Unit X — Indian Statistical System & Research Methodology

Topics Covered

1. Ministry of Statistics & Programme Implementation (MoSPI)

Why this section? The Indian Statistical System has a clear hierarchy — from policy (NSC) to operations (NSO) to ground-level surveys. Knowing who does what is essential for the factual questions in this unit.

Two Wings

1. National Statistical Office (NSO) — handles statistical activities. Includes:
   • Central Statistics Office (CSO).
   • National Sample Survey Office (NSSO).
   • Computer Centre.
2. Programme Implementation Wing — monitors twenty-point programme, infrastructure projects, and MPLADS (Members of Parliament Local Area Development Scheme).

Key Publications & Outputs

• National Accounts Statistics (GDP, NSDP).
• Index of Industrial Production (IIP).
• Consumer Price Index (CPI).
• Annual Survey of Industries (ASI).
• Periodic Labour Force Survey (PLFS).
• Household Consumer Expenditure Survey.

2. National Statistical Commission (NSC)

Composition

• Chairperson (eminent statistician/social scientist).
• Four Members (academic/government experts).
• Chief Statistician of India (Secretary of MoSPI) as Member-Secretary.

Functions

• Identify core statistics critical for development planning.
• Lay down national quality standards for official statistics.
• Coordinate statistical activities of central/state agencies.
• Resolve technical/legal issues on data dissemination.
• Monitor major surveys and censuses.

3. National Statistical Office (NSO)

Wings of NSO

• National Accounts Division: compiles GDP, GVA, savings, capital formation, NSDP.
• Economic Statistics Division: IIP, ASI, energy statistics.
• Social Statistics Division: PLFS, social-sector indicators, gender statistics.
• Survey Design & Research Division: sample design, methodology research.
• Field Operations Division: field-level data collection (NSSO field offices).

Major Surveys

• Periodic Labour Force Survey (PLFS) — quarterly (urban) & annual.
• Household Consumer Expenditure Survey (HCES).
• Time Use Survey.
• Multiple Indicator Survey.

4. Census & Large Sample Surveys

Phases of Census

1. Houselisting and Housing Census — buildings, amenities, assets.
2. Population Enumeration — individual demographic information.

Large Sample Surveys

• NSS (National Sample Survey): began 1950 by Mahalanobis; rounds covering employment, expenditure, health, education.
• NFHS (National Family Health Survey): by IIPS Mumbai with MoHFW; provides DHS-style indicators.
• SRS (Sample Registration System): for vital rates (birth, death, infant mortality).
• Agriculture Census: every 5 years; operational holdings.
• Economic Census: count of all establishments.

5. Contributions of Indian Statisticians

6. R as a Calculator

R is a free, open-source software for statistical computing and graphics, developed by Ross Ihaka and Robert Gentleman (1993). Successor to S.

Arithmetic Operators

Assignment

x <- 5         # preferred
x = 5          # also valid
assign("x", 5) # functional
5 -> x         # rare

> (3 + 5) * 2 / 4
[1] 4
> sqrt(16) + log(exp(1))
[1] 5

> x <- c(2, 4, 6, 8, 10)
> mean(x)
[1] 6
> sum(x^2)
[1] 220

7. Functions and Matrix Operations

Vectors

v <- c(1, 2, 3, 4, 5)        # combine
seq(1, 10, by = 2)            # 1 3 5 7 9
rep(0, 5)                     # 0 0 0 0 0
1:10                          # 1..10

Matrix Creation

A <- matrix(1:6, nrow = 2, ncol = 3)        # column-major
B <- matrix(1:6, nrow = 2, byrow = TRUE)    # row-major
diag(3)                                      # 3×3 identity

Matrix Operations

> A <- matrix(c(2, 1, 1, 3), nrow = 2)
> eigen(A)$values
[1] 3.618034 1.381966
> det(A)
[1] 5

> A <- matrix(c(1, 2, 3, 4), nrow = 2)   # column-major: rows (1,3) and (2,4)
> b <- c(7, 10)
> solve(A, b)
[1] 1 2

8. Built-in Functions, Missing Data & Logical Operators

Mathematical & Statistical Functions

abs(x)        # absolute value
sqrt(x)       # square root
exp(x)        # e^x
log(x)        # natural log
log(x, base)  # arbitrary base
mean(x)       # arithmetic mean
median(x)     # median
var(x)        # variance (n-1 divisor)
sd(x)         # standard deviation
quantile(x)   # quartiles
summary(x)    # 5-num summary + mean
cor(x, y)     # correlation
cov(x, y)     # covariance

Probability Distributions (prefixes d/p/q/r)

dnorm(x, mean, sd)     # density
pnorm(q, mean, sd)     # CDF
qnorm(p, mean, sd)     # quantile
rnorm(n, mean, sd)     # random sample

