SSC CGL Statistics – Analysis of Variance – Level 1 · Warm-up

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SSC CGL Statistics – Analysis of Variance – Level 1 · Warm-up – 12 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.  
One-way analysis of variance is used to test the equality of:

Correct Answer: A [Several population means]

Explanation:

ANOVA compares k means at once by comparing two variance estimates.

2.  
In a one-way ANOVA with 5 treatments and 30 observations in all, the error (within) degrees of freedom are:

Correct Answer: D [25]

Explanation:

Answer: 25. N − k = 30 − 5 = 25.

3.  
The F ratio in one-way ANOVA is:

Correct Answer: B [Mean square between ÷ mean square within]

Explanation:

F = MSB/MSE – mean squares, not sums of squares.

4.  
In a two-way ANOVA with one observation per cell for a 4 × 5 table, the error degrees of freedom are:

Correct Answer: C [12]

Explanation:

Answer: 12. (r − 1)(c − 1) = 3 × 4 = 12.

5.  
Which of these is NOT an assumption of one-way ANOVA?

Correct Answer: C [Equal sample sizes in all groups]

Explanation:

Groups may have different sizes; normality, independence and equal variances are assumed.

6.  
In a one-way ANOVA, SS between = 40 and SS within = 60. The total SS is:

Correct Answer: A [100]

Explanation:

Answer: 100. TSS = SSB + SSE = 100.

7.  
SS within = 48 with 16 degrees of freedom. The mean square within is:

Correct Answer: B [3]

Explanation:

Answer: 3. MS = SS/df = 48/16 = 3.

8.  
The grand total of 24 observations is 120. The correction factor CF = G²/N is:

Correct Answer: D [600]

Explanation:

Answer: 600. 120²/24 = 14,400/24 = 600.

9.  
Statement-basedWhich is/are correct?
I. Adding the same constant to every observation leaves all sums of squares unchanged.
II. Multiplying every observation by 2 doubles the F ratio.

Correct Answer: A [Only I]

Explanation:

Scaling multiplies MSB and MSE by 4 – F is unchanged.

10.  
Fill in the blankThe sum of squares within groups is also called the ______ sum of squares.

Correct Answer: D [error (residual)]

Explanation:

Within-group variation is attributed to experimental error.

11.  
Match the followingMatch:
P. Completely randomised design Q. Randomised block design R. Mean square error
1. analysed by two-way ANOVA 2. analysed by one-way ANOVA 3. estimate of the error variance σ²

Correct Answer: C [P-2, Q-1, R-3]

Explanation:

CRD ↔ one-way; RBD (treatments × blocks) ↔ two-way; MSE estimates σ².

12.  
If all the sample (treatment) means are exactly equal, the between-groups sum of squares is:

Correct Answer: B [0]

Explanation:

SSB = Σnᵢ(x̄ᵢ − x̄)² = 0 when every x̄ᵢ = x̄.

➤ 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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