true/right answer.

⭐ 20. Q: How are systematic error, bias, and validity related?

Systematic error produces bias, so increasing systematic error lowers study validity.

🔎 What this means:

A systematic error is a built-in problem that repeatedly pushes results away from the truth.

Because the problem has a consistent direction, simply collecting more animals does not remove it.

The lecture specifically states that bias reduces validity.

💡 Think: Systematic problem → biased answer → lower validity.

⭐ 21. Q: How does this course use the terms precision and reliability?

Precision and reliability describe how consistently repeated measurements produce similar results. In this lecture, treat them as the same term

🔎 What this means:

Reliability asks:

“If I measure this again, do I keep getting approximately the same answer?”

It includes ideas such as:

• repeatability

• reproducibility

• observer consistency

• instrument consistency

💡 Think: Reliability/precision = same answer.

⭐ 22. Q: How does random error affect precision, and how can sample size help?

More random error decreases precision, while a larger sample can reduce the influence of random error by allowing unusually high and low values to balance out.

🔎 What this means:

Random error creates unpredictable scatter.

Some observations end up too high and others too low.

With more observations, those random deviations tend to balance better.

This improves precision, but it does not fix systematic error or validity.

⭐ 24. Q: How do internal and external validity differ?

Internal validity asks whether the results are trustworthy within the study/source population, while external validity asks whether the findings can be generalized to a target population.

27. Q: What are important ways selection bias can occur?

Selection bias can occur through biased initial selection, unequal loss to follow-up, or nonresponse/volunteer effects.

What this means:

Pig example: the first pigs caught may already be bigger, healthier, or more dominant, so treatment groups differ before treatment begins.

Loss to follow-up: animals that disappear, die, or are culled may differ systematically from animals remaining in the study.

Nonresponse: people who answer a survey may differ from those who refuse to answer. A higher response rate reduces this problem.

28. Q: What forms can information bias take?

Information bias is systematic error in measuring or classifying variables and can include instrument, recall/reporting, or investigator bias.

🔎 What this means:

Instrument bias: the tool consistently gives wrong measurements.

Recall bias: subjects remember past events inaccurately.

Reporting bias: groups differ in what or how accurately they report.

Investigator bias: the researcher's expectations affect interpretation; blinding can reduce it.

⭐ 30. Q: How should you assess whether a study is generalizable?

Compare the source and study populations with the target population and ask whether important differences could make the results apply poorly.

🔎 What this means:

Differences could include:

• region,

• breed,

• hospital setting,

• management,

• environment.

If the source population is very different from the population you care about, external validity is lower.

31. Q: Why can enrolling animals from multiple diverse farms improve generalizability?

Multiple diverse farms improve generalizability because they represent a wider range of management systems, locations, and populations, not simply because sample size is larger.

🔎 What this means:

More variety of sources can make the study population look more like the larger target population.

Simply adding more animals from the same narrow source does not automatically improve external validity.

⭐ 33. Q: What should you consider when appraising whether a scientific paper is useful?

Consider the study design, internal validity and bias, and whether the results are generalizable to the population or patient you care about.

🔎 What this means:

Ask:

1. Was the study design appropriate for the question?

2. Can I trust the results?

• selection bias?

• information bias?

• confounding?

3. Do the results apply to my patient or population?

The notes emphasize evaluating how subjects were selected, how exposures/outcomes were measured, and where bias may have been introduced.

⭐ 43. Q: What does statistical significance mean in this course?

In these course notes, p < 0.05 is treated as statistically significant, while p ≥ 0.05 is treated as not statistically significant.

🔎 What this means:

A small enough p-value gives evidence against H₀ according to the course's chosen cutoff.

Your friend's study guide explicitly uses:

p < 0.05 → statistically significant

p ≥ 0.05 → not statistically significant

45. Q: When a study has high validity, which statement is correct?

A. Systematic error is high
B. Systematic error is low
C. Bias is high
D. Bias is very high

B. Systematic error is low.

🔎 What this means:

High validity means little systematic error and therefore relatively little bias.

46. Q: Precision is associated with which type of error?

A. Systematic error
B. Random error
C. Bias
D. None of the above

B. Precision is associated with random error

47. Q: Study validity is related to which type of error?

A. Random error
B. Systematic error
C. No error
D. Both random and systematic error
E. Validity is unimportant

B. Study validity is related to systematic error

51. Q: Dogs with pancreatitis and control dogs without pancreatitis are enrolled, and past dietary exposures are obtained from medical records. What study design is this?

A. RCT
B. Case-control
C. Cohort

B. This is a case-control study.

🔎 What this means:

Researchers begin with the outcome — pancreatitis versus control — and then look backward for previous dietary exposures. Measurement Properties 3- 2026(…

52. Q: What measurement scale is Body Condition Score?

Body Condition Score is ordinal.

🔎 What this means:

BCS values can be ranked, but the distance between neighboring scores is not assumed to be equal.

53. Q: Is it appropriate to calculate the mean and standard deviation for Body Condition Score?

No, because Body Condition Score is ordinal data.

🔎 What this means:

The numbers represent ordered categories rather than equally spaced measurements, so mean and standard deviation are not the recommended summaries.

54. Q: What measure of central tendency is appropriate for Body Condition Score?

The median is appropriate for ordinal Body Condition Score data.

55. Q: What measurement scale is locomotion score?

Locomotion score is ordinal.

🔎 What this means:

The scores progress in severity from normal toward severely lame, but equal numerical gaps between scores are not assumed.

56. Q: What measurement scale is the diarrhea score shown in the lecture?

The diarrhea score is ordinal.

🔎 What this means:

The categories have a natural progression from less severe to more severe stool changes, but they are not equal-interval measurements

57. Q: In the right-skewed BHBA frequency distribution, which is higher: the mean or median?

The mean is higher than the median.

🔎 What this means:

The long right tail pulls the mean upward.

59. Q: What is the median of {1, 2, 2, 3, 3, 3, 4, 4, 5}?

The median is 3.

60. Q: What is the range of {1, 2, 2, 3, 3, 3, 4, 4, 5}?

The range is 4.

🔎 What this means:

Maximum minus minimum is 5 minus 1.