# Same family for: binom, pois, exp, gamma, beta, t, chisq, f, unif

Missing Data

x <- c(1, NA, 3, NA, 5)
is.na(x)             # FALSE TRUE FALSE TRUE FALSE
mean(x)              # NA
mean(x, na.rm = TRUE) # 3
na.omit(x)           # drop NAs
complete.cases(x)    # logical: not NA

Logical Operators

> pnorm(1.96)
[1] 0.9750021
> qchisq(0.95, df = 5)
[1] 11.07050

> x <- c(2, 5, NA, 7, 1)
> x[!is.na(x) & x > 3]
[1] 5 7

9. Conditional Execution & Loops

If-Else

if (condition) {
  expr1
} else if (condition2) {
  expr2
} else {
  expr3
}

# Vectorised
ifelse(x > 0, "positive", "non-positive")

For Loop

for (i in 1:10) {
  print(i^2)
}

While Loop

x <- 1
while (x < 100) {
  x <- x * 2
}

Repeat / Break / Next

i <- 0
repeat {
  i <- i + 1
  if (i %% 7 == 0) next
  if (i > 30) break
  print(i)
}

Apply Family (preferred over loops)

apply(M, 1, sum)    # row sums
apply(M, 2, mean)   # column means
sapply(1:5, function(x) x^2)
lapply(list(...), FUN)
mapply(FUN, ...)
tapply(x, group, FUN)

fact <- function(n) {
  if (n <= 1) return(1)
  result <- 1
  for (i in 2:n) result <- result * i
  result
}
fact(5)   # 120

# Mean of each column of mtcars
sapply(mtcars, mean)

10. Data Management: Sequences, Repeats, Sorting, Ordering, Strings

Sequences and Repeats

seq(1, 20, by = 2)
seq(0, 1, length.out = 11)
rep(c(1, 2, 3), times = 3)   # 1 2 3 1 2 3 1 2 3
rep(c(1, 2, 3), each = 3)    # 1 1 1 2 2 2 3 3 3

Sorting and Ordering

x <- c(3, 1, 4, 1, 5, 9, 2, 6)
sort(x)                      # ascending
sort(x, decreasing = TRUE)   # descending
order(x)                     # indices to sort
rank(x)                      # ranks
rev(x)                       # reverse

Strings

nchar("statistics")            # 10
toupper("hello")               # "HELLO"
tolower("WORLD")               # "world"
paste("UGC", "NET", sep = "-") # "UGC-NET"
paste0("Unit", 1:3)            # "Unit1" "Unit2" "Unit3"
substr("statistics", 1, 4)     # "stat"
sub("a", "@", "banana")        # "b@nana"
gsub("a", "@", "banana")       # "b@n@n@"
strsplit("a,b,c", ",")

> x <- c(20, 5, 30, 10)
> order(x)
[1] 2 4 1 3
> x[order(x)]    # same as sort(x)
[1]  5 10 20 30

> sprintf("Mean = %.2f", 3.14159)
[1] "Mean = 3.14"

11. Lists, Factors, Display & Formatting

Lists

L <- list(name = "Asha", age = 25, scores = c(85, 90, 78))
L$name
L[["age"]]
L[[3]][2]   # 90

Factors

g <- factor(c("M", "F", "M", "F", "M"))
levels(g)            # "F" "M"
as.numeric(g)        # 2 1 2 1 2
table(g)             # frequency table

# Ordered factors
edu <- factor(c("BA", "MA", "PhD"),
              levels = c("BA", "MA", "PhD"),
              ordered = TRUE)

Display & Formatting

print(x)
cat("Result:", x, "\n")
format(3.14159, nsmall = 2)        # "3.14"
formatC(1234567, big.mark = ",")   # "1,234,567"
round(3.14159, 2)                  # 3.14
signif(1234567, 3)                 # 1230000

student <- list(roll = 101, marks = c(80, 75, 90),
                grade = factor("A", levels = c("F","C","B","A")))
mean(student$marks)   # 81.67

income <- factor(c("Low","High","Med","Low","High"),
                 levels = c("Low","Med","High"),
                 ordered = TRUE)
income[1] < income[2]   # TRUE

12. Data Frames, Data Input and Output

Creating Data Frames

df <- data.frame(
  name = c("A", "B", "C"),
  age = c(25, 30, 22),
  score = c(85, 92, 78)
)
df$age            # column
df[1, ]           # row
df[df$age > 24, ] # subset
str(df)           # structure
summary(df)       # summary
nrow(df); ncol(df); dim(df)

Importing Data

read.csv("file.csv", header = TRUE)
read.table("file.txt", sep = "\t", header = TRUE)
readxl::read_excel("file.xlsx")        # excel
foreign::read.spss("file.sav")          # SPSS

Exporting

write.csv(df, "output.csv", row.names = FALSE)
write.table(df, "output.txt", sep = "\t")
saveRDS(df, "df.rds")
df <- readRDS("df.rds")

data(iris)
head(iris, 3)
mean(iris$Sepal.Length[iris$Species == "setosa"])

