Non-Parametric Tests

Important Chi-Square Test MCQs with Answers 4

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The post is about the Chi-Square Test MCQS with Answers. The Chi-square test is used to find the association between attributes. Let us start with the Chi-Square Test MCQs with Answers.

Online Multiple Choice Questions about Chi-square Association

1. If $(AB) < \frac{(A)(B)}{n}$ then the two attributes $A$ and $B$ are said to be

 
 
 
 

2. If $\chi^2_{calculated}$ is greater than the critical region, then the attributes are

 
 
 
 

3. The two attributes are said to be ———–, if for every cell of the contingency table, the observed frequency $O_{ij}$ is equal to the expected frequency $e_{ij}$

 
 
 
 

4. In a $3 \times 3$ contingency table, the degrees of freedom is

 
 
 
 

5. In a Chi-Square test of independence, no expected frequencies should be

 
 
 
 

6. The $\chi^2$ distribution is

 
 
 
 

7. The eye colour of students in a girls college is an example of

 
 
 
 

8. $(\alpha \beta)$ is the frequency of the class of the order

 
 
 
 

9. Which of the following is not an example of an attribute

 
 
 
 

10. The Spearman’s coefficient of rank correlation always lies between

 
 
 
 

11. The coefficient of contingency is measured by

 
 
 
 

12. If $(AB) = \frac{(A)(B)}{n}$ the attributes $A$ and $B$ are said to be

 
 
 
 

13. Religions of the people of a country is

 
 
 
 

14. The degree of relationship between two attributes is called

 
 
 
 

15. The value of $\chi^2$ is always

 
 
 
 

16. If $\chi^2_{calculated} = 0$ then

 
 
 
 

17. If $A$ and $B$ are independent attributes then the coefficient of associate is

 
 
 
 

18. The Yule’s coefficient of association lies between

 
 
 
 

19. In a contingency table with $r$ rows and $c$ columns, the degree of freedom is

 
 
 
 

20. A characteristic which cannot be measured numerically is called

 
 
 
 


The relationship/ Dependency between the attributes is called association and the measure of degrees of relationship between attributes is called the coefficient of association. The Chi-Square Statistic is used to test the association between the attributes. The Chi-Square Association is defined as

$$\chi^2 = \sum \frac{(of_i – ef_i)^2}{ef_i}\sim \chi^2_{v}$$

where $v$$ denotes the degrees of freedom.

The Chi-Square tests:

  • are appropriate for categorical data, not continuous data (like height or weight).
  • The data needs to be from a random sample and have sufficient sample size for the test to be reliable.
  • The test results in a chi-square statistic and a p-value.

Chi-Square Test MCQs with Answers

  • A characteristic which cannot be measured numerically is called
  • Which of the following is not an example of an attribute
  • The eye colour of students in a girl’s college is an example of
  • Religions of the people of a country is
  • The degree of relationship between two attributes is called
  • In a contingency table with $r$ rows and $c$ columns, the degree of freedom is
  • The $\chi^2$ distribution is
  • If $\chi^2_{calculated}$ is greater than the critical region, then the attributes are
  • In a $3 \times 3$ contingency table, the degrees of freedom is
  • The Spearman’s coefficient of rank correlation always lies between
  • The Yule’s coefficient of association lies between
  • If $(AB) < \frac{(A)(B)}{n}$ then the two attributes $A$ and $B$ are said to be
  • If $(AB) = \frac{(A)(B)}{n}$ the attributes $A$ and $B$ are said to be
  • The coefficient of contingency is measured by
  • If $\chi^2_{calculated} = 0$ then
  • $(\alpha \beta)$ is the frequency of the class of the order
  • If $A$ and $B$ are independent attributes then the coefficient of associate is
  • The value of $\chi^2$ is always
  • In a Chi-Square test of independence, no expected frequencies should be
  • The two attributes are said to be ———–, if for every cell of the contingency table, the observed frequency $O_{ij}$ is equal to the expected frequency $e_{ij}$
Chi-Square Test MCQs with Answers

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Easy MCQs Non-Parametric Methods

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Most of the MCQs on this page covered Estimate and Estimation, Testing of Hypothesis when the assumption of population parameters are unknown, that is Non-Parametric Methods, etc.

MCQs Non-Parametric Methods Quizzes List

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The relationship/ Dependency between the attributes is called association and the measure of degrees of relationship between the attributes is called the coefficient of association. The Chi-Square Statistic is used to test the association between the attributes. The Chi-Square Association is defined as

$$\chi^2 = \sum \frac{(of_i – ef_i)^2}{ef_i}\sim \chi^2_{v},$$

where $v$ denotes the degrees of freedom.

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Wilcoxon Signed Rank Test Made Easy

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The Wilcoxon Signed Rank test assumes that the population of interest is both continuous and symmetric (not necessarily normal). Since the mean and median are the same (for symmetrical distribution), the hypothesis tests on the median are the same as the hypothesis test on the mean.

