Statistics MCQs
Topic Notes: Statistics
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
1
What is a primary assumption required for the application of the sign test?
Answer:
Samples are paired or dependent
The sign test is a non-parametric statistical test used to compare the medians of two related groups. It assumes that the data points are paired or dependent, meaning each observation in one group is directly linked to a specific observation in the other group.
2
Under what data conditions are non-parametric statistical tests typically employed?
Answer:
Both a and b
Non-parametric tests are used when data do not meet the assumptions of parametric tests, such as normality. They are particularly useful for qualitative (nominal/ordinal) data and ranked data, where the distribution of the population is unknown or the measurement scale is not interval or ratio.
3
When performing a sign test, how should tied scores be handled?
Answer:
We discard them
In the sign test, tied observations (where the difference between paired values is zero) provide no information regarding the direction of the difference. Therefore, they are typically excluded from the analysis, reducing the effective sample size.
4
Which branch of statistics is utilized when data is measured using nominal or ordinal scales, often without assuming a specific population distribution?
Answer:
non-parametric statistics
Non-parametric statistics are methods that do not rely on assumptions about the probability distribution of the population. These tests are particularly useful for ordinal or nominal data, where traditional parametric assumptions like normality or interval-level measurement cannot be met.
5
Which non-parametric test is typically associated with a two-sided alternative hypothesis?
Answer:
Sign test
The sign test is used to determine if there is a significant difference between the medians of two paired samples. Because it evaluates whether the median difference is non-zero, the standard null hypothesis is that the median difference is zero, making the two-sided alternative hypothesis (that the median difference is not zero) the most common application.
6
Which of the following non-parametric tests can be utilized to evaluate the difference between two distinct populations?
Answer:
Either of the above
Both the Wilcoxon Rank-Sum test and the Sign test are non-parametric statistical procedures used to compare two populations. The Wilcoxon Rank-Sum test compares the distributions of two independent samples, while the Sign test is often used for paired data or to test the median of a distribution, making both valid options for comparing two populations depending on the study design.
7
Which category of statistical tests is appropriate for analysis when the assumption of normality is violated?
Answer:
Non parametric tests
Non-parametric tests are distribution-free statistical methods that do not rely on the assumption that the data follows a specific probability distribution, such as the normal distribution. They are particularly useful when sample sizes are small or when the data contains outliers that violate the normality requirements of parametric tests.