OBJ - Descriptive Stats

Question 1

Qualitative Scales of Measurement

Answer 1

Categories: Nominal or Ordinal

NOMINAL – no ordering/ranking – just categories
• Names or labels. Numbers, if present, act as labels
• Blood group: A, B, AB, O

ORDINAL - Natural ranking present (differences/spacing between categories, unclear)
• Tumor stage (1-4)

Question 2

Quantitative Scales of Measurement

Answer 2

Numbers: Continuous or Discrete

COUNT/DISCRETE = Numeric but can only take on specific values
• Number of seizures in a given month

CONTINUOUS = Measured or numerical data that can (in theory) take on any value
• Body mass index (kg/m2); BP, HR, etc

Question 3

Summarizing Qualitative Medical Dat

Answer 3

Categories

1) Count = Number of cases
2) Proportion = Count in category / total count
3) Percentage = 100 x proportion
4) Ratio = Count in category A / count in category B
5) Rate = Proportion per period time
6) Odds = Proportion / (1- proportion)

Question 4

Representations/Displaying Quantitative Data

Answer 4

Continuous Data

1) Histogram
2) Box plot (concisely displays Max, Min, 75th%, 25th%, median & **outliers)

Ordinal Data

1) Pie Graph
2) Bar Chart

Question 5

Summarizing Quantitative Medical Data

Answer 5

Numbers

1) Mean – Arithmetic average (sum / sample size)
2) Median – Middle value of sorted data
3) Mode – Most frequent value
4) Geometric mean – Nth root of the product of the data (Money or titers and other data expressed as powers)

Question 6

Spread of Variability

Answer 6

How far apart are the data are from each other

1) Range – Maximum – minimum
2) Interquartile range – 75th percentile – 25th percentile (central 50% of data)

3) Variance – Average squared deviation from the mean
Σ ( X – mean(X))2 / (n - 1)

4) Standard deviation	– Square root of variance
      √ [Σ ( X – mean(X))2 / (n - 1)]
1 STDDEV = 68%	
2 STDDEV = 95%
3 STDDEV = 98%
Good if		
- Sample size is large
- Distribution has (single peak)
- Distribution is symmetric

5) Coefficient of variation = Standard deviation / mean (x 100%)

Report 
- BOTH location and spread
- Report corresponding measures of location and spread
Mean + standard deviation
Median + range or interquartile range

Question 7

Gaussian Distributions

Answer 7

• Bell-shaped
• σ = standard deviation
• μ = mean ( = median = mode)
• Total area under curve equal 1
• Extends to infinity in both directions
• Probability corresponds to area under the curve
• Completely described if two parameters (μ, σ) known
• Also called “Z” distribution (z = 1.5 ~ z = 1.5 std deviations from mean)
• Probabilities (areas under the curve) are tabled in most texts (Campbell table T1) – probability of BOTH tails
• Reference range if not clarified is 95%

Question 8

Sources of Variation

Answer 8

Biologic variation

• Between-individual: two individuals have different values
• Within-individual: same individual measured twice has different values

Measurement variation

• Between-observer: two observers obtain different values when they measure the same thing
• Within-observer: same observer obtains different values when measuring the same thing twice

Instrument or analytical error
- Different equipment yields different values when measuring the same thing

Question 9

Sources of Variability

Answer 9

• Reliability (Precise – to each other)
• Random error
• Measurements close to each other
• Validity (Accuracy – to “target”)
• Systematic error
• Measurements close to the true value