The Wilcoxon test is performed by ranking the non-zero deviations in order of increasing magnitude (that is, the smallest non-zero deviation has a rank of 1 and the largest deviation has a rank of $n$). The ranks of the deviations with positive and negative values are summed.

These sums are used to determine whether or not the deviations are significantly different from zero. Wilcoxon Signed Rank Test is an alternative to the Paired Sample t-test.

One-Tailed Test

$H_0: \mu = \mu_0\quad $ vs $\quad H_1: \mu < \mu_0$

Test Statistics: $T^-$: an absolute value of the sum of the negative ranks

Two-tailed Test

$H_0: \mu = \mu_0 \quad$ vs $\quad H_1:\mu \ne \mu_0$

Test Statistics: $min(T^+, T^-)$

Wilcoxon Signed Ranked Test

Because the underlying population is assumed to be continuous, ties are theoretically impossible, however, in practice ties can exist, especially if the data has only a couple of significant digits.

Two or more deviations having the same magnitude are all given the same average rank. The deviations of zero are theoretically impossible but practically possible. Any deviations of exactly zero are simply thrown out and the value of $n$ is reduced accordingly.

Single Sample Wilcoxon Signed Rank Test

Wilcoxon Signed Rank Test

The Wilcoxon Signed Rank Test is important for researchers as it fills a critical gap in statistical analysis.

  • Non-normal data: Most of the statistical tests, like the dependent samples t-test, assume that the data follows a normal distribution (bell curve). The Wilcoxon Signed Rank Test supersede the assumption of normality, making it ideal for analyzing data that is skewed, ranked, or ordinal (like survey responses on a Likert scale Questions).
  • Robust against outliers: Outliers (very large or small observations in the data) can significantly skew the results of some statistical tests. The Wilcoxon Signed Rank Test focuses on the ranks of the differences, making it less sensitive to extreme values (outliers) in the data compared to tests that rely on raw numbers.
  • Focuses on changes within subjects: The Wilcoxon Signed Rank Test is designed for paired data (dependent samples), to look at the same subjects before and after situation (like a treatment) or under two different conditions.

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NonParametric Tests: Introduction Easy Version (2023)

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Nonparametric tests are experiments that do not require the underlying population for assumptions. It does not rely on data referring to any particular parametric group of probability distributions. Nonparametric methods are also called distribution-free tests since they do not have any underlying population.

Nonparametric Tests/ Statistics are Helpful when

  • Inferences must be made on categorical or ordinal data
  • The assumption of normality is not appropriate
  • The sample size is small

Advantages of NonParametric Methods

  • Easy application (does not even need a calculator in many cases)
  • It can serve as a quick check to determine whether or not further analysis is required
  • Many assumptions concerning the population of the data source can be relaxed
  • Can be used to test categorical (yes/ no) data
  • Can be used to test ordinal (1, 2, 3) data

Disadvantages of NonParametric Methods

  • Nonparametric procedures are less efficient than parametric procedures. It means that nonparametric tests require a larger sample size to have the same probability of a type-I error as the equivalent parametric procedure.
  • Nonparametric procedures often discard helpful information. That is, the magnitudes of the actual data values are lost. As a result, nonparametric procedures are typically less powerful.

That is they produce conclusions that have a higher probability of being incorrect. Examples of widely used Parametric Tests: include the paired and unpaired t-test, Pearson’s product-moment correlation, Analysis of Variance (ANOVA), and multiple regression.

Note: Do not use nonparametric procedures if parametric procedures can be used.

nonparametric-tests

Some widely used Non-Parametric Tests are:

  • Sign Test
  • Runs Test
  • Wilcoxon Signed Rank Test
  • Wilcoxon Rank Sum Test
  • Spearman’s Rank Correlation
  • Kruskal Wallis Test
  • Chi-Square Goodness of Fit Test

Nonparametric tests are crucial tools in statistics because they offer valuable analysis even when the data doesn’t meet the strict assumptions of parametric tests. NonParametric tests provide a valuable alternative for researchers who encounter data that doesn’t fit the mold of parametric tests. They ensure that valuable insights can still be extracted from the data without compromising the reliability of the analysis.

However, it is important to remember that nonparametric tests can sometimes be less powerful than the related parametric tests. This means NonParametric Tests might be less likely to detect a true effect, especially with smaller datasets.

In summary, nonparametric tests are valuable because these kind of tests offer flexibility in terms of data assumptions and data types. They are particularly useful for small samples, skewed data, and situations where data normality is uncertain. These tests also ensure researchers to draw statistically sound conclusions from a wider range of data types and situations. But, it is always a good practice to consider both parametric and non-parametric approaches when appropriate.

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