SSC CGL Statistics – Analysis of Variance – Level 2 · Exam Level · Paper II Sprint

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SSC CGL Statistics – Analysis of Variance – Level 2 · Exam Level · Paper II Sprint – 15 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.  
Three groups: (3, 5, 7), (8, 10, 12), (4, 6, 8). The one-way ANOVA F ratio is:

Correct Answer: A [21/4 = 5.25]

Explanation:

Means 5, 10, 6; grand mean 7; SSB = 3(4 + 9 + 1) = 42, SSE = 8 + 8 + 8 = 24; F = (42/2)/(24/6) = 21/4 = 5.25.

2.  
TSS = 120 and SSB = 48 for k = 4 groups and N = 16 observations. The F ratio is:

Correct Answer: B [8/3 ≈ 2.67]

Explanation:

MSB = 48/3 = 16; SSE = 72, MSE = 72/12 = 6; F = 16/6 ≈ 2.67.

3.  
Reverse questionAn ANOVA table shows treatment df 3, error df 20, MS treatment 18 and F = 4.5. The error sum of squares is:

Correct Answer: D [80]

Explanation:

MSE = 18/4.5 = 4; SSE = 4 × 20 = 80.

4.  
A one-way ANOVA gives F = 3.10 with (2, 12) df. The 5% table value is 3.89. The conclusion is:

Correct Answer: C [Do not reject H₀ – the means do not differ significantly]

Explanation:

Answer: Do not reject H₀ – the means do not differ significantly. 3.10 < 3.89.

5.  
Two-quantity comparison
Quantity I: error df in a one-way ANOVA with k = 4 and N = 24
Quantity II: error df in a two-way ANOVA (one observation per cell) with a 5 × 6 table

Correct Answer: C [Quantity I = Quantity II]

Explanation:

QI = 24 − 4 = 20; QII = 4 × 5 = 20.

6.  
Assertion–Reason
A: With only two groups, the one-way ANOVA F equals the square of the pooled two-sample t.
R: F with (1, ν) df is the square of t with ν df.

Correct Answer: D [Both A and R are true and R explains A]

Explanation:

For two groups MSB/MSE = (x̄₁ − x̄₂)²/[sₚ²(1/n₁ + 1/n₂)] = t², and t²(ν) has the F(1, ν) distribution – so both tests give the same decision.

7.  
Trick SpotterGroup totals are known. The quickest way to get the between-groups SS is:

Correct Answer: B [ΣTᵢ²/nᵢ − G²/N]

Explanation:

The CF route uses only totals; Σx² − CF is the TOTAL SS.

8.  
Spot My Mistake“k = 5 treatments, N = 30 observations, so the error df = N − 1 = 29.” The correct error df is:

Correct Answer: A [25]

Explanation:

Error df = N − k = 25; N − 1 = 29 is the TOTAL df.

9.  
Observations are 503, 507, 512, … . An analyst subtracts 500 from every value before the ANOVA. The effect on SS and F is:

Correct Answer: A [No change in any SS or in F]

Explanation:

A shift changes the CF and Σx² equally – every SS and F stay the same.

10.  
Two-way ANOVA (4 rows × 4 columns, one observation per cell): SS rows = 30, SS columns = 45, SS error = 12. The F ratio for rows is:

Correct Answer: B [7.5]

Explanation:

MSR = 30/3 = 10; MSE = 12/9 = 4/3; F = 10/(4/3) = 7.5.

11.  
To compare 6 group means with separate two-sample t tests, how many tests would be needed?

Correct Answer: D [15]

Explanation:

⁶C₂ = 15 – one reason to use one ANOVA instead.

12.  
Three groups of 6 observations have variances 5, 7 and 9 (divisor n − 1). The mean square error of the one-way ANOVA is:

Correct Answer: C [7]

Explanation:

SSE = 5(5 + 7 + 9) = 105; df = 18 − 3 = 15; MSE = 7 (the pooled variance).

13.  
Three groups of 5 observations have means 10, 12 and 14. The between-groups sum of squares is:

Correct Answer: B [40]

Explanation:

Grand mean 12: SSB = 5[(−2)² + 0 + 2²] = 40.

14.  
In a two-way ANOVA with one observation per cell, which sum of squares is normally found by subtraction?

Correct Answer: D [Error (residual) SS]

Explanation:

SSE = TSS − SSR − SSC; the others come directly from totals and Σx².

15.  
Diagram-basedBoth panels have the same two group means.

Which panel gives the larger one-way ANOVA F ratio?

Correct Answer: C [Panel X]

Explanation:

Same between-group SS, but Panel X has much smaller within-group spread (F = 37.5 against 1.5).

➤ 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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