## Important Chi-Square Test MCQs with Answers 4

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

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

#### Single Sample 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.

Online MCQs Test Website

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## NonParametric Tests: Introduction Easy Version (2023)

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

• 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

• 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.

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.