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ANOVA, Time Series & Index Numbers

Paper-II Statistics (Post-specific) · Statistics Syllabus

Useful for: SSC CGL

Overview

ANOVA compares several means; time-series analysis separates trend and seasonal effects; index numbers measure relative change.

Key points

ANOVA F-ratio = mean square between groups ÷ mean square within groups.
Time-series components: trend, seasonal, cyclical and irregular.
Moving averages smooth short-term fluctuations to show trend.
Laspeyres index uses base-year quantities; Paasche uses current-year quantities.
Fisher’s ideal index = √(Laspeyres × Paasche).

Explanation

Fisher’s index satisfies the time-reversal and factor-reversal tests.
CPI measures retail prices for consumers; WPI measures wholesale prices.
A chain index links each year to the previous year.
Seasonal indices average 100 over a year.

Step by step

Identify the measure or test asked and its formula.
Organise the data (table, totals) before computing.
Interpret the result (sign, size, significance).

Examples

Laspeyres 120, Paasche 125 → Fisher = √15,000 ≈ 122.47.
Three-year moving averages of 10, 12, 14, 16 → 12 and 14.
Between-group mean square 40 and within-group 10 → F = 4.

Traps and advanced points

Trap: Using quantities from the wrong year.
Trap: Taking Fisher as the arithmetic mean.
Trap: Mixing trend and seasonal effects.

Quick revision

Fisher = √(L × P).
Four time-series components.
F = between/within.

Practice MCQs

ANOVA is used to test the equality of
1. proportions only
2. two variances only
3. several means
4. correlation
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Answer: (c) several means. It splits total variation into between and within groups.
The test statistic in ANOVA follows the
1. normal distribution only
2. t distribution
3. F distribution
4. binomial distribution
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Answer: (c) F distribution. F = between-group mean square ÷ within-group mean square.
The long-term movement in a time series is called the
1. trend
2. seasonal variation
3. irregular variation
4. cyclical noise
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Answer: (a) trend. Moving averages can estimate it.
Regular variations that repeat within a year are
1. seasonal variations
2. trend
3. cyclical variations
4. random walks
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Answer: (a) seasonal variations. Festival sales are an example.
Laspeyres' price index uses the quantities of the
1. base year
2. current year
3. average of both years
4. next year
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Answer: (a) base year. Paasche's index uses current-year quantities.
Fisher's ideal index number is the
1. sum of both
2. arithmetic mean of both
3. geometric mean of Laspeyres' and Paasche's indices
4. difference of both
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Answer: (c) geometric mean of Laspeyres' and Paasche's indices. It satisfies the time and factor reversal tests.