SAS statistical certifications (Statistical Business Analyst, Applied Statistics Associate, Statistics for Machine Learning) · USA / global · SAS Institute
Original practice questions written to the published syllabus · not past papersLooking at data before modelling it: summaries, robust statistics, graphs that show distributions and relationships honestly, outlier detection, and the tidy-data and reporting habits that make an analysis checkable. Deliberately practical and software-based.
In the exams: Not an explicit unit in the catalogued exams; programme course and the daily practice of every role in the ladder. GATE DA data handling (present)
How our questions for SAS statistical certifications spread across the units of Exploratory Data Analysis & Statistical Graphics. Difficulty: 12 easy, 29 medium, 13 hard.
| Histograms, density estimates and quantile-quantile plots | 9 | |
| Scatterplots, smoothing (LOESS) and scatterplot matrices | 9 | |
| Graphical perception and honest chart design | 8 | |
| Five-number summaries, box plots and robust statistics (median, MAD, trimmed means) | 7 | |
| Outliers and influential observations | 7 | |
| Transformations to symmetry and constant variance | 6 | |
| Tidy data: variables, observations and tables | 5 | |
| Types of data and measurement scales | 2 | |
| Tables for reports and publications | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
For which variable is the coefficient of variation a meaningful summary?
A. Milk yield per cow in litres per day
The CV divides the SD by the mean, which is meaningful only on a ratio scale with a true zero. With Celsius or dates, moving the zero changes the CV arbitrarily; codes for soil series are nominal.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
A sample of 1,000 plant heights has IQR 4.0 cm. What bin width does the Freedman-Diaconis rule suggest?
A. 0.80 cm
h = 2 IQR n^(−1/3) = 2 × 4.0 × 1000^(−1/3) = 8.0/10 = 0.80 cm. 8.00 omits the n^(−1/3) factor; 0.40 omits the factor 2.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
Silverman's rule of thumb is h = 0.9 min(s, IQR/1.34) n^(−1/5). For n = 256, s = 2.0 and IQR = 2.4, what is h?
B. 0.532
IQR/1.34 = 1.791 < 2.0, so min = 1.791; 256^(−1/5) = 0.3299; h = 0.9 × 1.791 × 0.3299 = 0.532. Using s instead of the minimum gives 0.594.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
A kernel density estimate of germination percentages shows positive density below 0% and above 100%. What causes this?
B. Kernels near a natural boundary leak probability across it
Each kernel spreads mass on both sides of its observation, so values near 0 or 100 spill over the boundary. Boundary corrections or estimating on a transformed scale (logit) avoid it.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
In a sample of 5 observations, what is the largest possible absolute z-score, (x − x̄)/s, using s with divisor n − 1?
B. 1.79
The bound is (n − 1)/√n = 4/√5 = 1.79. So in small samples a |z| > 3 rule can never flag anything: an extreme value inflates the s that defines its own z (masking). 2.24 is √5.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
Seven yields have median 3.4 t/ha and MAD 0.2 t/ha. What is the modified z-score of a yield of 8.9 t/ha?
C. 18.55
Mᵢ = 0.6745 (8.9 − 3.4)/0.2 = 0.6745 × 27.5 = 18.55, far above the 3.5 flag. 27.50 omits the 0.6745 constant; 3.50 is the flagging threshold itself.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
What is the Box-Cox transformation when λ = 0?
D. log y
y(λ) = (y^λ − 1)/λ tends to log y as λ → 0, which is why the log occupies the zero place on the ladder.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
According to Cleveland and McGill, which visual encoding is read most accurately?
B. Position on a common scale
Their ranking runs from position on a common scale, through non-aligned position, length, angle and area, to volume and colour. This is why dot and bar charts beat pie and bubble charts.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
Which chart is least accurate for comparing the shares of 9 crops that each occupy 9% to 14% of a region's area?
D. A pie chart
Small differences in angle and area are hard to judge. A sorted dot or bar chart puts the shares on a common scale, where differences of a percentage point are visible.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
When is a table preferable to a graph?
D. When readers need to look up exact values
Tables serve look-up of precise numbers; graphs show patterns, trends, shapes and relations better. Many reports pair a graph for the message with a table for the record.
Further reading: Tukey, Exploratory Data Analysis; Cleveland, Visualizing Data; Wickham, Tidy Data; Tufte, The Visual Display of Quantitative Information
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