SSC CGL Statistics – Analysis of Variance – Level 3 · Challenge

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SSC CGL Statistics – Analysis of Variance – Level 3 · Challenge – 8 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
Groups of unequal size: A (3, 5, 4), B (6, 8, 7, 7), C (9, 10, 11). The one-way F ratio is:

Correct Answer: A [31.5]

Explanation:

G = 70, N = 10, CF = 490; SSB = 12²/3 + 28²/4 + 30²/3 − 490 = 54; SSE = 2 + 2 + 2 = 6; F = (54/2)/(6/7) = 31.5.

2.  
Four group means are compared by all possible pairwise tests, each at 5%. If the tests were independent, the chance of at least one false 'significant' result is about:

Correct Answer: C [0.2649]

Explanation:

⁴C₂ = 6 tests: 1 − 0.95⁶ ≈ 0.2649.

3.  
A two-way ANOVA with 3 rows, 4 columns and 2 observations in every cell has how many degrees of freedom for error (within cells)?

Correct Answer: A [12]

Explanation:

rc(m − 1) = 3 × 4 × 1 = 12; interaction takes (r − 1)(c − 1) = 6.

4.  
Statement-basedIn one-way ANOVA, which of these is/are true?
I. MSE is an unbiased estimate of σ² whether or not H₀ is true.
II. MSB is an unbiased estimate of σ² only when H₀ is true.
III. A large F supports H₀.

Correct Answer: B [Only I and II]

Explanation:

I and II are true. III is false: a large F means MSB is inflated by real differences – evidence against H₀.

5.  
A one-way ANOVA gives F = 0.62. The best interpretation is:

Correct Answer: D [No evidence of differences among treatment means]

Explanation:

F below 1 simply means the between-group variation is no larger than chance variation.

6.  
Reverse questionIn a one-way ANOVA with k = 3 groups of 6 each, MSE = 5 and F = 4. The between-groups SS is:

Correct Answer: A [40]

Explanation:

MSB = 4 × 5 = 20; SSB = 20 × (k − 1) = 40.

7.  
Arrange in orderArrange the steps of a one-way ANOVA by the correction-factor method in order:
(i) MSB and MSE (ii) CF = G²/N (iii) SSB from totals and SSE by subtraction (iv) TSS = Σx² − CF (v) F ratio

Correct Answer: D [(ii), (iv), (iii), (i), (v)]

Explanation:

CF first, then TSS, SSB, SSE, mean squares, F.

8.  
All observations in an experiment are divided by 5 (a change of unit). The error sum of squares becomes:

Correct Answer: B [1/25 of the old value]

Explanation:

Each deviation ÷ 5, so each square ÷ 25; F is unchanged.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics

📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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