# Add a new column
df$pass <- ifelse(df$score >= 80, "Yes", "No")

13. Graphics & Plots

Base R Plots

Common Arguments

plot(x, y,
     main = "Title",
     xlab = "X-axis", ylab = "Y-axis",
     col  = "blue",
     pch  = 19,           # point character
     type = "b",          # both points and lines
     lty  = 2,            # dashed
     lwd  = 2)            # line width
abline(h = 0, v = 0)
abline(lm(y ~ x), col = "red")
legend("topright", legend = c("Group A","Group B"), col = c(1,2), pch = 19)

Multiple Plots

par(mfrow = c(2, 2))   # 2 x 2 grid
plot(...)              # 4 plots

Saving Plots

png("plot.png", width = 800, height = 600)
plot(...)
dev.off()

x <- rnorm(100)
hist(x, breaks = 20, col = "skyblue",
     main = "Histogram of N(0,1) sample")
abline(v = 0, col = "red", lwd = 2)

boxplot(Sepal.Length ~ Species, data = iris,
        col = c("red","green","blue"),
        main = "Sepal Length by Species")

14. Scripts, Functions, and Programming Basics

Defining Functions

square <- function(x) {
  return(x^2)
}

# Multiple arguments with defaults
mysum <- function(x, y = 10) {
  x + y
}

# Variable arguments
myfun <- function(...) {
  args <- list(...)
  sum(unlist(args))
}

Scope

• Variables defined inside a function are local.
• <<- assigns to global scope (lexical scoping).

Error Handling

result <- tryCatch({
  log(-1)
}, warning = function(w) "Warning caught",
   error   = function(e) "Error caught")

Scripts

Useful Packages

• dplyr — data manipulation (filter, mutate, summarise).
• ggplot2 — grammar of graphics.
• tidyr — reshaping wide/long.
• MASS — robust regression, multivariate methods.
• forecast — time series.
• survey — complex survey designs.

se <- function(x) sd(x) / sqrt(length(x))
x <- c(2, 4, 6, 8, 10)
se(x)         # 1.414214

# t-test wrapper
mytest <- function(x, mu0 = 0, alpha = 0.05) {
  n  <- length(x)
  t  <- (mean(x) - mu0) / (sd(x) / sqrt(n))
  p  <- 2 * pt(-abs(t), df = n - 1)
  list(t = t, p = p, reject = (p < alpha))
}
mytest(rnorm(30, 0.5))

15. LaTeX & Other Word Processing Software

Document Structure

\documentclass[12pt]{article}
\usepackage{amsmath, amssymb, graphicx}
\title{My Statistics Paper}
\author{Author Name}
\date{\today}
\begin{document}
\maketitle
\section{Introduction}
Content goes here...
\end{document}

Math Mode

Common Sections

\section{Title}
\subsection{Title}
\subsubsection{Title}
\paragraph{Title}

Lists, Tables, Figures

\begin{itemize}
  \item Bullet 1
  \item Bullet 2
\end{itemize}

\begin{enumerate}
  \item Numbered 1
  \item Numbered 2
\end{enumerate}

\begin{tabular}{|c|c|}
\hline
A & B \\
\hline
1 & 2 \\
\hline
\end{tabular}

\begin{figure}[h]
  \centering
  \includegraphics[width=0.8\linewidth]{plot.png}
  \caption{My Figure}
  \label{fig:plot}
\end{figure}

Bibliography (BibTeX)

\bibliographystyle{plain}
\bibliography{refs}        % refs.bib file
\cite{author2020}

Other Word Processing Software

• Microsoft Word: WYSIWYG editor; equation editor for math (Insert → Equation).
• LibreOffice Writer: open-source alternative to Word; native ODF format.
• Google Docs: cloud-based, real-time collaboration.
• R Markdown: integrates R code with Markdown; produces PDFs (via LaTeX), HTML, Word.
• Overleaf: browser-based LaTeX editor with collaboration and templates.

The likelihood is
\[
L(\theta;x) = \prod_{i=1}^n f(x_i;\theta).
\]
The MLE satisfies
\[
\frac{\partial}{\partial\theta}\log L(\theta;x) = 0.
\]

R Markdown chunk:
```{r}
x <- rnorm(100)
mean(x); sd(x)
```
Knit produces report with code, output and plots — preferred for reproducible research.

Final Revision Checklist

• Indian Statistical System: MoSPI, NSC, NSO, CSO, NSSO, Census, SRS, NFHS, PLFS.
• Indian Statisticians and one signature contribution each.
• R: data structures (vector, matrix, list, data frame), control flow, plotting.
• R distributions: d/p/q/r prefixes for norm, binom, pois, etc.
• LaTeX: document structure, math mode, sections, tables, figures, bibliography.

Tip: Unit X questions are largely factual (names, years, contributions) and direct R syntax / output prediction — quick wins if memorized.