Statistics and Hypothesis Testing Interview Questions for R Programming
25 Statistics and Hypothesis Testing questions with answers for r programming roles — 6 easy, 11 medium, 8 hard.
About Statistics and Hypothesis Testing
Statistics is the core reason many teams use R. Revise descriptive statistics, distributions, the Central Limit Theorem, p-values, confidence intervals, t-tests, chi-square, ANOVA, correlation, power analysis, multiple testing and bootstrapping. Interviews focus on interpreting results correctly, especially for A/B tests, and on choosing the right test when assumptions fail.
Sheet progressStart practicing
3 QUESTIONS FREESign up to unlock the full question bank and track your progress.Unlock every question and answer, then continue practising company-wise and package-wise.
✓ 3 questions free • Unlock the rest in seconds
01
When would you report the median instead of the mean?
The mean uses every value and is sensitive to outliers, while the median is the middle value and is robust to them. I report the median for skewed data such as salaries, house prices, order values or delivery times, where a few extreme values pull the mean up. For example, if most employees earn 6 LPA and a few earn 80 LPA, the median describes a typical employee better. The mode suits categorical data.
02
What is the difference between variance and standard deviation?
Variance is the average squared deviation from the mean, and standard deviation is its square root. Because variance is in squared units, standard deviation is easier to interpret since it uses the same units as the data. In R, var() and sd() both use the sample formula with n - 1 in the denominator. For example, delivery times with mean 30 minutes and SD 5 minutes are far more consistent than with SD 15.
Two variables can move together because of a third confounding variable, reverse causation or pure chance. For example, ice cream sales and drowning incidents are correlated because both rise in summer. To claim causation you need a randomized experiment such as an A/B test, or careful causal methods like difference-in-differences or regression with controls. In interviews, mention that observational correlations are useful for hypotheses but not proof of impact.
04
How do you produce descriptive statistics for each group in R?
Skewness measures asymmetry of a distribution. Positive or right skew has a long right tail, typical of income and order values, so the mean exceeds the median. Negative skew has a long left tail. Kurtosis measures how heavy the tails are compared with a normal distribution; high kurtosis means more extreme values, common in financial returns. In R, the moments or e1071 packages provide skewness() and kurtosis() functions.
06
How do you keep improving your statistics knowledge?
I revise core concepts from a standard textbook and practise each method in R on public datasets, so I understand both the theory and the code. For example, after learning hypothesis testing, I reproduced published A/B test results from Kaggle datasets. I follow the R Weekly newsletter and read package vignettes. When I meet a method at work that I do not understand, I note it and study it that weekend.
07
What is the Central Limit Theorem and why is it important?
The Central Limit Theorem says that the distribution of sample means approaches a normal distribution as sample size grows, roughly beyond 30, regardless of the population's shape, provided observations are independent with finite variance. It is why t-tests, confidence intervals and A/B test calculations work on non-normal data such as order values. You can demonstrate it in R by repeatedly sampling from rexp() and plotting a histogram of the means.
A p-value is the probability of seeing results at least as extreme as the observed ones if the null hypothesis were true. A small p-value, typically below 0.05, means the data would be unusual under the null, so we reject it. It is not the probability that the null hypothesis is true and does not measure effect size. A tiny, unimportant difference can be significant with a huge sample, so always report effect sizes and confidence intervals too.
A Type I error is rejecting a true null hypothesis, a false positive, and its probability is the significance level alpha, usually 0.05. A Type II error is failing to reject a false null hypothesis, a false negative, with probability beta; power is 1 - beta. For example, launching a feature that does not actually help is a Type I error, while dropping a feature that really works is Type II. Larger samples reduce Type II errors.
t.test() handles one-sample, two-sample and paired tests. Welch's test, which does not assume equal variances, is the default.
# two independent groups
t.test(score ~ batch, data = students)
# paired: before vs after training
t.test(after, before, paired = TRUE)
# one-sample against a target of 30 minutes
t.test(delivery_time, mu = 30, alternative = 'greater')
res <- t.test(score ~ batch, data = students)
res$p.value; res$conf.int
11
How do you test whether two categorical variables are related in R?
Use a chi-square test of independence on a contingency table; use Fisher's exact test when expected counts are small.
tab <- table(survey$city_tier, survey$preferred_plan)
tab
res <- chisq.test(tab)
res$p.value
res$expected # check expected counts >= 5
fisher.test(tab) # for small samples
# effect size
library(rcompanion)
cramerV(tab)
12
What is the difference between Pearson and Spearman correlation?
Pearson correlation measures the strength of a linear relationship between two numeric variables and is sensitive to outliers. Spearman correlation is computed on ranks, so it measures monotonic relationships and is robust to outliers and non-normal data. In R, cor(x, y, method = 'spearman') and cor.test() compute them. For example, ad spend and sales with diminishing returns may show a moderate Pearson value but a high Spearman value.
13
You ran an A/B test on a checkout page: 4.1 percent conversion versus 4.6 percent. How do you decide if the difference is real?
Conversion is a proportion, so I use a two-proportion test: prop.test(c(conv_a, conv_b), c(n_a, n_b)). I check the p-value and, more importantly, the confidence interval for the difference. Before trusting it, I confirm the sample size was planned in advance, the test ran for full weeks to cover weekday effects, users were randomized properly and nobody stopped the test early when results looked good. Then I judge business significance.
14
Your data is heavily skewed and the sample is small. Can you still use a t-test?
