Japan Statistical Society Certificate (Toukei Kentei)

Japan · Japan Statistical Society (certificate operated with the Japan Statistical Association) · professional

54practice questions written to this syllabus
1subjects

Format

Graded certificate exams; the graded levels are mostly computer-based.

Sections

Over the years

Grade list read on the certificate site. Contents and formats per grade were not read.

Official source: https://www.toukei-kentei.jp/about/

Subjects this exam draws on

Exploratory Data Analysis & Statistical Graphics54 questions

Five practice questions, worked

Original questions written to this exam's published syllabus and pattern. Not past papers.

1. For which variable is the coefficient of variation a meaningful summary?

  1. Milk yield per cow in litres per day
  2. Air temperature in degrees Celsius
  3. Calendar date of sowing
  4. Soil series coded 1 to 6
Answer and working

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.

Exploratory Data Analysis & Statistical Graphics · Types of data and measurement scales

2. Plot yields have Q₁ = 2.8 and Q₃ = 3.6 t/ha. Where is Tukey's upper inner fence?

  1. 4.8 t/ha
  2. 1.6 t/ha
  3. 6.0 t/ha
  4. 4.4 t/ha
Answer and working

A. 4.8 t/ha

IQR = 0.8; upper inner fence = Q₃ + 1.5 IQR = 3.6 + 1.2 = 4.8. 6.0 is the outer fence (3 IQR); 1.6 is the lower inner fence; measuring from the median (3.2) gives 4.4.

Exploratory Data Analysis & Statistical Graphics · Five-number summaries, box plots and robust statistics (median, MAD, trimmed means)

3. A sample of 1,000 plant heights has IQR 4.0 cm. What bin width does the Freedman-Diaconis rule suggest?

  1. 0.80 cm
  2. 0.40 cm
  3. 8.00 cm
  4. 1.39 cm
Answer and working

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.

Exploratory Data Analysis & Statistical Graphics · Histograms, density estimates and quantile-quantile plots

4. A kernel density estimate of germination percentages shows positive density below 0% and above 100%. What causes this?

  1. The bandwidth was chosen too small for the data
  2. Kernels near a natural boundary leak probability across it
  3. Germination data are always bimodal, with peaks at exactly 0% and 100%
  4. The Gaussian kernel cannot be used for continuous percentage data at all
Answer and working

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.

Exploratory Data Analysis & Statistical Graphics · Histograms, density estimates and quantile-quantile plots

5. Across all regions, fertiliser use and yield are negatively related, but within every region the relation is positive. What is this called?

  1. Regression to the mean
  2. Simpson's paradox
  3. Masking
  4. Heteroscedasticity
Answer and working

B. Simpson's paradox

A relation that reverses when groups are pooled is Simpson's paradox, here because regions differ in both baseline yield and fertiliser use. Plotting by group (colour or small multiples) reveals it.

Exploratory Data Analysis & Statistical Graphics · Scatterplots, smoothing (LOESS) and scatterplot matrices

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