With small, heavily skewed samples the t-test's normality assumption is doubtful. I would check with a histogram, Q-Q plot or shapiro.test(). Options are a non-parametric test, wilcox.test() for two groups or kruskal.test() for more, a log transformation if the data is right-skewed and positive, or a bootstrap confidence interval for the difference in means. With large samples, the Central Limit Theorem usually makes the t-test acceptable.
If we repeated the sampling many times and built an interval each time, about 95 percent of those intervals would contain the true population value. It does not mean there is a 95 percent probability that this specific interval contains it. A narrow interval shows precise estimation and a wide one shows uncertainty. For example, average order value of 850 INR with CI 820 to 880 is far more useful than CI 600 to 1100.
16
Explain the d, p, q and r functions for probability distributions in R.
Each distribution has four functions: d for density, p for cumulative probability, q for quantiles and r for random draws.
dnorm(0) # density at 0
pnorm(1.96) # P(Z <= 1.96) = 0.975
qnorm(0.975) # 1.96
rnorm(5, mean = 50, sd = 10)
dbinom(3, size = 10, prob = 0.2) # exactly 3 successes
ppois(2, lambda = 4) # P(X <= 2)
qt(0.975, df = 20) # t critical value
17
How do you check whether data is normally distributed in R?
Combine visual checks with formal tests, because tests become oversensitive with large samples.
hist(x, breaks = 30)
qqnorm(x); qqline(x, col = 'red')
shapiro.test(x) # works for n between 3 and 5000
library(ggplot2)
ggplot(df, aes(sample = x)) +
stat_qq() + stat_qq_line()
# for model residuals
plot(lm_fit, which = 2)
18
How do you compare means across more than two groups in R?
Use one-way ANOVA, then a post-hoc test to see which pairs differ.
fit <- aov(sales ~ region, data = stores)
summary(fit) # overall F-test
TukeyHSD(fit) # pairwise comparisons
# check assumptions
plot(fit, which = 2) # Q-Q of residuals
bartlett.test(sales ~ region, data = stores)
# non-parametric alternative
kruskal.test(sales ~ region, data = stores)
19
Product wants to detect a lift in conversion from 5 to 5.5 percent. How many users do you need per group?
I use power analysis before the test starts. In R, power.prop.test(p1 = 0.05, p2 = 0.055, power = 0.8, sig.level = 0.05) gives roughly 31,000 users per group. Smaller lifts need far larger samples, since sample size scales with the inverse square of the effect. I would then convert the sample into test duration using daily traffic, round up to full weeks, and agree on the stopping rule in advance to avoid peeking bias.
20
What is the multiple testing problem and how do you correct for it?
When you run many hypothesis tests, the chance of at least one false positive rises sharply. With 20 independent tests at alpha 0.05, it is about 64 percent. Corrections adjust p-values: Bonferroni multiplies by the number of tests and is conservative, Holm is a less strict step-down version, and Benjamini-Hochberg controls the false discovery rate. In R, p.adjust(pvals, method = 'BH') applies them, which is common when testing many metrics or segments.
Bootstrapping estimates the sampling distribution of a statistic by resampling the data with replacement many times and recomputing the statistic each time. The spread of those results gives standard errors and confidence intervals without assuming normality. It is useful for medians, ratios or complex metrics like revenue per user, where formulas are hard. In R, the boot package or a simple replicate() loop with sample(x, replace = TRUE) does it.
22
A manager says a test with p = 0.06 proves the change had no effect. How do you respond?
I explain that failing to reject the null is not proof of no effect. A p-value of 0.06 means the evidence is weak or the test was underpowered, and the 0.05 cut-off is a convention, not a law. I would show the confidence interval for the effect, which probably ranges from slightly negative to clearly positive, check whether the sample size met the planned power and suggest extending the test or weighing the decision on cost and risk.
23
You are analysing a national survey where some groups were deliberately oversampled. How do you compute correct averages?
Simple averages would be biased toward oversampled groups, so I use the survey weights provided with the data. In R, the survey package defines the design with svydesign(ids = ~psu, strata = ~stratum, weights = ~wt, data = df), then svymean(), svytotal() and svyglm() give weighted estimates with correct standard errors that account for clustering and stratification. The srvyr package offers the same with dplyr-style syntax.
24
Overall, treatment A has a higher success rate than B, but B is better in every hospital. How is that possible?
This is Simpson's paradox. It happens when a confounding variable, here hospital or patient severity, is unevenly distributed between groups. If A was used mostly in hospitals with easier cases, its overall rate looks better even though B wins within each hospital. In R I would group by hospital and compare rates, then use a stratified analysis or regression with hospital as a covariate to estimate the adjusted effect.
25
Tell me about a time your analysis did not support what a stakeholder hoped to see.
Situation: a marketing head expected a new campaign to have doubled sign-ups. Task: evaluate its impact. Action: my analysis in R using a pre-post comparison with a control region showed only a 6 percent lift, much of it seasonal. I presented the method and confidence interval openly, acknowledged what went well and suggested a cleaner randomized test. Result: the stakeholder accepted the finding, and the next campaign was run as a proper experiment.
Frequently asked questions
How important is Statistics and Hypothesis Testing in R Programming interviews?
Statistics is the core reason many teams use R. Revise descriptive statistics, distributions, the Central Limit Theorem, p-values, confidence intervals, t-tests, chi-square, ANOVA, correlation, power analysis, multiple testing and bootstrapping. Interviews focus on interpreting results correctly, especially for A/B tests, and on choosing the right test when assumptions fail.
How should I use the Statistics and Hypothesis Testing sheet?
Go top to bottom — easy to hard. Answer before opening each answer, tick what you solved and save misses to Last-Minute Revision.